Director's Quotations Page

and one of the arguments of this book is that economics has encouraged ways of thinking that made crises more probable. Economists have brought the problem upon themselves by pretending that they can forecast.

Mervyn King

The most fruitful areas for the growth of the sciences were those which had been neglected as a no-man's land between the various established fields.

Norbert Wiener

Ironically, the cracking of the genetic code, together with other developments, has ushered in a very different era in biology, that of big data. Computers now burst at the seams with DNA and protein sequences that derive from the whole genomes of thousands of species sequenced by automated machines. Many biologists use sophisticated statistics in an attempt to infer patterns from these data. Increasingly, biologists seem drawn to such inference, however indirect, and fewer seem captivated by the ideal of the decisive experiment. These indirect approaches have certainly yielded valuable insights and it would be absurd to doubt that they will continue to do so. Big data provide important new tools to biology and medicine. But the larger lesson of Life’s Greatest Secret is one that may be worth remembering. When scientists require definitive answers, not merely suggestive patterns, they require experiments that are decisive and, if all goes well, beautiful.

H. Allen Orr

The search for a unifying theory continued. Two years after Born's lecture, his Cambridge colleague, Paul Dirac, wondered in a Naturepaper whether the constants were indeed constant if one were to look at the entire history of the cosmos. Measurements on earth are useful but it is a tiny blue dot in the vast universe. What Dirac asked decades ago is what physicists continue to ask today. Is it a constant everywhere in the universe? Why is it a constant? How constant? The question lingered even as the decades rolled on. “The most exact value at present for the ratio of proton to electron mass is 1836.12 +/-0.05,” wrote Friedrich Lenz in a 1951 Physical Review Letters paper. “It may be of interest to note that this number coincides with 6pi^2=1836.12.” That was the entire paper.

Venkat Srinivasan

The mood of the astronomical community is perfectly captured, Laughlin says, by something British astronomer John Herschel said to the British Association for the Advancement of Science in a talk on September 10, 1846. Irregularities had been spotted in the orbit of Uranus, suggesting that the gravity of an unknown, massive planet was tugging on it. Referring to the mystery object, Hershel said:

“We see it as Columbus saw America from the shores of Spain. Its movements have been felt along the far-reaching line of our analysis with a certainly hardly inferior to ocular demonstration.” Just two weeks later Neptune was discovered, right where the theorists’ calculations said it should be.

Michael D. Lemonick

The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.

Bertrand Russell

The authorities of the more important cattle shows might do service to statistics if they made a practice of preserving the sets of cards of this description, that they may obtain on future occasions, and loaned them under proper restrictions, as those have been, for statistical discussion.

Francis Galton

In their eight-month-long investigation, reporters at InsideClimate News interviewed former Exxon employees, scientists and federal officials and analyzed hundreds of pages of internal documents. They found that the company’s knowledge of climate change dates back to July 1977, when its senior scientist James Black delivered a sobering message on the topic. “In the first place, there is general scientific agreement that the most likely manner in which mankind is influencing the global climate is through carbon dioxide release from the burning of fossil fuels," Black told Exxon’s management committee. A year later he warned Exxon that doubling CO2 gases in the atmosphere would increase average global temperatures by two or three degrees—a number that is consistent with the scientific consensus today. He continued to warn that “present thinking holds that man has a time window of five to 10 years before the need for hard decisions regarding changes in energy strategies might become critical." In other words, Exxon needed to act.

Scientific American

“We will delve into quantum physics’ understanding of disease and alternative medicine to provide a scientific hypothesis of how these modalities may work…” Ms. Landau-Halpern promised those considering registering for her course, Alternative Health: Practice and Theory.

Tabatha Suthey

The distinguished Oxford historian Keith Thomas is reported to have said that academic life has three things to recommend it: July, August and September.

Robert Douglas-Fairhurst

In the 1950s, Henry Ford II, the CEO of Ford, and Walter Reuther, the head of the United Auto Workers union, were touring a new engine plant in Cleveland. Ford gestured to a fleet of machines and said, “Walter, how are you going to get these robots to pay union dues?” The union boss famously replied: “Henry, how are you going to get them to buy your cars?”

As Martin Ford (no relation) writes in his new book, The Rise of the Robots, this story might be apocryphal, but its message is instructive.

Derek Thompson

He has waged cruel war against human nature itself, violating its most sacred rights of life and liberty in the persons of a distant people who never offended him, captivating and carrying them into slavery in another hemisphere, or to incur miserable death in their transportation hither … And he is now exciting those very people to rise in arms among us, and to purchase that liberty of which he had deprived them, by murdering the people upon whom he also obtruded them: thus paying off former crimes committed against the liberties of one people, with crimes which he urges them to commit against the lives of another.

Thomas Jefferson

Scientists these days tend to keep up a polite fiction that all science is equal. Except for the work of the misguided opponent whose arguments we happen to be refuting at the time, we speak as though every scientist's field and methods of study are as good as every other scientist's, and perhaps a little better. This keeps us all cordial when it comes to recommending each other for government grants.

John R. Platt

Data from the WoS database and the ORI offer strong evidence that researchers and journal editors have become more aware of and more proactive about scientific misconduct, and provide no evidence that recorded cases of fraud are increasing, at least amongst US federally funded research. The recent rise in retractions, therefore, is most plausibly the effect of growing scientific integrity, rather than growing scientific misconduct.

Rosie Cima

Enough is enough, say the physicists who have come together to renew respect for experimental evidence and work on alternatives to ever more contrived theory.

IT WAS, in many ways, a declaration of war. A group of physicists has launched a rearguard action to restore experimental data to what they see as its rightful place, back on their subject's throne.

Last week, the Perimeter Institute in Waterloo, Canada, hosted its inaugural Convergence conference at the same time as Strings 2015, the world's largest string theory conference, was taking place in Bangalore, India. The timing wasn't entirely accidental, says Perimeter director Neil Turok. Although string theory attempts to describe the universe in one theoretical framework, it makes no attempt to explain experimental results, he says.

"We've been given these incredible clues from nature and we're failing to make sense of them," he told New Scientist. "In fact, we're doing the opposite: theory is becoming ever more complex and contrived. We throw in more fields, more dimensions, more symmetry – we're throwing the kitchen sink at the problem and yet failing to explain the most basic facts."

The New Scientist

In the July 1945 issue of The Atlantic, Bush outlined his vision for a head-mounted camera attached to “a pair of ordinary glasses” that would record comments, photographs, and data from scientific experiments: “One can now picture a future investigator in his laboratory. His hands are free, and he is not anchored.” His “camera … of the future,” no “larger than a walnut,” worn on “a pair of ordinary glasses … where it is out of the way of ordinary visions” was in many ways a forerunner of today’s augmented-reality devices.

Ava Kofman

The letter itself reads:

“You would render to me and our friend Kuhn a most valuable service, putting us greatly in your debt, most learned sir, if you would send us the solution, which you know well, to the problem of the seven Konigsberg bridges together with a proof. It would prove to an outstanding example of the calculus of position [calculi situs] worthy of your great genius. I have added a sketch of the said bridges”.[6] Euler replied to Ehler and Kuhn in April 1736:

“Thus you see, most noble sir, how this type of solution bears little relationship to mathematics and I do not understand why you expect a mathematician to produce it rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle. Because of this, I do not know why even questions which bear so little relationship to mathematics are solved more quickly by mathematicians than by others. In the meantime most noble sir, you have a assigned this question to the geometry of position but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed this way.”


The literary-journalistic world in which Burgess flourished seems remote now. Today’s is more pluralist and fragmented – busier, too, with online reviews and blogs as well as book pages. Burgess claimed that the only response he ever had to the many reviews he wrote for the Yorkshire Post was from a woman disputing a passing claim he had made that British orchids have no smell. Reviews have little effect, he concluded, though a New Statesman review of one of his books once came in handy, by implying he was homosexual. At the time, a lady dentist who was treating his teeth had been making advances; when she proposed they make love in her surgery, he showed her the review, to prove she’d be wasting her time.

Blake Morrison

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. — 'Ah, so you shall be sure to be misunderstood.' — Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood.

Ralph Waldo Emerson
“Companies that make products must show that their products work,” he said. “They must be certified. There is no such case for algorithms. We have a lot of uninformed consumers of big data algorithms that are using tools that haven’t been tested for reproducibility and accuracy.

Emily Ayshford

Four key elements of some mental illnesses --- mania depression --- appear to promote crisis leadership: realism, resilience, empathy, and creativity.

Nasser Ghaemi

“There’s an aphorism: ‘If you torture the data long enough, they will confess.’ You can always get the data to produce something that is publishable,” says the Center for Open Science’s Nosek, who is a University of Virginia professor of psychology.

Joel Achenbach

Matthew Emerton, a professor of math at the University of Chicago, also met Zhang at Princeton. “I wouldn’t say he was a standard person,” Emerton told me. “He wasn’t gregarious. I got the impression of him being reasonably internal. He had received another prize, so the people around him were talking about that. Probably most mathematicians are very low-key about getting a prize, because you’re not in it for the prize, but he seemed particularly low-key. It didn’t seem to affect him at all.”

Deane Yang attended three lectures that Zhang gave at Columbia in 2013. “You expect a guy like that to want to show off or explain how smart he is,” Yang said. “He gave beautiful lectures, where he wasn’t trying to show off at all.” The first talk that Zhang gave on his result was at Harvard, before the result was published. A professor there, Shing-Tung Yau, heard about Zhang’s paper, and invited him. About fifty people showed up. One of them, a Harvard math professor, thought Zhang’s talk was “pretty incomprehensible.”

He added, “The problem is that this stuff is hard to talk about, because everything hinges on some delicate technical understandings.” Another Harvard professor, Barry Mazur, told me that he was “moved by his intensity and how brave and independent he seemed to be.”

Alec Wilkinson

The mathematician and blogger Cathy “Mathbabe” O’Neil, as quoted in a great essay by Caroline Chen called “The Paradox of the Proof,” is not interested in Mochizuki’s supergenius fucking around. “You don’t get to say you’ve proved something if you haven’t explained it. A proof is a social construct. If the community doesn’t understand it, you haven’t done your job.”

Michael Byrne


In addition, KAUST’s offer of an assistant professorship was very attractive financially. Along with a $2 million research package over 5 years, Tamer would receive a $250,000 sign-up and relocation bonus and a tax-free annual salary of $180,000, plus free housing.

Those factors made KAUST the best available route to a successful scientific career. “The job was my ticket out, and the money I would make would be enough to secure my family’s future,” he writes. “I knew I could publish in reputable journals in my field and build a strong research group regardless of how the university functioned, unless they interfered with my professional space.”

In retrospect, Tamer writes, he never believed that KAUST would succeed. “It had a very noble cause: To bring back the science renaissance in Islam the way it had been from the 13th to the 16th centuries,” he writes. “[But] the idea of having an independent little utopia within the boundaries of an undemocratic monarchy was simply utter nonsense.”. Still, Tamer says he remains extremely grateful to KAUST for offering him the chance to do science.

Jeffrey Mervis

Sayre's law states, in a formulation quoted by Charles Philip Issawi: "In any dispute the intensity of feeling is inversely proportional to the value of the issues at stake." By way of corollary, it adds: "That is why academic politics are so bitter." Sayre's law is named after Wallace Stanley Sayre (1905–1972), U.S. political scientist and professor at Columbia University.


PAUL W. ANDREWS, A PROFESSOR of evolutionary psychology at McMaster University, looks at depression from a different angle. His research looks at rumination, which he defines as “intense, persistent, intrusive, distraction-resistant thoughts.” Such thoughts are common in depression, and they’re generally thought of as a bad thing. But Dr. Andrews thinks rumination could be an adaptation — something humans developed to help them solve complex problems.

Anna North

Mathematics has a fearsome rep as the discipline of iron logic. But for its practitioners sometimes the best way to think clearly is to think vaguely.

Mathematics is like a language – but one that, thanks to its inbuilt logic, writes itself. That's how mathematician Ian Stewart sees it, anyway. "You can start writing things down without knowing exactly what they are, and the language makes suggestions to you." Master enough of the basics, and you rapidly enter what sports players call "the zone". "Suddenly it gets much easier," Stewart says. "You're propelled along."

But what if you don't have such a maths drive? It's wrong to think it's all down to talent, says mathematician and writer Alex Bellos: even the best exponents can take decades to master their craft. "One of the reasons people don't understand maths is they don't have enough time," he says.

Catherine de Lange

Elsewhere than in government man has accomplished marvels: invented the means in our lifetime to leave the earth and voyage to the moon. In the past, harnessed wind and electricity, raised earthbound stones into soaring cathedrals, woven silk brocades out of the spinnings of a worm, constructed the instruments of music, derived motor power from steam, controlled or eliminated diseases. pushed back the North Sea and created land in its place, classified the forms of nature, penetrated the mysteries of the cosmos. "While all other sciences have advanced," confessed our second President, John Adams, "government is at a stand; little better practiced now than three or four thousand years ago".

Barbara W. Tuchman

There are men who will kill and maim with a tranquil conscience under the influence of the words and writings of some of those who are certain that they know perfection can be reached.

Isaiah Berlin

Is there, then, any reason for hope? Indeed there is. [Isaiah] Berlin concludes, disarmingly, “there is always the part played by pure luck—which, mysteriously enough, men of good judgment seem to enjoy rather more often than others.”

Christopher Benfey

But there is one field of human thought in which the highest idea of genius still seems to some to make sense. That is mathematics. In the popular imagination mathematical genius now seems to be the dominant model and it is not hard to see why. Not only do mathematical achievements require extraordinary intellectual abilities, unimaginable to non mathematicians, they also have certainty and permanence. The fallible human mind participates in the beauty of an infallible abstract realm that, in the view of many mathematicians, exists independently of the mental and physical worlds. Kurt Gödel, Einstein’s friend and colleague at the Institute for Advanced Study in Princeton, took this kind of mathematical Platonism to be a consequence of his First Incompleteness Theorem. He proved that for any finitely specifiable, consistent formal system of sufficient complexity to express arithmetic, there will exist truths of arithmetic that are not provable within that system. Gödel inferred from this that it was impossible to think of mathematics as a human construction.

That position is philosophically controversial but it allows us to imagine possibilities for a new theodicy of mind based on the mathematical model. The phenomenon that Eugene Wigner, in his 1960 paper, called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” expands our sense of living in a universe designed somehow to be intelligible to us. But for those who believe in this possibility, it is an article of faith. The fact that laws of physics can be expressed (revealed to us) through mathematical concepts, such as complex numbers, which are not derived from any experience of the world, is mysterious to us. And the fact that the human mind has evolved in such a way that it can recognize these utterly unintuitive mathematical truths is equally mysterious. We are very far indeed from developing a coherent and persuasive theory of how the mental, the physical, and the “third realm” of abstract objects, such as mathematical results, might all be related, explaining the miracle of comprehensibility.

Tamsin Shaw

In the aftermath of World War I, at the insistence of the Allied Powers, the 1920 ICM in Strasbourg and the 1924 ICM in Toronto excluded mathematicians from the countries formerly comprising the Central Powers. This resulted in a still unresolved controversy as to whether to count the Strasbourg and Toronto congresses as true ICMs. At the opening of the 1932 ICM in Zürich, Hermann Weyl said: "We attend here to an extraordinary improbable event. For the number of n, corresponding to the just opened International Congress of Mathematicians, we have the inequality 7 ≤ n ≤ 9; unfortunately our axiomatic foundations are not sufficient to give a more precise statement”. As a consequence of this controversy, from the 1932 Zürich congress onward, the ICMs are not numbered.


Stefan Bergman went around and posed a mathematical problem to people. If you tried to solve it in a straightforward manner, it involved a little calculation and the summation of a geometric series. If you gave it a slight turn, however, the solution was obvious. When von Neumann immediately gave the correct solution, Bergman said: "You are the only one of the people I have asked who did not sum the series." "No", von Neumann said, "I did sum it."

Jan Peter Schäfermeyer

In your book "Mathematics by Experiment you recount the often told story of John von Neumann summing up the infinite series at lightning speed. Recently I found a source that could be the original one, namely Werner Fenchel's account of his times of study in Berlin. According to him it was Stefan Bergman who went around Berlin University to test the mathematicians.

Jan Peter Schäfermeyer

By the way, I was reading Dyson's "Selected Papers". On page 51 he says "Professor Littlewood, when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in a few lines by anybody obtuse enough to feel the need of verification". However, Dyson then goes on to say "My object in the following pages is to confute this assertion". What's OK for Littlewood may not be OK for mere mortals :-)

Richard Brent

When I Wrote It, Only God and I Knew the Meaning; Now God Alone Knows

Robert Browning

There is no margin of error for the poll because it was conducted online, and is therefore considered to be non-probabilistic.

CBC News

"a thrill which is indistinguishable from the thrill I feel when I enter the Sagrestia Nuovo of the Capella Medici and see before me the austere beauty of the four statues representing 'Day', 'Night', 'Evening', and 'Dawn' which Michelangelo has set over the tomb of Guiliano de'Medici and Lorenzo de'Medici."

G. N. Watson, 1886-1965

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

Bertrand Russell, 1872-1970

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

G.H. Hardy

Is it likely that any astonishing new developments are lying in wait for us? Is it possible that the cosmology of 500 years hence will extend as far beyond our present beliefs as our cosmology extends beyond Newton? I doubt whether this will be so. I am prepared to believe that there will be many advances in understanding of matters that still baffle us, but by and large I think that our present picture will turn out to bear an approximate resemblance to the cosmologists of the future.

Fred Hoyle

Late in life Auden wrote self-revealing poems and essays that portrayed him as insular and nostalgic, still living imaginatively in the Edwardian world of his childhood. His “Doggerel by a Senior Citizen” began, “Our earth in 1969/Is not the planet I call mine,” and continued with disgruntled complaints against the modern age: “I cannot settle which is worse,/The Anti-Novel or Free Verse.” A year after he wrote this, I chanced on a first book by a young poet, N.J. Loftis, Exiles and Voyages. Some of the book was in free verse; much of it alluded to Harlem and Africa; the author’s ethnic loyalties were signaled by the name of the publisher, the Black Market Press. The book was dedicated “To my first friend, W.H. Auden.”

Edward Mendelson

"a certain impression I had of mathematicians was ... that they spent immoderate amounts of time declaring each other's work trivial."

(Richard Preston)

"It's about as interesting as going to the beach and counting sand. I wouldn't be caught dead doing that kind of work."

(Professor Take Your Pick ...)
"The universe contains at most 'two to the power fifty' grains of sand."

"Americans are broad-minded people. They'll accept the fact that a person can be alcoholic, a dope fiend or a wife-beater, but if a man doesn't drive a car, everybody thinks that something is wrong with him."

(Art Buchwald, local newspaper, March 1996)
"Caution, skepticism, scorn, distrust and entitlement seem to be intrinsic to many of us because of our training as scientists... . These qualities hinder your job search and career change."

(Quoted in Science, 4 August 1995, page 637)

"Consider a precise number that is well known to generations of parents and doctors: the normal human body temperature of 98.6 Farenheit. Recent investigations involving millions of measurements reveal that this number is wrong; normal human body temperature is actually 98.2 Farenheit. The fault, however, lies not with Dr. Wunderlich's original measurements - they were averaged and sensibly rounded to the nearest degree: 37 Celsius. When this temperature was converted to Farenheit, however, the rounding was forgotten and 98.6 was taken to be accurate to the nearest tenth of a degree. Had the original interval between 36.5 and 37.5 Celsius been translated, the equivalent Farenheit temperatures would have ranged from 97.7 to 99.5. Apparently, discalculia can even cause fevers."

(Quoted in Science, August 18, 1995, page 992)


"When Gladstone was British Prime Minister he visited Michael Faraday's laboratory and asked if some esoteric substance called 'Electricity' would ever have practical significance.

"One day, sir, you will tax it."

was the answer."

(Quoted in Science, 1994).

"the proof is left as an exercise" occurred in 'De Triangulis Omnimodis' by Regiomontanus, written 1464 and published 1533. He is quoted as saying "This is seen to be the converse of the preceding. Moreover, it has a straightforward proof, as did the preceding. Whereupon I leave it to you for homework."

(Quoted in Science, 1994)
"As the fading light of a dying day filtered through the window blinds, Roger stood over his victim with a smoking .45, surprised at the serenity that filled him after pumping six slugs into the bloodless tyrant that had mocked him day after day, and then he shuffled out of the office with one last look back at the shattered computer terminal lying there like a silicon armidillo left to rot on the information highway."

From the winner of the 1994 Bulwer-Lytton Fiction contest for lousy literature

"I imagine most of that stuff on the information highway is roadkill anyway."

(John Updike, 1994)
"It's going to be about bad news. It's going to be about the future of this country, about foreign policy, about defense policy. There are a lot of issues left. I'm certain something will pop up in November. So we'll be able to put it together."

(Quoted in the Economist, March 16, 1996, page 23)

"My dearest Miss Dorothea Sankey

My affectionate & most excellent wife is as you are aware still living - and I am proud to say her health is good. Nevertheless it is always well to take time by the forelock and be prepared for all events. Should anything happen to her, will you supply in her place - as soon as the proper period for decent mourning is over.

Till then I am your devoted servant
Anthony Trollope."

(Quoted from The Oxford Book of Letters in the Economist, March 23, 1996, page 90)

"I believe that the motion picture is destined to revolutionize our educational system and that in a few years it will supplant largely, if not entirely, the use of textbooks."

(Thomas Alva Edison, 1922)

"Keynes distrusted intellectual rigour of the Ricardian type as likely to get in the way of original thinking and saw that it was not uncommon to hit on a valid conclusion before finding a logical path to it.

'I don't really start', he said, 'until I get my proofs back from the printer. Then I can begin serious writing.' "

(Sir Alec Cairncross, in the Economist, April 20, 1996)

"One major barrier to entry into new markets is the requirement to see the future with clarity. It has been said that to so fortell the future, one has to invent it. To be able to invent the future is the dividend that basic research pays."

(In Nature, May 16, 1996, pages 178-9)

" 'Ace, watch your head!' hissed Wanda urgently, yet somehow provocatively, through red, full, sensuous lips, but he couldn't, you know, since nobody can actually watch more than part of his nose or a little cheek or lips if he really tries, but he appreciated her warning."

Janice Estey of Aspen 1996 Bulwer-Lytton Grand Prize Winner "Because the Indians of the high Andes were believed to have little sense of humor, Professor Juan Lyner was amazed to hear this knee-slapper that apparently had been around for centuries at all of the Inca spots: 'Llama ask you this. Guanaco on a picnic? Alpaca lunch.' " John Ashman of Houston 1995 Bulwer-Lytton Grand Prize Winner

"We know [smoking is] not good for kids. But a lot of other things aren't good. Drinking's not good. Some would say milk's not good."

(Page 27 in the Economist, July 6, 1996)

"I feel so strongly about the wrongness of reading a lecture that my language may seem immoderate .... The spoken word and the written word are quite different arts .... I feel that to collect an audience and then read one's material is like inviting a friend to go for a walk and asking him not to mind if you go alongside him in your car."

(Page 76 in Science, July 5, 1996)

"I know, it's hard to believe that Microsoft would release a product before it was ready, but there you have it. A Seattle cyberwag says, "At Microsoft, quality is job 1.1." We had him killed. "

A take-off of Microsoft's "webzine", Slate, Stale, August 1996.

"No presidential candidate in the future will be so inept that four of his major speeches can be boiled down to these four historic sentences: Agriculture is important. Our rivers are full of fish. You cannot have freedom with out liberty. The future lies ahead."

(From pp. 107-112 in the Atlantic Monthly, September 1996)

"Writers often thank their colleagues for their help. Mine have given none. .. Writers often thank their typists. I thank mine. Mrs George Cook is not a particularly good typist, but her spelling and grammar are good. The responsibility for any mistakes is mine, but the fault is hers. Finally, writers too often thank their wives. I have no wife."

(From p. 83 in the Economist, September 7th 1996)

"I see some parallels between the shifts of fashion in mathematics and in music. In music, the popular new styles of jazz and rock became fashionable a little earlier than the new mathematical styles of chaos and complexity theory. Jazz and rock were long despised by classical musicians, but have emerged as art-forms more accessible than classical music to a wide section of the public. Jazz and rock are no longer to be despised as passing fads. Neither are chaos and complexity theory. But still, classical music and classical mathematics are not dead. Mozart lives, and so does Euler. When the wheel of fashion turns once more, quantum mechanics and hard analysis will once again be in style."

(From p. 612 in the American Mathematical Monthly, August-September 1996)

"I was sitting by Dr. Franklin, who perceived that I was not insensible to these mutilations. I have made a rule, said he, whenever in my power, to avoid becoming the draughtsman of papers to be reviewed by a public body."

"My morale has never been higher than since I stopped asking for grants to keep my lab going."

(Quoted from p. 1805 in the September 27, 1996 Science)


"smugness, brutality, unctuous rectitude and tact"

(Quoted from Cecil Rhodes Traduced, pp. 80-81 in the October 5, 1996 Economist)

"The dictum that everything that people do is 'cultural' ... licenses the idea that every cultural critic can meaningfully analyze even the most intricate accomplishments of art and science. ... It is distinctly weird to listen to pronouncements on the nature of mathematics from the lips of someone who cannot tell you what a complex number is!"

(Quoted from p. 183 in the October 11, 1996 Science)

"Church discipline is also somewhat of a remove from the time when the Emperor Henry IV was made to stand in the snow for three days outside the Pope's castle at Canossa, awaiting forgiveness. A French Bishop, Jacques Gaillot, because of his ultra-liberal views was recently transferred from his position at Evreux, in Normandy, and given charge instead of the defunct dioscese of Partenia, in Southern Algeria, which has been covered by sand since the Middle Ages. Gaillot has retaliated by creating a virtual dioscese on the Internet, which can be reached at "

(Quoted from p. 24 in the November, 1996 Atlantic Monthly)

"We were a polite society and I expected to lead a quiet life teaching mechanics and listening to my senior colleagues gently but obliquely poking fun at one another. This dream of somnolent peace vanished very quickly when Rutherford came to Cambridge. Rutherford was the only person I have met who immediately impressed me as a great man. He was a big man and made a big noise and he seemed to enjoy every minute of his life. I remember that when transatlantic broadcasting first came in, Rutherford told us at a dinner in Hall how he had spoken into a microphone to America and had been heard all over the continent. One of the bolder of our Fellows said "Surely you did not need to use apparatus for that." "

(Quoted in "Vignettes: Yesteryear in Oxbridge" p. 733 in Science November 1, 1996)

"Then, owls and bats,
Cowls and twats,
Monks and nuns, in a cloister's moods,
Adjourn to the oak-stump pantry."

(Quoted on page 56-66 of Bill Byerson, Mother Tongue: The English Language, Penguin, 1990.)

"Two major advances are responsible for both the recent progress and current optimism. First, recombinant DNA technology has made it possible to identify every gene and protein in an organism and to manipulate them in order to explore their functions. Second, it has been discovered that the molecular mechanisms of development have been conserved during animal evolution to a far greater extent than had been imagined. This conservation means that discoveries about the development of worms and files, which come from the kind of powerful genetic studies that are not possible in mammals, greatly accelerate the rate at which we can discover the mechanisms and molecules that operate during our own development.
It is tempting to think that the main principles of neural development will have been discovered by the end of the century and that the cellular and molecular basis of the mind will be the main challenge for the next. An alternative view is that this feeling that understanding is just a few steps away is a recurring and necessary delusion that keeps scientists from dwelling on the complexity the face and how much more remains to be discovered."

(Editorial on page 1063 of Science November 15, 1996)


Vice President Gore, who was clearly on top of the technical issues, met on Wednesday with a group of tough-minded scientists, clergy and fuzzy romantics to discuss the questions raised by evidence of extraterrestrial life. For physicist/astronomer John Bahcall, the remarkable thing was not that such questions were being asked, but that we have the tools to answer them."

(From WHAT'S NEW by Robert L. Park -- Friday, 13 Dec 96)

"As the test beds begin to prove WDM ('wavelength division multiplexing') networks feasible, telephone company executives will have to judge whether they are wise. If a single glass fiber can carry all the voice, fax, video and data traffic for a large corporation yet costs little more than today's high-speed Internet connections, how much will they be able to charge for telephone service? Peter Cochrane of BT Laboratories in Ipswich, England, predicts that "photonics will transform the telecoms industry by effectively making bandwidth free and distance irrelevant." Joel Birnbaum, director of Hewlett-Packard Laboratories, expects that this will relegate telephone companies to the role of digital utilities. "You will buy computing like you now buy water or power," he says.

Others, such as industry analyst Francis McInerney, believe the double-time march of technology has already doomed them to fall behind. AT&T and its ilk, he claims, "are already dead. When individuals have [megabits per second of bandwidth], telephone service should cost about three cents a month." Having discovered how to offer high-bandwidth service, telephone companies may now need to invent useful things to do with it, just to stay in business. "

(From BANDWIDTH, UNLIMITED by W. Wayt Gibbs)

"Before Canada jeopardizes its scientific future and compromises its scientific community to achieve short-term budgetary solutions, it must recognize that the funding of university sicence is both a government responsibility and a long-range investment. Without government support, Canada's university science infrastructure will erode, and along with it, the country's competitiveness in a world economy increasingly based on knowledge."

(Editorial on page 139 of Science January 10, 1997)


178 new bills were introduced in the Senate on Tuesday -- one, S.124, is a thing of beauty: "The National Research Investment Act of 1997." It calls for doubling the federal investment in basic science and medical research over a 10-year period (WN 17 Jan 97). Funds must be allocated by a peer review system and can not be used for the commercialization of technologies. A dozen non-defense agencies and programs are covered by the bill, which is the work of Phil Gramm (R-TX). Gramm pointed out that in 1965, 5.7% of the federal budget went for non-defense R&D -- 32 years later, that has dropped to only 1.9%, and real spending on research has declined for four straight years. Ten-year doubling requires an annual increase of 7% -- just what leaders of the science community have been calling for (WN 10 Jan 97)."

(From WHAT'S NEW by Robert L. Park -- Friday, 24 January, 1997)

"a British officer told a sergeant to post four lookouts to watch for the German army which was advancing through Belgium. Later, the officer discovered that the sergeant had posted only three. Asked to explain his lapse, the soldier said he had judged the fourth guard unnecessary. 'The enemy would hardly come from that direction,' he explained, 'it's private property.' "

(Quoted from Back to the Front by Stephen O'Shea)

"Admirers of Thomas Jefferson have long quoted his statement about black men and women that is inscribed on the Jefferson Memorial: 'Nothing is more certainly written in the book of fate than that these people are to be free.' But they and the inscription, as Conor Cruise O'Brien pointed out in 'Thomas Jefferson: Radical and Racist' (October, 1996, Atlantic), omit Jefferson's subsequent clause: 'Nor is it less certain that the two races, equally free, cannot live in the same government.'"

(Quoted from What Jefferson Helps to Explain by Benjamin Schwarz)

"A centre of excellence is, by definition, a place where second class people may perform first class work."

"A truly popular lecture cannot teach, and a lecture that truly teaches cannot be popular."

"The most prominent requisite to a lecturer, though perhaps not really the most important, is a good delivery; for though to all true philosophers science and nature will have charms innumerably in every dress, yet I am sorry to say that the generality of mankind cannot accompany us one short hour unless the path is strewed with flowers."

(Three quotes from Michael Faraday)

"The body of mathematics to which the calculus gives rise embodies a certain swashbuckling style of thinking, at once bold and dramatic, given over to large intellectual gestures and indifferent, in large measure, to any very detailed description of the world. It is a style that has shaped the physical but not the biological sciences, and its success in Newtonian mechanics, general relativity and quantum mechanics is among the miracles of mankind. But the era in thought that the calculus made possible is coming to an end. Everyone feels this is so and everyone is right."

(From Vignettes: Changing Times in Science, 28 February 1997, page 1276)

"[8] 94m:94015 Beutelspacher, Albrecht Cryptology. An introduction to the art and science of enciphering, encrypting, concealing, hiding and safeguarding described without any arcane skullduggery but not without cunning waggery for the delectation and instruction of the general public. Transformation from German into English succored and abetted by J. Chris Fisher. MAA Spectrum. Mathematical Association of America, Washington, DC, 1994. xvi+156 pp. ISBN: 0-88385-504-6 94A60 (94-01)"

(From Math Reviews)

"It's generally the way with progress that it looks much greater than it really is."

(From The Wittgenstein Controversy, by Evelyn Toynton in the Atlantic Monthly June 1997, pp. 28-41.)

"In 1965 the Russian mathematician Alexander Konrod said "Chess is the Drosophila of artificial intelligence." However, computer chess has developed as genetics might have if the geneticists had concentrated their efforts starting in 1910 on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies."

(From John McCarthy's review of Kasparov versus Deep Blue by Monty Newborn (Springer, 1996) in Science, 6 June 1997, page 1518)

"A research policy does not consist of programs, but of hiring high-quality scientists. When you hire someone good, you've made your research policy for the next 20 years."

Chief CNRS advisor Vincent Courtillot quoted in New CNRS Chief Gets Marching Orders, Science, 18 July, 1997, page 308)
"Mathematicians are like pilots who maneuver their great lumbering planes into the sky without ever asking how the damn things stay aloft.

The computer has in turn changed the very nature of mathematical experience, suggesting for the first time that mathematics, like physics, may yet become an empirical discipline, a place where things are discovered because they are seen.

The existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself."

(From David Berlinski's somewhat negative review of The Pleasures of Counting by T. W. Korner (Cambridge, 1996)
in The Sciences, July/August 1997, pages 37-41)

"If I can give an abstract proof of something, I'm reasonably happy. But if I can get a concrete, computational proof and actually produce numbers I'm much happier. I'm rather an addict of doing things on the computer, because that gives you an explicit criterion of what's going on. I have a visual way of thinking, and I'm happy if I can see a picture of what I'm working with."

(John Milnor)

"The term "reviewed publication" has an appealing ring for the naive rather than the realistic... Let's face it: (1) in this day and age of specialization, you may not find competent reviewers for certain contributions; (2) older scientists may agree that over the past two decades, the relative decline in research funds has been accompanied by an increasing number of meaningless, often unfair reviews; (3) some people are so desperate to get published that they will comply with the demands of reviewers, no matter how asinine they are."

(August Epple)

"The NYT also has a stunning revelation about the way the Ivy League used to do business. Last Friday, the President of Darmouth used the occasion of dedicating a campus Jewish student center to haul out a 1934 letter between an alumnus of the school and the director of admissions. The alum complained that "the campus seems more Jewish each time I arrive in Hanover. And unfortunately many of them (on quick judgment) seem to be the 'kike' type." And the Dartmouth admissions man wrote back, "I am glad to have your comments on the Jewish problem, and I shall appreciate your help along this line in the future. If we go beyond the 5 percent or 6 percent in the Class of 1938, I shall be grieved beyond words." In reacting to the revelation, Elie Wiesel summons a simple fact that suggests how much times have changed: the current presidents of Harvard, Yale, and Princeton are Jewish."

(SLATE, Tuesday November 11, 1997)
"This is the essence of science. Even though I do not understand quantum mechanics or the nerve cell membrane, I trust those who do. Most scientists are quite ignorant about most sciences but all use a shared grammar that allows them to recognize their craft when they see it. The motto of the Royal Society of London is 'Nullius in verba' : trust not in words. Observation and experiment are what count, not opinion and introspection. Few working scientists have much respect for those who try to interpret nature in metaphysical terms. For most wearers of white coats, philosophy is to science as pornography is to sex: it is cheaper, easier, and some people seem, bafflingly, to prefer it. Outside of psychology it plays almost no part in the functions of the research machine."

(Steve Jones, University College, London)

"If you have a great idea, solid science, and earthshaking discoveries, you are still only 10% of the way there,"

(David Tomei, LXR Biotechnology Inc.)

"There he received his hardest job of the war - a rush request to convert typewriters to twenty-one different languages of Asia and the South Pacific.

The implications of the work and its difficulty brought him to near collapse, but he completed it with only one mistake: on the Burmese typewriter he put a letter upside down. Years later, after he had discovered his error, he told the language professor he had worked with that he would fix that letter on the professor's Burmese typewriter. The professor said not to bother; in the intervening years, as a result of typewriters copied from Martin's original, that upside-down letter had been accepted in Burma as proper typewriter style."

(Ian Frazier)

The T-bone terror proves that ministers have no grasp of science or maths - let alone our liberties

"The giant finger whooshes out of the night sky and points at the dumbstruck face in the window. "It could be you," says a voice. This week the Agriculture Minister Jack Cunningham impersonated the National Lottery advertiser. As the nation's fork was poised with a T-bone steak on its way to the nation's mouth, Dr Cunningham screamed: "Don't touch it." According to the great god science, new variant Creutzfeldt-Jakob disease (nvCJD) could be lurking in that mouthful. There is a small risk, and where there is risk, a government must ban.

Perhaps only mathematicians are aware of the enormity of what the Government did this week. It took a risk that is statistically negligible and exploited it as an act of insufferable nannying. Beef ribs, T-bones and oxtails present a public health risk publicised as "very small" and "a chance of one case per year" (though none of Britain's 22 nvCJD cases has been positively linked to beef). Most newspapers cluelessly converted "a chance" into a certainty, and ridiculed the risk as a tiny one in 56 million. But that is not what the scientists said. They suggested the chance was "5 per cent", so the risk is nearer to one in 1.1 billion, or one in 560 million among the half of the population that eats beef. There can have been no more tenuous basis for an infringement of personal liberty."

(Simon Jenkins)

"The common situation is this: An experimentalist performs a resolution analysis and finds a limited-range power law with a value of D smaller than the embedding dimension. Without necessarily resorting to special underlying mechanistic arguments, the experimentalist then often chooses to label the object for which she or he finds this power law a "fractal". This is the fractal geometry of nature."

(David Avnir et al, Hebrew University)

"Most nonscientists who like to think of themselves as knowledgeable about modern science really know only about technologies - and specifically those technologies likely to bring economic profits in the short term."

(Takashi Tachibana, Japanese Journalist)

"Another thing I must point out is that you cannot prove a vague theory wrong. ... Also, if the process of computing the consequences is indefinite, then with a little skill any experimental result can be made to look like the expected consequences."

(Richard Feynman, 1964)

"Renyi would become one of Erdos's most important collaborators. ... Their long collaborative sessions were often fueled by endless cups of strong coffee. Caffeine is the drug of choice for most of the world's mathematicians and coffee is the preferred delivery system. Renyi, undoubtedly wired on espresso, summed this up in a famous remark almost always attributed to Erdos: "A mathematician is a machine for turning coffee into theorems." ... Turan, after scornfully drinking a cup of American coffee, invented the corollary: "Weak coffee is only fit for lemmas." "

(Bruce Schechter, 1998)

"Once the opening ceremonies were over, the real meat of the Congress was then served up in the form of about 1400 individual talks and posters. I estimated that with luck I might be able to comprehend 2% of them. For two successive weeks in the halls of a single University, ICM'98 perpetuated the myth of the unity of mathematics; which myth is supposedly validated by the repetition of that most weaselly of rhetorical phrases: "Well, in principle, you could understand all the talks." "

(Philip Davis, 1998)

"Looking over the past 150 years -- at the tiny garden at Brno, the filthy fly room at Columbia, the labs of the New York Botanical Garden, the basement lab at Stanford, and the sun-drenched early gatherings at Cold Spring Harbor -- it seems that the fringes, not the mainstream, are the most promising places to discover revolutionary advances."

(Paul Berg and Maxine Singer, 1998)

"Should we teach mathematical proofs in the high school? In my opinion, the answer is yes...Rigorous proofs are the hallmark of mathematics, they are an essential part of mathematics' contribution to general culture." George Polya (1981). Mathematical discovery: On understanding, learning, and teaching problem solving (Combined Edition), New York, Wiley & Sons (p. 2-126) "A mathematical deduction appears to Descartes as a chain of conclusions, a sequence of successive steps. What is needed for the validity of deduction is intuitive insight at each step which shows that the conclusion attained by that step evidently flows and necessarily follows from formerly acquired knowledge (acquired directly by intuition or indirectly by previous steps) ... I think that in teaching high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning." (ibid, p. 2-128) This "quasi-experimental" approach to proof can help to de-emphasis a focus on rigor and formality for its own sake, and to instead support the view expressed by Hadamard when he stated "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it" (J. Hadamard, in E. Borel, Lecons sur la theorie des fonctions, 3rd ed. 1928, quoted in Polya, (1981), (p. 2/127). "intuition comes to us much earlier and with much less outside influence than formal arguments which we cannot really understand unless we have reached a relatively high level of logical experience and sophistication. Therefore, I think that in teaching high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning." (ibid, p. 2-128)

"In the first place, the beginner must be convinced that proofs deserve to be studied, that they have a purpose, that they are interesting." (ibid, p. 2-128)

"The purpose of a legal proof is to remove a doubt, but this is also the most obvious and natural purpose of a mathematical proof. We are in doubt about a clearly stated mathematical assertion, we do not know whether it is true or false. Then we have a problem: to remove the doubt, we should either prove that assertion or disprove it." (ibid, p. 2-129)

(Polya quotes are thanks to Laurie Edwards)
"The basic difference between playing a human and playing a supermatch against Deep Blue is the eerie and almost empty sensation of not having a human sitting opposite you. With humans, you automatically know a lot about their nationality, gender, mannerisms, and such minor things as a persistent cough or bad breath. Years ago we had to endure chain-smokers who blew smoke our way. But Deep Blue wasn't obnoxious, it was simply nothing at all, an empty chair not an opponent but something empty and relentless."

(Garry Kasparov, 1998)

"All professions look bad in the movies ... why should scientists expect to be treated differently?"

(Michael Crichton, 1999)

"the academy was a sort of club for retired Parisian scientists, happy to be able to come together once a week to talk about science for 2 hours after lunch and a little nap."

(Guy Ourison, January 1999)

"User-interface criticism is a genre to watch. It will probably be more influential and beneficial to the next century than film criticism was to the twentieth century. The twenty-first century will be filled with surprises, but one can safely count on it to bring more complexity to almost everything. Bearing the full brunt of that complexity, the great user-interface designers of the future will provide people with the means to understand and enrich their own humanity, and to stay human."

(Jaron Lanier, June 1999)

"A real number complexity model appropriate for this context is given in the recent landmark work of Blum, Cucker, Shub and Smale . In discussing their motivation for seeking a suitable theoretical foundation for modern scientific computing, where most of the algorithms are 'real number algorithms' the authors of this work quote the following illuminating remarks of John von Neumann, made in 1948: "There exists today a very elaborate system of formal logic, and specifically, of logic applied to mathematics. This is a discipline with many good sides but also serious weaknesses.... Everybody who has worked in formal logic will confirm that it is one of the technically most refactory parts of mathematics. The reason for this is that it deals with rigid, all-or-none concepts, and has very little contact with the continuous concept of the real or the complex number, that is with mathematical analysis. Yet analysis is the technically most successful and best-elaborated part of mathematics. Thus formal logic, by the nature of its approach, is cut off from the best cultivated portions of mathematics, and forced onto the most difficult mathematical terrain, into combinatorics.

The theory of automata, of the digital, all-or-none type as discussed up to now, is certainly a chapter in formal logic. It would, therefore, seem that it will have to share this unattractive property of formal logic. It will have to be, from the mathematical point of view, combinatorial rather than analytical."

( l. Blum, P. Cucker, M. Shub and S. Smale (1998), Complexity and Real Computation, Springer-Verlag, New York)

"Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane."

(Augustus De Morgan)

"In 1831, Fourier's posthumous work on equations showed 33 figures of solution, got with enormous labour. Thinking this is a good opportunity to illustrate the superiority of the method of W. G. Horner, not yet known in France, and not much known in England, I proposed to one of my classes, in 1841, to beat Fourier on this point, as a Christmas exercise. I received several answers, agreeing with each other, to 50 places of decimals. In 1848, I repeated the proposal, requesting that 50 places might be exceeded: I obtained answers of 75, 65, 63, 58, 57, and 52 places."

(Augustus De Morgan)

"I think we need more institutes, but then you run into the question, Is it better to spend $2 million and have another institute or to fund another twenty-five or so researchers each year? It's a question of trying to keep the discipline alive and thriving. There's no doubt the really big ideas in mathematics come from maybe 5 percent of the people, but you need a broad base to nourish the 5 percent and to work out all the details as they move on to more adventuresome things. Look at, say, mathematicians at Group III universities. It's a rarity when they get funding. How do you keep them in the system? ... We're under terrific pressure to increase the size of our grants. If we did what the [National Science] board wants us to do, we would fund 800 people instead of 1,400. It's a question of whether DMS did the right thing when they pulled so many people down to one month of summer support. This took some of the pressure off the Foundation to put more money in mathematics. Suppose we funded 800 people. How much noise would it create? Would there be a march on Washington? I often think that's the way to go. See whether mathematicians would stand up for themselves or whether they'd just meekly accept. In chemistry, people get declined, and in two months they turn around with another proposal. Mathematicians --- they get declined twice, and they fold. I think mathematicians have such a personal investment in their problems that if you turn down their proposals, they take it as if you're judging them as mathematicians. They're not as flexible and often don't seem to be able to move to another class of problems. We fund proposals, not individuals."

(D. J. Lewis)

"Notices: After your time at the NSF, do you have any advice for the math community about what they should be doing to try to improve the funding for mathematics?

Lewis: I don't think that up to this date they've made a very good case for why they should be funded. The bottom line is, What are you doing for the citizens of the country?

Notices: When you say "make the case," what do you mean concretely? Do groups of mathematicians have to descend on Capitol Hill?

Lewis: They've got to do some demonstrations of what mathematics has accomplished for the good of society. One of the things mathematicians have done is education. For example, if mathematicians took seriously the job of training elementary and middle school teachers, they could make some claim that they really improve things. Also, science is getting so complicated, it can be done only with the help of mathematics. Is the math community willing to step up and participate?

If so, they will have nonmathematicians making the case for greater funding of mathematics. It is always best to have outsiders make your case for you. Once upon a time I thought going to Capitol Hill would be effective. I don't think it will get very far if mathematicians go to Capitol Hill without the support of others. These days information technology and biology and medicine are the themes that echo well with the president and Congress."

(D. J. Lewis)


"The work then proceeds in a manner unique to science. Because practitioners publish their work electronically, through the e-print archives at the Los Alamos National Laboratory in New Mexico, the entire community can read a paper hours after its authors finish typing the last footnote. As a result, no one theorist or even a collaboration does definitive work. Instead, the field progresses like a jazz performance: A few theorists develop a theme, which others quickly take up and elaborate. By the time it's fully developed, a few dozen physicists, working anywhere from Princeton to Bombay to the beaches of Santa Barbara, may have played important parts."

(Gary Taubes)


'where almost one quarter hour was spent, each beholding the other with admiration before one word was spoken: at last Mr. Briggs began "My Lord, I have undertaken this long journey purposely to see your person, and to know by what wit or ingenuity you first came to think of this most excellent help unto Astronomy, viz. the Logarithms: but my Lord, being by you found out, I wonder nobody else found it out before, when now being known it appears so easy." '

(Henry Briggs, 1617)

"Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise."

(J. W. Tuckey, 1962)


One of the beauties of learning is that it admits its provisionality, its imperfections. This scholarly scrupulousness, this willingness to admit that even the best-supported of theories is still a theory, is now being exploited by the unscrupulous. But that we do not know everything does not mean we know nothing. Not all theories are of equal weight. The moon, even the moon over Kansas, is not made of green cheese. Genesis, as a theory, is bunk.

If the overabundant new knowledge of the modern age is, let's say, a tornado, then Oz is the extraordinary, Technicolored new world in which it has landed us, the world from which --- life not being a movie --- there is no way home. In the immortal words of Dorothy Gale, 'Toto, something tells me we're not in Kansas any more.' To which one can only add: Thank goodness, baby, and amen.

(Salman Rushdie)


"The mental maps, gave rise to industries that could not have been predicted, and created a new class of technological workers whom wise societies took pains to nurture. Are we about to go through this process again? A renowned social analyst and management philosopher looks to history for insights."

(Peter Drucker)

"When the facts change, I change my mind. What do you do, sir?"

(John Maynard Keynes)

"Look miss, if I disagree with Darwin, he's not going to send me to hell."

(An anonymous student's "Pascal wager-style" rationale)

" Most working scientists may be naive about the history of their discipline and therefore overly susceptible to the lure of objectivist mythology. But I have never met a pure scientific realist who views social context as entirely irrelevant, or only as an enemy to be expunged by the twin lights of universal reason and incontrovertible observation. And surely, no working scientist can espouse pure relativism at the other pole of the dichotomy. (The public, I suspect, misunderstands the basic reason for such exceptionless denial. In numerous letters and queries, sympathetic and interested nonprofessionals have told me that scientists cannot be relativists because their commitment to such a grand and glorious goal as the explanation of our vast and mysterious universe must presuppose a genuine reality "out there" to discover. In fact, as all working scientists know in their bones, the incoherence of relativism arises from virtually opposite and much more quotidian motives. Most daily activity in science can only be described as tedious and boring, not to mention expensive and frustrating. Thomas Edison was just about right in his famous formula for invention as 1% inspiration mixed with 99% perspiration. How could scientists ever muster the energy and stamina to clean cages, run gels, calibrate instruments, and replicate experiments, if they did not believe that such exacting, mindless, and repetitious activities can reveal truthful information about a real world? If all science arises as pure social construction, one might as well reside in an armchair and think great thoughts.)

Similarly, and ignoring some self-promoting and cynical rhetoricians, I have never met a serious social critic or historian of science who espoused anything close to a doctrine of pure relativism. The true, insightful, and fundamental statement that science, as a quintessentially human activity, must reflect a surrounding social context does not imply either that no accessible external reality exists, or that science, as a socially embedded and constructed institution, cannot achieve progressively more adequate understanding of nature's facts and mechanisms. "

(Stephen J. Gould)

" caused Thorstein Veblen to comment acerbically in 1908 that "business principles" were transforming higher education into "a merchantable commodity, to be produced on a piece-rate plan, rated, bought, and sold by standard units, measured, counted and reduced to staple equivalence by impersonal, mechanical tests. "

"New products and new processes do not appear full-grown," Vannevar Bush, President Franklin Roosevelt's chief science adviser, declared in 1944. "They are founded on new principles and new conceptions, which in turn are painstakingly developed by research in the purest realms of science." "

(Eyal Press and Jennifer Washburn)

"Most important to Fox was a young instructor who had arrived at Cornell two years before from Williams and Mary. William Lloyd Garrison Williams had written his Ph.D thesis under Leonard Dickson at Chicago in 1920. Born in Friendship, Kansas, Williams, who was named for the famous abolitionist William LLoyd Garrison, attended a small Quaker school in Indiana, taught school briefly in North Dakota and then attended Haverford College where he earned a B.A. degree. From 1910-13 he attended Oxford University as a Rhodes Scholar, and after receving a B.A. and M.A., he took a faculty position at Miami University of Ohio. His Ph.D. work at Chicago was done during the summers. He also taught briefly at Gettysburg College and William and Mary before coming to Cornell.

In 1924, Williams moved to McGill University, where he helped develop the graduate program. He was the founder and organizer of the Canadian Mathematical Congress, the first meeting of which was in Montreal in 1945. Nearly all of the support the Congress was able to acquire was due to William's efforts (see W.L.G. Williams, 1888-1976, G. De B. Robinson, Proc. Royal Society of Canada, 1976). A man of remarkable ability and compassion, Williams took a strong personal interest in his fellowman. A lifelong member of the Society of Friends, he was a tireless worker for Quaker causes."

(James A. Donaldson and Richard J. Fleming)

Gravity Turntable Sets New Record

'LONG BEACH, CALIFORNIA--Scientists have been scrutinizing gravity since the time of Newton, but they've had difficulty measuring the power of its pull. Now, thanks to a clever device, physicists have the most precise measurement yet.


"[It] should have been obvious" that previous measures of big G were off, says physicist Randy Newman of the University of California, Irvine. The new result, announced this week at the American Physical Society meeting, sets big G tentatively at 6.67423 0.00009 x 10-11 m3/(kg s2). "It's one of the fundamental constants," Gundlach says. "Mankind should just know it. It's a philosophical thing."'

"Imagine Dostoyevsky. There are some incidents like this, two boys killing other children, in his famous diary. Imagine what Dostoyevsky would do with that. He would deal with the transcendentally important question of evil in the child. Today the editor would say, "Fyodor, tomorrow, please, your piece. Don't tell me you need ten months for thinking. Fyodor, tomorrow!" "

(George Steiner)

"So my reaction surprises me. I tell Natalie that math is important and relevant and that I wished I'd made the effort to understand. I wish somebody had found a way of making sense of it all. This revelation comes from reading a stack of magazines about the future, about computers and artificial intelligence, cars and planes, food production and global warming. And I have come to the conclusion that Mr. Kool was right.

Math has something to do with calculations, formulas, theories and right angles. And everything to do with real life. Mathematicians not only have the language of the future (they didn't send Taming of the Shrew into space, just binary blips) but they can use it to predict when Andromeda will perform a cosmic dance with the Milky Way. It's mathematicians who are designing the intelligent car that knows when you're falling asleep at the wheel or brakes to avoid an accident. It can predict social chaos and the probability of feeding billions. It even explains the stock market and oil prices."


Paulette Bourgeois lives in Toronto where she is calculating the probability of ever balancing her chequebook. She is the author of the Franklin the Turtle books for children.

(Paulette Bourgeois)

" Mathematics is the language of high technology. Indeed it is, but I think it is also becoming the eyes of science."

(Tom Brzustowski, NSERC President)


"This is fundamentally wrong. We are not entering a time when copyright is more threatened than it is in real space. We are instead entering a time when copyright is more effectively protected than at any time since Gutenberg. The power to regulate access to and use of copyrighted material is about to be perfected. Whatever the mavens of the mid-1990s may have thought, cyberspace is about to give the holders of copyrighted property the biggest gift of protection they have ever known.

"In such an age -- in a time when the protections are being perfected -- the real question for law is not, how can law aid in that protection? but rather, is that protection too great? The mavens were right when they predicted that cyberspace will teach us that everything we thought about copyright was wrong. But the lesson in the future will be that copyright is protected far too well. The problem will center not on copy-right but on copy-duty -- the duty of owners of protected property to make that property available."

(Lawrence Lessig)

"An informed list of the most profound scientific developments of the 20th century is likely to include general relativity, quantum mechanics, big bang cosmology, the unraveling of the genetic code, evolutionary biology, and perhaps a few other topics of the reader's choice. Among these, quantum mechanics is unique because of its profoundly radical quality. Quantum mechanics forced physicists to reshape their ideas of reality, to rethink the nature of things at the deepest level, and to revise their concepts of position and speed, as well as their notions of cause and effect. "

(Daniel Kleppner and Roman Jackiw)

"A wealthy (15th Century) German merchant, seeking to provide his son with a good business education, consulted a learned man as to which European institution offered the best training. "If you only want him to be able to cope with addition and subtraction," the expert replied, "then any French or German university will do. But if you are intent on your son going on to multiplication and division -- assuming that he has sufficient gifts -- then you will have to send him to Italy."

(Georges Ifrah)

"2000 was a banner year for scientists deciphering the "book of life"; this year saw the completion of the genome sequences of complex organisms ranging from the fruit fly to the human.

Genomes carry the torch of life from one generation to the next for every organism on Earth. Each genome--physically just molecules of DNA--is a script written in a four-letter alphabet. Not too long ago, determining the precise sequence of those letters was such a slow, tedious process that only the most dedicated geneticist would attempt to read any one "paragraph"--a single gene. But today, genome sequencing is a billion-dollar, worldwide enterprise. Terabytes of sequence data generated through a melding of biology, chemistry, physics, mathematics, computer science, and engineering are changing the way biologists work and think. Science marks the production of this torrent of genome data as the Breakthrough of 2000; it might well be the breakthrough of the decade, perhaps even the century, for all its potential to alter our view of the world we live in."

(Elizabeth Pennisi)

"Not until the creation and maintenance of decent conditions of life for all people are recognized and accepted as a common obligation of all people and all countries - not until then shall we, with a certain degree of justification, be able to speak of humankind as civilized."

(Albert Einstein, 1945)


"Capitalism is the extraordinary belief that the nastiest of men, for the nastiest of reasons, will somehow work for the benefit of us all."

(John Maynard Keynes)
"When we have before us a fine map, in which the line of the coast, now rocky, now sandy, is clearly indicated, together with the winding of the rivers, the elevations of the land, and the distribution of the population, we have the simultaneous suggestion of so many facts, the sense of mastery over so much reality, that we gaze at it with delight, and need no practical motive to keep us studying it, perhaps for hours altogether. A map is not naturally thought of as an aesthetic object... And yet, let the tints of it be a little subtle, let the lines be a little delicate, and the masses of the land and sea somewhat balanced, and we really have a beautiful thing; a thing the charm of which consists almost entirely in its meaning, but which nevertheless pleases us in the same way as a picture or a graphic symbol might please. Give the symbol a little intrinsic worth of form, line and color, and it attracts like a magnet all the values of things it is known to symbolize. It becomes beautiful in its expressiveness."

(George Santayana)

"If my teachers had begun by telling me that mathematics was pure play with presuppositions, and wholly in the air, I might have become a good mathematician, because I am happy enough in the realm of essence. But they were overworked drudges, and I was largely inattentive, and inclined lazily to attribute to incapacity in myself or to a literary temperament that dullness which perhaps was due simply to lack of initiation."

(George Santayana)

"He designed and built chess-playing, maze-solving, juggling and mind-reading machines. These activities bear out Shannon's claim that he was more motivated by curiosity than usefulness. In his words 'I just wondered how things were put together.' "

(Claude Shannon)

"The price of metaphor is eternal vigilance"

(Arturo Rosenblueth and Norbert Wiener)

What is particularly ironic about this is that it follows from the empirical study of numbers as a product of mind that it is natural for people to believe that numbers are not a product of mind!"

(George Lakoff and Rafael E. Nunez)

Recent Discoveries about the Nature of Mind. In recent years, there have been revolutionary advances in cognitive science ---- advances that have a profound bearing on our understanding of mathematics. Perhaps the most profound of these new insights are the following:
1. The embodiment of mind. The detailed nature of our bodies, our brains and our everyday functioning in the world structures human concepts and human reason. This includes mathematical concepts and mathematical reason.
2. The cognitive unconscious. Most thought is unconscious -- not repressed in the Freudian sense but simply inaccessible to direct conscious introspection. We cannot look directly at our conceptual systems and at our low-level thought processes. This includes most mathematical thought.
3. Metaphorical thought. For the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in sensory-motor systems. The mechanism by which the abstract is comprehended in terms of the concept is called conceptual metaphor. Mathematical thought also makes use of line."

(George Lakoff and Rafael E. Nunez)

"The early study of Euclid made me a hater of geometry."

(James Joseph Sylvester, 1814-97, Second LMS President)

"a thrill which is indistinguishable from the thrill I feel when I enter the Sagrestia Nuovo of the Capella Medici and see before me the austere beauty of the four statues representing 'Day', 'Night', 'Evening', and 'Dawn' which Michelangelo has set over the tomb of Guiliano de'Medici and Lorenzo de'Medici."

(G. N. Watson, 1886-1965)
"All physicists and a good many quite respectable mathematicians are contemptuous about proof."

(G. H. Hardy, 1877-1947)

A century after biology started to think physically:

"The idea that we could make biology mathematical, I think, perhaps is not working, but what is happening, strangely enough, is that maybe mathematics will become biological!"

(Greg Chaitin, Interview, 2000.)
"The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology, and all of them the physicist can more or less easily read and adequately solve."

(D'Arcy Thompson, "On Growth and Form" 1917)

"A doctorate compels most of us to be detailed and narrow, and to carve out our own specialities, and tenure commitees rarely like boldness. Later, when our jobs are safe we can be synthetic, and generalize."

(Paul Kennedy)

"... it is no doubt important to attend to the eternally beautiful and true. But it is more important not to be eaten."

(Jerry Fodor)
Distinguishing effortless early learning of language and social customs from later labourious general purpose concept acquisition, Egan writes:
"The bad news is that our evolution equipped us to live in small, stable, hunter-gatherer societies. We are Pleistocene people, but our languaged brains have created massive, multicultural, technologically sophisticated and rapidly changing societies for us to live in."

"The cement-like learning of our early years can accomodate almost anything, then it fixes and becomes almost unmovable."

"we can, as a result, change our earlier beliefs and commitments. We also know this is difficult for most people."

(Kieran Egan)


This is what Albert Einstein said quoting Max Planck
"...a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents die and a new generation grows up that's familiar with it."
or ...
"A new scientific truth usually does not make its way in the sense that its opponents are persuaded and declare themselves enlightened, but rather that the opponents become extinct and the rising generation was made familiar with the truth from the very beginning".

Max Planck, in THE QUANTUM BEAT by F.G.Major, Springer (1998).
"And Max Planck, surveying his own career in his Scientific Autobiography, sadly remarked that 'a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.'"

(Thomas Kuhn)

"the idea that we could make biology mathematical, I think, perhaps is not working, but what is happening, strangely enough, is that maybe mathematics will become biological, not that biology will become mathematical, mathematics may go in that direction!"

(Interview with Gregory Chaitin by Hans-Ulrich Obrist (Musee d'Art Moderne de la Ville de Paris), Paris/CDG Airport, October 2000.)

"The message is that mathematics is quasi-empirical, that mathematics is not the same as physics, not an empirical science, but I think it's more akin to an empirical science than mathematicians would like to admit."

"Mathematicians normally think that they possess absolute truth. They read God's thoughts. They have absolute certainty and all the rest of us have doubts. Even the best physics is uncertain, it is tentative. Newtonian science was replaced by relativity theory, and then---wrong!---quantum mechanics showed that relativity theory is incorrect. But mathematicians like to think that mathematics is forever, that it is eternal. Well, there is an element of that. Certainly a mathematical proof gives more certainty than an argument in physics or than experimental evidence, but mathematics is not certain. This is the real message of Godel's famous incompleteness theorem and of Turing's work on uncomputability."

"You see, with Godel and Turing the notion that mathematics has limitations seems very shocking and surprising. But my theory just measures mathematical information. Once you measure mathematical information you see that any mathematical theory can only have a finite amount of information. But the world of mathematics has an infinite amount of information. Therefore it is natural that any given mathematical theory is limited, the same way that as physics progresses you need new laws of physics."

"Mathematicians like to think that they know all the laws. My work suggests that mathematicians also have to add new axioms, simply because there is an infinite amount of mathematical information. This is very controversial. I think mathematicians, in general, hate my ideas. Physicists love my ideas because I am saying that mathematics has some of the uncertainties and some of the characteristics of physics. Another aspect of my work is that I found randomness in the foundations of mathematics. Mathematicians either don't understand that assertion or else it is a nightmare for them..."


"This skyhook-skyscraper construction of science from the roof down to the yet unconstructed foundations was possible because the behaviour of the system at each level depended only on a very approximate, simplified, abstracted characterization at the level beneath 1. This is lucky, else the safety of bridges and airplanes might depend on the correctness of the "Eightfold Way" of looking at elementary particles.

1 ... More than fifty years ago Bertrand Russell made the same point about the architecture of mathematics. See the "Preface" to Principia Mathematica "... the chief reason in favour of any theory on the principles of mathematics must always be inductive, i.e., it must lie in the fact that the theory in question allows us to deduce ordinary mathematics. In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reason rather for believing the premises because true consequences follow from them, than for believing the consequences because they follow from the premises." Contemporary preferences for deductive formalisms frequently blind us to this important fact, which is no less true today than it was in 1910."

(Herbert A. Simon)

Hardy 'asked 'What's your father doing these days. How about that esthetic measure of his?' I replied that my father's book was out. He said, 'Good, now he can get back to real mathematics'.

(Garret Birkoff)


"I DO CONSIDER it appropriate to pay one's tribute to Prof. Subramanyan Chandrasekhar at the outset, before taking a plunge into the aesthetics of macro-causality, based on his book Truth and Beauty: Aesthetics and Motivations in Science.

Brought up on the refined diet of music, mathematics and aesthetics, Chandrasekhar's own writing is probably the most appropriate mirror of his personality. I quote: "When Michelson was asked towards the end of his life, why he had devoted such a large fraction of his time to the measurement of the velocity of light, he is said to have replied 'It was so much fun'." Prof. Chandrasekhar goes on to some length to explain the term quoting even the Oxford Dictionary -- "fun" means "drollery", what Michelson really meant, Chandrasekhar asserts is "pleasure" and "enjoyment" - evidently "fun" in the colloquial sense, a concept, so familiar in our so called ordinary life has no place in Chandrasekhar's dictionary..."

(Bikash Sinha)


'His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his preeminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary---"so happy in his conjectures", said de Morgan, "as to seem to know more than he could possibly have any means of proving."'-- J. M. Keynes 1956


If Edison, Fineman, Gauss, and Newton had all been intensely tutored from the age of three by brilliant parents, as J.S. Mill was, then I might at least consider the possibility that my own mental muscles might have been stronger if my own parents had been more demanding. But they were not and I will not. 'When you see [Edison's] mind at play in his notebooks, the sheer multitude and richness of his ideas makes you recognize that there is something that can't be understood easily---that we may never be able to understand.' (historian Paul Israel, quoted in McAuliffe 1995). I think what lies at the heart of these mysteries is genetic, probably emergenic. The configuration of traits of intellect, mental energy, and temperament with which, during the plague years of 1665--6, Isaac Newton revolutionized the world of science were, I believe, the consequence of a genetic lottery that occurred about nine months prior to his birth, on Christmas day, in 1642.


Gauss's second son, Eugene, emigrated to the United States in 1830, enlisted in the army, and later went into business in Missouri. Eugene is said to have had some of his father's gift for languages and the ability to perform prodigious arithmetic calculations, which he did for recreation after his sight failed him in old age.

(David T. Lykken)

'For Poincare, ignoring the emotional sensibility, even in mathematical demonstrations "would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility" (p. 2047).'

(Nathalie Sinclair)

"The controversy between those who think mathematics is discovered and those who think it is invented may run and run, like many perennial problems of philosophy. Controversies such as those between idealists and realists, and between dogmatists and sceptics, have already lasted more than two and a half thousand years. I do not expect to be able to convert those committed to the discovery view of mathematics to the inventionist view. However what I have shown is that a better case can be put for mathematics being invented than our critics sometimes allow. Just as realists often caricature the relativist views of social constructivists in science, so too the strengths of the fallibilist views are not given enough credit. For although fallibilists believe that mathematics has a contingent, fallible and historically shifting character, they also argue that mathematical knowledge is to a large extent necessary, stable and autonomous. Once humans have invented something by laying down the rules for its existence, like chess, the theory of numbers, or the Mandelbrot set, the implications and patterns that emerge from the underlying constellation of rules may continue to surprise us. But this does not change the fact that we invented the game in the first place. It just shows what a rich invention it was. As the great eighteenth century philosopher Giambattista Vico said, the only truths we can know for certain are those we have invented ourselves. Mathematics is surely the greatest of such inventions."

(Paul Ernst)

Who owns the Internet? Until recently, nobody. That's because, although the Internet was "Made in the U.S.A.," its unique design transformed it into a resource for innovation that anyone in the world could use. Today, however, courts and corporations are attempting to wall off portions of cyberspace. In so doing, they are destroying the Internet's potential to foster democracy and economic growth worldwide.

(Lawrence Lessig)

"Predicting the future is an activity fraught with error. Wilbur Wright, co-inventor of the motorized airplane that successfully completed the first manned flight in 1903, seems to have learned this lesson when he noted: "In 1901, I said to my brother Orville that man would not fly for 50 years. Ever since I have ... avoided predictions." Despite the admonition of Wright, faulty future forecasting seems a favored human pastime, especially among those who would presumably avoid opportunities to so easily put their feet in their mouths.

What follows are some of the more striking exemplars of expert error in forecasting the future of technological innovations.

"Louis Pasteur's theory of germs is ridiculous fiction." -- Piem Pachet, Professor of Physiology, 1872

"The abdomen, the chest, and the brain will forever be shut from the intrusion of the wise and humane surgeon." -- Sir John Eric Erickren, British surgeon to Queen Victoria, 1873

"Radio has no future. Heavier than air flying machines are impossible. X-rays will prove to be a hoax." -- William Thomson (Lord Kelvin), English physicist and inventor, 1899

"There is not the slightest indication that nuclear energy will ever be obtainable. It would mean that the atom would have to be shattered at will." -- Albert Einstein, 1932

"Man will never reach the moon, regardless of all future scientific advances." -- Lee De Forest, Radio pioneer, 1957

Computers and information technologies seem to hold a special place in the forecasters' hall of humiliation, be they predictions from the media, business, politicians, scientists, or technologists. Here are some examples:

"This 'telephone' has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us." -- Western Union internal memo, 1876

"I think there is a world market for maybe five computers." -- Thomas Watson, chair of IBM, 1943

"The problem with television is that people must sit and keep their eyes glued on a screen; the average American family hasn't time for it." -- New York Times, 1949

"Where ... the ENIAC is equipped with 18,000 vacuum tubes and weights 30 tons, computers in the future may have only 1,000 vacuum tubes and weigh only 1.5 tons." -- Popular Mechanics, 1949

"Folks, the Mac platform is through -- totally." -- John C. Dvorak, PC Magazine, 1998

"There is no reason anyone would want a computer in their home." -- Ken Olson, president, chairman and founder, Digital Equipment Corp, 1977

"640K ought to be enough for anybody." -- Attributed to Bill Gates, Microsoft chair, 1981

"By the turn of this century, we will live in a paperless society." -- Roger Smith, chair of General Motors, 1986

"I predict the Internet ... will go spectacularly supernova and in 1996 catastrophically collapse." -- Bob Metcalfe, 3Com founder and inventor, 1995

"Credit reports are particularly vulnerable ... [as] are billing, payroll, accounting, pension and profit-sharing programs." -- Leon A Kappelman [author of this article] on likely Y2K problems, 1999 "

(Leon A Kappelman)

Computation with Roman numerals is certainly algorithmic - it's just that the algorithms are complicated.

In 1953, I had a summer job at Bell Labs in New Jersey (now Lucent), and my supervisor was Claude Shannon (who has died only very recently). On his desk was a mechanical calculator that worked with Roman numerals. Shannon had designed it and had it built in the little shop Bell Labs had put at his disposal. On a name plate, one could read that the machine was to be called: Throback I.

Martin from a foggy morning in Berkeley

(Martin Davis)

" [1] If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of everyone, and the receiver cannot dispossess himself of it. [2] Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lites his taper at mine, receives light without darkening me. [3] That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement, or exclusive appropriation. [4] Inventions then cannot, in nature, be a subject of property. "

(Thomas Jefferson)

The question of the ultimate foundations and the ultimate meaning of mathematics remains open: we do not know in what direction it will find its final solution or even whether a final objective answer can be expected at all. 'Mathematizing' may well be a creative activity of man, like language or music, of primary originality, whose Historical decisions defy complete objective rationalisation."

(Hermann Weyl)

Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate."

(Bertrand Russell)

"The problems of mathematics are not problems in a vacuum. There pulses in them the life of ideas which realize themselves in concreto through our [or throught] human endeavors in our historical existence, but forming an indissoluble whole transcending any particular science."

(Hermann Weyl)

THE FUTURE OF E-PUBLISHING. Although e-publishing has suffered a series of setbacks this year, Wired magazine still found plenty of optimism about the future of e-books. Michael S. Hart of Project Guttenberg, which offers books in electronic form, says: "The number of e-books available for free download on the Net will pass 20,000. The number of Net users will start heading towards 1 billion." Librarian Cynthia Orr, a co-founder of, thinks e-publishers should pay more attention to libraries, and says that if the major publishers worked with librarians or distributors "to figure out how to let libraries purchase or license their e-books, and let readers 'check them out' for free," that would help build "a market that otherwise threatens to just collapse for lack of interest. Librarians have been careful defenders of copyright over the years ... and our budgets are far higher than they realize." And Mark Gross, president of Data Conversion Laboratory, thinks that the e-publishing has already won a stealth war: ""What people forget is e-books were going strong before they were called e-books and they went on to sweep into many aspects of business and publishing. Most of this has gone unnoticed by the media. Probably because it has been a kind of backdoor revolution. To cite one example: Print law books are just about gone. People don't use them in law firms anymore. It's all electronic books or online. A revolution has occurred, but no one's noticed."

(Wired Magazine)

"Dear brother;
I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause; viz. that though Reason is feasted, Imagination is starved; while Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. To assist Reason by the stimulus of Imagination is the design of the following production."

Samuel Taylor Coleridge then launches into an ode on mathematics, the first verses of which are as follows:

" On a given finite line
Which must no way incline;
To describe an equi -
- lateral tri -
A -N -G -L -E.
Now let AB
Be the given line
Which must no way incline;
The great Mathematician
Makes this requisition,
That we describe an Equi -
- lateral Tri -
- angle on it;
Aid us, Reason - aid us, Wit!

From the centre A at the distance AB,
Describe the circle BCD
At the distance BA from B the centre
The round ACE to describe boldly venture.
(Third postulate see)
And from the point C
In which the circles make a pother
cutting and slashing one another
Bid the straight lines a journeying go.
CACB those lines will show
To the points, which by AB are reckoned
And postulate the second
For authority you know
ABC Triumphant shall be
An equilateral Triangle
No Peter Pindar carp, nor Zoilus can wrangle."

(Samuel Coleridge)

"There is a story, no doubt exaggerated, that the Pope once remarked that two types of proposals exist for peace in the Middle East: The realistic and the miraculous. The realistic solution is divine intervention. The miraculous involves a voluntary agreement between the two sides."

(Paul Adams)

"Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock our efforts. It should be to us a guidepost on the mazy path to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Besides it is an error to believe that rigor in the proof is the enemy of simplicity."

(David Hilbert)

"... waved his manuscript and confessed his publishing woes. ... "I said, 'I'm afraid no one's going to get to read these words. And I love these words.'"

Ann Sparanese, a librarian in the audience, sent an SOS over the Internet to fellow librarians. Within hours, they inundated HarperCollins with angry e-mails - and orders for Stupid White Men. Some also threatened a boycott.

"Those librarians," says Moore, ... "That's one terrorist group you don't want to mess with."

HarperCollins caved.


(Jan Wong)


" Old ideas give way slowly; for they are more than abstract logical forms and categories. They are habits, predispositions, deeply engrained attitudes of aversion and preference. Moreover, the conviction persists-though history shows it to be a hallucination that all the questions that the human mind has asked are questions that can be answered in terms of the alternatives that the questions themselves present. But in fact intellectual progress usually occurs through sheer abandonment of questions together with both of the alternatives they assume an abandonment that results from their decreasing vitality and a change of urgent interest. We do not solve them: we get over them.

Old questions are solved by disappearing, evaporating, while new questions corresponding to the changed attitude of endeavor and preference take their place. Doubtless the greatest dissolvent in contemporary thought of old questions, the greatest precipitant of new methods, new intentions, new problems, is the one effected by the scientific revolution that found its climax in the " Origin of Species."

(John Dewey)

"The first [axiom] said that when one wrote to the other (they often preferred to exchange thoughts in writing instead of orally), it was completely indifferent whether what they said was right or wrong. As Hardy put it, otherwise they could not write completely as they pleased, but would have to feel a certain responsibility thereby. The second axiom was to the effect that, when one received a letter from the other, he was under no obligation whatsoever to read it, let alone answer it, - because, as they said, it might be that the recipient of the letter would prefer not to work at that particular time, or perhaps that he was just then interested in other problems.... The third axiom was to the effect that, although it did not really matter if they both thought about the same detail, still, it was preferable that they should not do so. And, finally, the fourth, and perhaps most important axiom, stated that it was quite indifferent if one of them had not contributed the least bit to the contents of a paper under their common name; otherwise there would constantly arise quarrels and difficulties in that now one, and now the other, would oppose being named co-author."

(Harald Bohr)

"I got into a research project which can be very simply described as concerned with the realization of the "Nash program" (making use of words made conventional by others that refer to suggestions I had originally made in my early works in game theory).

In this project a considerable quantity of work in the form of calculations has been done up to now. Much of the value of this work is in developing the methods by which tools like Mathematica can be used with suitable special programs for the solution of problems by successive approximation methods."

(John Nash)

"A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven."

(Jean Chretien)

"No man can worthely praise Ptolemye ... yet muste ye and all men take heed, that both in him and in all mennes workes, you be not abused by their autoritye, but evermore attend to their reasons, and examine them well, ever regarding more what is saide, and how it is proved, than who saieth it, for autorite often times deceaveth many menne."

(Robert Record)

"The future has arrived; it's just not evenly distributed."

(William Gibson)

"The plural of 'anecdote' is not 'evidence'."

(Alan L. Leshner)


" ... Several years ago I was invited to contemplate being marooned on the proverbial desert island. What book would I most wish to have there, in addition to the Bible and the complete works of Shakespeare? My immediate answer was: Abramowitz and Stegun's Handbook of Mathematical Functions. If I could substitute for the Bible, I would choose Gradsteyn and Ryzhik's Table of Integrals, Series and Products. Compounding the impiety, I would give up Shakespeare in favor of Prudnikov, Brychkov And Marichev's of Integrals and Series ... On the island, there would be much time to think about waves on the water that carve ridges on the sand beneath and focus sunlight there; shapes of clouds; subtle tints in the sky... With the arrogance that keeps us theorists going, I harbor the delusion that it would be not too difficult to guess the underlying physics and formulate the governing equations. It is when contemplating how to solve these equations - to convert formulations into explanations - that humility sets in. Then, compendia of formulas become indispensable."

(Michael Berry)

"I will be glad if I have succeeded in impressing the idea that it is not only pleasant to read at times the works of the old mathematical authors , but this may occasionally be of use for the actual advancement of science."

(Constantin Caratheodory)

"I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can. There are some peaks which he can distinguish easily, while others are less clear. He sees A sharply, while of B he can obtain only transitory glimpses. At last he makes out a ridge which leads from A, and following it to its end he discovers that it culminates in B. B is now fixed in his vision, and from this point he can proceed to further discoveries. In other cases perhaps he can distinguish a ridge which vanishes in the distance, and conjectures that it leads to a peak in the clouds or below the horizon. But when he sees a peak he believes that it is there simply because he sees it. If he wishes someone else to see it, he points to it, either directly or through the chain of summits which led him to recognize it himself. When his pupil also sees it, the research, the argument, the proof is finished.

The analogy is a rough one, but I am sure that it is not altogether misleading. If we were to push it to its extreme we should be led to a rather paradoxical conclusion; that we can, in the last analysis, do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of pupils. This is plainly not the whole truth, but there is a good deal in it. The image gives us a genuine approximation to the processes of mathematical pedagogy on the one hand and of mathematical discovery on the other; it is only the very unsophisticated outsider who imagines that mathematicians make discoveries by turning the handle of some miraculous machine. Finally the image gives us at any rate a crude picture of Hilbert's metamathematical proof, the sort of proof which is a ground for its conclusion and whose object is to convince ."

(G.H. Hardy)

"[T]o suggest that the normal processes of scholarship work well on the whole and in the long run is in no way contradictory to the view that the processes of selection and sifting which are essential to the scholarly process are filled with error and sometimes prejudice."

(Kenneth Arrow)

"Mathematical proofs like diamonds should be hard and clear, and will be touched with nothing but strict reasoning."

(John Locke)


"In his review of Winchester's previous book, The Map That Changed the World (3), Stephen Jay Gould wrote:

I don't mean to sound like an academic sourpuss, but I just don't understand the priorities of publishers who spare no expense to produce an elegantly illustrated and beautifully designed book and then permit the text to wallow in simple, straight-out factual errors, all easily corrected for the minimal cost of one scrutiny of the galleys by a reader with professional expertise... (4)

With Krakatoa, the publisher clearly spared considerable expense, and this new book also wallows in errors. Perhaps, given our popular culture's appetite for sensationalized disasters, a modern publisher would rather not see all those pesky details corrected."

(Tom Simkin and Richard S. Fiske)

"Again, I have to repeat the dictum of Harvard's president, Larry Summers: "In the history of the world, no one has ever washed a rented car." Most Iraqis still feel they are renting their own country --- first from Saddam and now from us. They have to be given ownership. If the Bush team is ready to put in the time, energy and money to make that happen --- great. But if not, it's going to have to make the necessary compromises to bring in the U.N. and the international community to help. "

(Thomas Freedman)

"The paomnnehil pweor of the hmuan mnid. Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe."

" "The great tragedy of science," the biologist Thomas Henry Huxley lamented, is "the slaying of a beautiful hypothesis by an ugly fact." By that standard, political science is going through a homely phase. It's not even three weeks since the Iowa caucuses, and voters have wiped out several decades' worth of conventional wisdom about presidential primaries."

Some columnist in February 2004.

"By 1948, the Marxist-Leninist ideas about the proletariat and its political capacity seemed more and more to me to disagree with reality ... I pondered my doubts, and for several years the study of mathematics was all that allowed me to preserve my inner equilibrium. Bolshevik ideology was, for me, in ruins. I had to build another life."

(Jean Van Heijenoort, 1913-1986)

"Numbers are not the only thing that computers are good at processing. Indeed, only a cursory familiarity with fractal geometry is needed to see that computers are good at creating and manipulating visual representations of data. There is a story told of the mathematician Claude Chevalley, who, as a true Bourbaki, was extremely opposed to the use of images in geometric reasoning. He is said to have been giving a very abstract and algebraic lecture when he got stuck. After a moment of pondering, he turned to the blackboard, and, trying to hide what he was doing, drew a little diagram, looked at it for a moment, then quickly erased it, and turned back to the audience and proceeded with the lecture. It is perhaps an apocryphal story, but it illustrates the necessary role of images and diagrams in mathematical reasoning-even for the most diehard anti-imagers. The computer offers those less expert, and less stubborn than Chevalley, access to the kinds of images that could only be imagined in the heads of the most gifted mathematicians, images that can be coloured, moved and otherwise manipulated in all sorts of ways. "

(Nathalie Sinclair, 2004)


Greenwood: It was quite a popular course. There used to be a saying that if Wedderburn says something is true, accept it but don't try to prove it because you won't be able to. If Eisenhart says something is true, get out his book and by using cross references 20 to 30 times you can work up a proof for it. And if Lefschetz says something is true ...

Tucker: It is probably false.

Greenwood: ... my apologies to Professor Lefschetz, look for a proof and for a counterexample at the same time.


Aspray: Since you both had close associations with Church, I was wondering if you could tell me something about him. What was his wider mathematical training and interests? What were his research habits? I understood he kept rather unusual working hours. How was he as a lecturer? As a thesis director?

Rosser: In his lectures he was painstakingly careful. There was a story that went the rounds. If Church said it's obvious, then everybody saw it a half hour ago. If Weyl says it's obvious, von Neumann can prove it. If Lefschetz says it's obvious, it's false.


Excerpts from Google's filing with the SEC

-- Google is not a conventional company. We do not intend to become one.
-- A management team distracted by a series of short-term targets is as pointless as a dieter stepping on the scale every half hour.
-- We will not hesitate to place major bets on promising new opportunities.
-- For example, we would fund projects that have a 10 percent chance of earning a billion dollars over the long term. Do not be surprised if we place smaller bets in areas that seem very speculative or even strange.
-- Our employees, who have named themselves Googlers, are everything.
-- We provide many unusual benefits for our employees, including meals free of charge, doctors and washing machines.
-- Don't be evil. We believe strongly that in the long term, we will be better served
-- as shareholders and in all other ways -- by a company that does good things for the world even if we forgo some short-term gains."

(John Shinal)


"The discussion was going beautifully until I discovered that he was talking about the Peloponnesian War while I was discussing WW II."

(Nicholas Katzenbach)


"A coded message, for example, might represent gibberish to one person and valuable information to another. Consider the number 14159265... Depending on your prior knowledge, or lack thereof, it is either a meaningless random sequence of digits, or else the fractional part of pi, an important piece of scientific information."

(Hans Christian von Baeyer)


The metaphor of shooting naturally became a familiar one in writings about his photography. Cartier-Bresson himself used it often: "approach tenderly, gently . . . on tiptoe even if the subject is a still life," he said. "A velvet hand, a hawk's eye these we should all have." He also said: "I adore shooting photographs. It's like being a hunter. But some hunters are vegetarians which is my relationship to photography." And later, explaining his dislike of the automatic camera, he said, "It's like shooting partridges with a machine gun."

With a Brownie that he had received as a gift, he began to snap photographs in Africa, but they ended up ruined. Contracting blackwater fever, he nearly died. The way he told the story, a witch doctor got him out of a coma. While still feverish, he wrote a postcard to his grandfather asking that he be buried in Normandy, at the edge of the Eawy forest, with Debussy's string quartet to be played at the funeral. An uncle wrote back: "Your grandfather finds all that too expensive. It would be preferable that you return first."

(New York Times)

Despite the narrative force that the concept of entropy appears to evoke in everyday writing, in scientific writing entropy remains a thermodynamic quantity and a mathematical formula that numerically quantifies disorder. When the American scientist Claude Shannon found that the mathematical formula of Boltzmann defined a useful quantity in information theory, he hesitated to name this newly discovered quantity entropy because of its philosophical baggage. The mathematician John Von Neumann encouraged Shannon to go ahead with the name entropy, however, since "no one knows what entropy is, so in a debate you will always have the advantage.


"The connections between chemical science and technology in the new synthetic-dye industry that began to develop after William Henry Perkin's synthesis of mauve in 1856 are complex. But one contribution of the science of carbon chemistry to the synthetic-dye industry was clearly crucial: chemical theory embodied in chemical formulae. Linear chemical formulae, like H2O for water, had been introduced by the Swedish chemist Jacob Berzelius (1779-1848) in 1813. They presented the composition of chemical compounds according to a theory of definite quantitative units or portions of substances. With atomism, this new quantitative theory shared the assumption of discontinuous composition of substances. But the algebraic form of Berzelian formulae avoided narrow definitions in terms of "atoms," which many chemists rejected as metaphysical entities. Letters, numbers, and additivity were sufficient to represent quantitative units of elements and discontinuous composition of compounds. Different arrangements of letters visually showed how units of elements were combined with each other. The structural formulae of the 1860s displayed chemical and spatial arrangements in an even more pictorial form.

Beginning in the late 1820s, chemists used chemical formulae as tools on paper to model the constitution of organic compounds. Using chemical formulae as paper tools, chemists reduced the complexity in the "jungle of organic chemistry" (F. Wehler). Chemical formulae enabled them, for example, to order organic chemical reactions by formula equations that distinguished between a main reaction, side reactions, and successive reactions.

In the 1860s, chemical formulae had become an emblem not only of academic chemistry but also of the synthetic-dye industry. Quantitative chemical theory was implemented in the new alliance between carbon chemistry and the synthetic-dye industry in the form of paper tools that were subordinated to chemists' experimental and technological goals (6). Compared with the connections between academic chemistry and the arts and crafts in the 18th

(Ursala Klein)

"Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged. Such fundamental notions as reality, space, time, and causality--notions found at the core of the scientific enterprise--all rely on particular metaphysical assumptions about the world."

(Christof Koch)

"And it is one of the ironies of this entire field that were you to write a history of ideas in the whole of DNA, simply from the documented information as it exists in the literature - that is, a kind of Hegelian history of ideas - you would certainly say that Watson and Crick depended on Von Neumann, because von Neumann essentially tells you how it's done. But of course no one knew anything about the other. It's a great paradox to me that this connection was not seen. Of course, all this leads to a real distrust about what historians of science say, especially those of the history of ideas."

(Sidney Brenner)

"Sometime in the 1970s Paul Turan spent part of a summer in Edmonton. I wanted to meet him so went there. He was a few days late so I had arrived a couple of days earlier. A group went to the airport to meet him, and stopped at a coffee shop before going to the university. It was very hot so I offered to stay in the car and keep the windows down. I said I did not drink coffee. Turan then told the joke about mathematicians being machines which turn coffee into theorems, and then added: "You prove good theorems. Just think how much better they would be if you drank coffee". I have heard the statement attributed to Renyi by more than one Hungarian, but this was somewhat later. Turan just stated it."

(Richard Askey)

Elsewhere Kronecker said "In mathematics, I recognize true scientific value only in concrete mathematical truths, or to put it more pointedly, only in mathematical formulas." ... I would rather say "computations" than "formulas", but my view is essentially the same.

(Harold M. Edwards)


"One little know piece of Mayr's history, Rubinoff said, was his service on a National Research Council committee, which formed in the late 1960's, to examine the consequences of building a sea-level canal through the Isthmus of Panama. Mayr was accused by one of the committee engineers of "having an elastic collision with reality." But, said Rubinoff, if it weren't for Mayr's tenacity, the proposed canal would have destroyed 3 million years of isolated evolution.

Frank Sulloway, author and former Mayr student, said that his career was influenced by meeting two minds: Darwin's and Mayr's. "The minute you meet one, you sooner or later meet the other," he said.

Both were famously persistent. Quoting 19th-century novelist Anthony Trollope, "Darwin once wrote: "It's dogged as does it... I have often and often thought that this is the motto for every scientific worker." "The only person I know who's about as dogged is Ernst Mayr," said Sulloway."

(The Scientist)


"Dear Friend Wollstein, By the time you receive these lines, we three will have solved the problem in another way - in the way which you have continually attempted to dissuade us. ... What has been done against the Jews in recent months arouses well-founded anxiety that we will no longer be allowed to experience a bearable situation. ... Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much). Forgive us also our desertion! We wish you and all our friends will experience better times.

Yours faithfully, Felix Hausdorff"

(Felix Hausdorff)


About H.E. Smith: In the book "Elementary Number Theory" (Chelsea, New York, 1958. An English translation of vol. 1 of the German book Vorlesungen ueber Zahlentheorie), p.31, the author, Edmund Landau, mentions the question whether the infinite series $sum mu(n)/n$ converges (TEX notation; mu is the Moebius function). After giving a reference to the answer in Part 7 of the same V.u.Z, and without saying what the answer is, Landau writes:

"Gordan used to say something to the effect that 'Number Theory is useful since one can, after all, use it to get a doctorate with.' n 1899 I received my doctorate by answering this question."

He was a brilliant talker and wit. Working in the purely speculative region of the theory of numbers, it was perhaps natural that he should take an anti-utilitarian view of mathematical science, and that he should express it in exaggerated terms as a defiance to the grossly utilitarian views then popular. It is reported that once in a lecture after explaining a new solution of an old problem he said, It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstances can it be of the smallest possible utility." I believe that it was at a banquet of the Red Lions that he proposed the toast "Pure mathematics; may it never be of any use to anyone."

This is taken from Alexander Macfarlane, _Ten British Mathematicians of the Nineteenth Century_ (1916), 63-4. The text is that of lectures he gave in 1903-1904, and the editors in their introduction say that "His personal acquaintance with British mathematicians of the nineteenth century imparts to many of these lectures a personal touch which greatly adds to their general interest."

A copy of the book is available on the Project Gutenberg website:


"By its own count, Wal-Mart has 460 terabytes of data stored on Teradata mainframes, made by NCR, at its Bentonville headquarters.

To put that in perspective, the Internet has less than half as much data, according to experts."

(Constance Hays)


Just what does it mean to prove something?

Although the Annals will publish Dr Hales's paper, Peter Annals, an editor of the Annals, whose own work does not involve the use of computers, says that the paper will be accompanied by an unusual disclaimer, stating that the computer programs accompanying the paper have not undergone peer review. There is a simple reason for that, Dr Sarnak says-it is impossible to find peers who are willing to review the computer code. However, there is a flip-side to the disclaimer as well-Dr Sarnak says that the editors of the Annals expect to receive, and publish, more papers of this type-for things, he believes, will change over the next 20-50 years. Dr Sarnak points out that maths may become "a bit like experimental physics" where certain results are taken on trust, and independent duplication of experiments replaces examination of a colleague's paper.

Why should the non-mathematician care about things of this nature? The foremost reason is that mathematics is beautiful, even if it is, sadly, more inaccessible than other forms of art. The second is that it is useful, and that its utility depends in part on its certainty, and that that certainty cannot come without a notion of proof. Dr Gonthier, for instance, and his sponsors at Microsoft, hope that the techniques he and his colleagues have developed to formally prove mathematical theorems can be used to "prove" that a computer program is free of bugs-and that would certainly be a useful proposition in today's software society if it does, indeed, turn out to be true.


Writers we admire and re-read are absorbed into the fine print of our consciousness, into the white noise of our thoughts, and in this sense, they can never die. Saul Bellow started publishing in the 1940's, and his work spreads across the century he helped to define. He also redefined the novel, broadened it, liberated it, made it warm with human sense and wit and grand purpose. Henry James once proposed an obvious but helpful truth: "the deepest quality of a work of art will always be the quality of the mind of the producer." We are saying farewell to a mind of unrivalled quality. He opened our universe a little more. We owe him everything.

(Ian McEwan)

Why should I refuse a good dinner simply because I don't understand the digestive processes involved?

(Oliver Heaviside)


Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so ubersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes.
[Mathematicians are a kind of Frenchman: whatever you say to them they translate into their own language, and right away it is something entirely different.]

(Johann Wolfgang von Goethe)


Ask Dr. Edward Witten of the Institute for Advanced Study in Princeton, New Jersey what he does all day, and it's difficult to get a straight answer.

"There isn't a clear task," Witten told CNN. "If you are a researcher you are trying to figure out what the question is as well as what the answer is.

"You want to find the question that is sufficiently easy that you might be able to answer it, and sufficiently hard that the answer is interesting. You spend a lot of time thinking and you spend a lot of time floundering around." "

(Ed Witten)


"I don't think biochemists are going to be the least bit interested in what philosophers think about genes," Jones replies. "As I've said in the past, philosophy is to science as pornography is to sex: It's cheaper, easier, and some people prefer it.", Moving swiftly along, Jones and Stangroom ponder racial differences in IQ, the debate over genetically modified crops, health insurance, and the future of the human race.

In the next chapter, Harvard evolutionary psychologist Steven Pinker is probed on "Evolutionary Psychology and the Blank Slate." The conversation moves from the structure of the brain to adaptive explanations for music, creationism, and beyond. Stangroom asks Pinker about the accusations that biological explanations of behavior are determinist and reduce human beings to the status of automatons. " "Most people have no idea what they mean when they level the accusation of determinism," "Pinker answers. "It's a nonspecific "boo" word, intended to make something seem bad without any content."

(Jeremy Stangroom's interviews)

Harald Bohr is reported to have remarked "Most analysts spend half their time hunting through the literature for inequalities they want to use, but cannot prove."

(D.J.H. Garling)

"How ridiculous to make evolution the enemy of God. What could be more elegant, more simple, more brilliant, more economical, more creative, indeed more divine than a planet with millions of life forms, distinct and yet interactive, all ultimately derived from accumulated variations in a single double-stranded molecule, pliable and fecund enough to give us mollusks and mice, Newton and Einstein? Even if it did give us the Kansas State Board of Education, too."

(Charles Krauthammer)

"The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics. "

(Johannes Kepler)

"[Maxwell asked whether he would like to see an experimental demonstration of conical refraction] No. I have been teaching it all my life, and I do not want to have my ideas upset."

(Isaac Todhunter)


"Rigour is the affair of philosophy, not of mathematics."

(Bonaventura Cavalieri)


"How dreadful are the curses which Mohammedanism lays on its votaries! Besides the fanatical frenzy, which is as dangerous in a man as hydrophobia in a dog, there is this fearful fatalistic apathy. The effects are apparent in many countries. Improvident habits, slovenly systems of agriculture, sluggish methods of commerce, and insecurity of property exist wherever the followers of the Prophet rule or live. A degraded sensualism deprives this life of its grace and refinement; the next of its dignity and sanctity. The fact that in Mohammedan law every woman must belong to some man as his absolute property, either as a child, a wife, or a concubine, must delay the final extinction of slavery until the faith of Islam has ceased to be a great power among men.

Individual Moslems may show splendid qualities, but the influence of the religion paralyses the social development of those who follow it. No stronger retrograde force exists in the world. Far from being moribund, Mohammedanism is a militant and proselytizing faith. It has already spread throughout Central Africa, raising fearless warriors at every step; and were it not that Christianity is sheltered in the strong arms of science, the science against which it had vainly struggled, the civilization of modern Europe might fall, as fell the civilization of ancient Rome." "

(Winston Churchill)


"How extremely stupid not to have thought of that!"

(T.H. Huxley)

"All truths are easy to understand once they are discovered; the point is to discover them."

(Galileo Galilei, 1564-1642)

Math Will Rock Your World. A generation ago, quants turned finance upside down. Now they're mapping out ad campaigns and building new businesses from mountains of personal data.

"These slices of our lives now sit in databases, many of them in the public domain. From a business point of view, they're just begging to be analyzed. But even with the most powerful computers and abundant, cheap storage, companies can't sort out their swelling oceans of data, much less build businesses on them, without enlisting skilled mathematicians and computer scientists. The rise of mathematics is heating up the job market for luminary quants, especially at the Internet powerhouses where new math grads land with six-figure salaries and rich stock deals. Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology, says: "All of my students have standing offers at Yahoo! and Google." Top mathematicians are becoming a new global elite. It's a force of barely 5,000, by some guesstimates, but every bit as powerful as the armies of Harvard University MBAs who shook up corner suites a generation ago."

"The formulas move in advance of thought, while the intuition often lags behind; in the oft-quoted words of d'Alembert, "L'algebre est genereuse, elle donne souvent plus qu'on lui demande.""

(Edward Kasner, 1905)

"Science is a differential equation. Religion is a boundary condition."

(Alan Turing, 1912 - 1954)

'Thirst for knowledge' may be opium craving

Neuroscientists have proposed a simple explanation for the pleasure of grasping a new concept: The brain is getting its fix. The "click" of comprehension triggers a biochemical cascade that rewards the brain with a shot of natural opium-like substances, said Irving Biederman of the University of Southern California. He presents his theory in an invited article in the latest issue of American Scientist.

"While you're trying to understand a difficult theorem, it's not fun," said Biederman, professor of neuroscience in the USC College of Letters, Arts and Sciences.

"But once you get it, you just feel fabulous."

The brain's craving for a fix motivates humans to maximize the rate at which they absorb knowledge, he said.

I think we're exquisitely tuned to this as if we're junkies, second by second."

(Irving Biederman, 2006)

"We [Kaplansky and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury."

(Irving Kaplansky, 1917-2006)

"The war became more and more bitter. The Dominican Father Caccini preached a sermon from the text, "Ye men of Galilee, why stand ye gazing up into heaven?" and this wretched pun upon the great astronomer's name ushered in sharper weapons; for, before Caccini ended, he insisted that "geometry is of the devil," and that "mathematicians should be banished as the authors of all heresies." The Church authorities gave Caccini promotion."

"Equations are more important to me, because politics is for the present, but an equation is something for eternity."

(Albert Einstein)

  • "Never Ascribe to malice that which is adequately explained by incompetence." (Napoleon Bonaparte?)
  • "Misunderstandings and neglect occasion more mischief in the world than even malice and wickedness. At all events, the two latter are of less frequent occurrence." (Goethe in The Sorrows of Young Werther)
  • "You have attributed conditions to villainy that simply result from stupidity". (Robert Heinlein in the Logic of Empire (1941). He calls this the "devil theory" of sociology.
  • "Many journalists have fallen for the conspiracy theory of government. I do assure you that they would produce more accurate work if they adhered to the cock-up theory." (Bernard Ingam, 1932-, who was Thatcher's press secretary.)

I'm here to help. (With the Poincare conjecture. As for the family, you're on your own.) Poincare conjectured that three-dimensional shapes that share certain easy-to-check properties with spheres actually are spheres. What are these properties? My fellow geometer Christina Sormani describes the setup as follows: "The Poincare Conjecture says, Hey, you've got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and [Columbia University's Richard] Hamilton proved this fact by heating the blob up, making it sing, stretching it like hot mozzarella, and chopping it into a million pieces. In short, the alien ain't no bagel you can swing around with a string through his hole."

(Jordan Ellenberg)


Thank you for your reply. I certainly understand what it means to recall something and have the trail disappear!

The reason I inquired, as in my Tobias conversations with George and his comments re how Tobias influenced him by "feeding" him thousands of geometry problems to solve (see More Mathematical People, Albers et al. (eds.) , Harcourt Brace Jovanovich, 1990), he never indicated that he (George) had any input to Tobias' work. In fact, it went the other way in one important instance. As you may not have encountered it, I cite the following. George wrote in his paper "Reminiscences about the origins of linear programming," 1, 2, Operations Research Letters, April 1982 (p. 47):

"The term Dual is not new. But surprisingly the term Primal, introduced around 1954, is. It came about this way. W. Orchard-Hays, who is responsible for the first commercial grade L.P. software, said to me at RAND one day around 1954: 'We need a word that stands for the original problem of which this is the dual.' I, in turn, asked my father, Tobias Dantzig, mathematician and author, well known for his books popularizing the history of mathematics. He knew his Greek and Latin. Whenever I tried to bring up the subject of linear programming, Toby (as he was affectionately known) became bored and yawned. But on this occasion he did give the matter some thought and several days later suggested Primal as the natural antonym since both primal and dual derive from the Latin. It was Toby's one and only contribution to linear programming: his sole contribution unless, of course, you want to count the training he gave me in classical mathematics or his part in my conception."

A lovely story. I heard George recount this a few times and, when he came to the "conception" part, he always had a twinkle in his eyes.

(Saul Gass)

"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity."

(Mary Somerville, 1780-1872)

Today's outcome may end the interest in future chess matches between human champions and computers, according to Monty Newborn, a professor of computer science at McGill University in Montreal. Professor Newborn, who helped organize the match between Mr. Kasparov and Deep Blue, said of future matches: "I don't know what one could get out of it at this point. The science is done."

Mr. Newborn said that the development of chess computers had been useful.

"If you look back 50 years, that was one thing we thought they couldn't do," he said. "It is one little step, that's all, in the most exciting problem of what can't computers do that we can do."

Speculating about where research might go next, Mr. Newborn said, "If you are interested in programming computers so that they compete in games, the two interesting ones are poker and go. That is where the action is."

(Dylan Loeb McClain)

"Je n'ai fait celle-ci plus longue que parceque je n'ai pas eu le loisir de la faire plus courte.(I have only made this letter rather long because I have not had time to make it shorter.)"

(Blaise Pascal)


Of course, identifying with one's captors is nothing new. Perhaps the most famous example is the 1973 Norrmalmstorg bank robbery in Stockholm. During the five days they were held hostage, the bank employees came to sympathize with the robbers and defended them against the police.

(Globe and Mail, January 2007)

"Bulls don't run reviews. Bulls of 25 don't marry old women of 55 and expect to be invited to dinner. Bulls do not get you cited as co-respondent in Society divorce trials. Bulls don't borrow money. Bulls are edible after they have been killed."

(Ernest Hemingway, 1925)

Memorable Ends

1. Here lies Ezekial Aikle.
Aged 102.
The good die young.

2. Here lies an Atheist.
All dressed up.
And no place to go.

3. A tomb now suffices him for whom the world was not enough.
(Alexander the Great)

4. The body of Benjamin Franklin, printer (like the cover of an old book, its contents worn out, and stript of its lettering and gilding) lies here, food for worms. Yet the work itself shall not be lost, for it will, as he believed appear once more. In a new and more beautiful edition, corrected and amended by its Author.
(Benjamin Franklin)

5. She did it the hard way.
(Bette Davis)

6. The best is yet to come.
(Frank Sinatra)

7. That's all folks!
(Mel Blanc - voice of Bugs Bunny)

8. I told you I was ill.
(Spike Milligan)

9. Ope'd my eyes.
Took a peep.
Didn't like it.
Went back to sleep.

10. Called back.
(Emily Dickinson)



And Bloomberg can also flash a hard-edged candor. At the breakfast with business leaders, he scoffed at a question about whether the schools' emphasis on math and reading testing was taking away from the "richness" of education in subjects such as art and music. "Well, I don't know about the 'richness of education,' " he said, his voice thick with sarcasm. "In my other life, I own a business, and I can tell you, being able to do 2-plus-2 is a lot more important than a lot of other things."


Giuliani seized on it to bolster his campaign's theme, saying, "Today's arrests remind us that we are at war." Bloomberg offered a noticeably milder response: "You can't sit there and worry about everything. You have a much greater danger of being hit by lightning than being struck by a terrorist. Get a life."

(Michael Bloomberg)

"This computer, although assigned to me, was being used on board the International Space Station. I was informed that it was tossed overboard to be burned up in the atmosphere when it failed."


"Rick Wilson, a Republican consultant based in Florida who has worked for Rudolph W. Giuliani, the former New York mayor, and Katherine Harris, the former Florida congresswoman, among others, said that most states have their own expressions for the circumstances under which open secrets stay secret. In Florida, he said, it's the 'Three County Rule': no girlfriends within three counties of your home district. In New York, it's the 'Bear Mountain Compact': nobody talks about what politicians do with their free time once they've crossed the Bear Mountain Bridge en route to Albany from points south."

(Abby Goodnough)

Easy as 1, 2, 3 -- Except for The Maybes.
Why No One Can Count On Those Delegates

"The lesson is not to trust the numbers too much. If math were a guy, math would be a pompous guy, the sort who's absolutely always sure about everything and never apologizes when he's wrong. And the fact is, math isn't actually ever wrong, not technically. Math is a perfectly logical and intelligent guy. He just sometimes makes the wrong assumptions. "

(Libby Copeland)

"the problem of course presents itself already when you are a student and I was thinking about the problem on and off, but the situation was more interesting than that. The great authority in those days was Zygmund and he was completely convinced that what one should produce was not a proof but a counter-example. When I was a young student in the United States, I met Zygmund and I had an idea how to produce some very complicated functions for a counter-example and Zygmund encouraged me very much to do so. I was thinking about it for about 15 years on and off, on how to make these counter-examples work and the interesting thing that happened was that I realised why there should be a counter-example and how you should produce it. I thought I really understood what was the background and then to my amazement I could prove that this "correct" counter-example couldn't exist and I suddenly realised that what you should try to do was the opposite, you should try to prove what was not fashionable, namely to prove convergence. The most important aspect in solving a mathematical problem is the conviction of what is the true result. Then it took 2 or 3 years using the techniques that had been developed during the past 20 years or so. .. "

(Lennart Carleson, 1966)


"In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. "You mean an actual number?" Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, "All right, take 57."

But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. "He doesn't think concretely." Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. "He really never worked on examples," Mumford observed. "I only understand things through examples and then gradually make them more abstract. I don't think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It's just very strange. That's the way his mind worked.""

(Allyn Jackson, 2004)


"The letter was written in German in 1954 to philosopher Eric Gutkind. It is to be auctioned in London, England, on Thursday by Bloomsbury Auctions, and is expected to fetch between $12,000 and $16,000 US. Einstein writes "the word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honourable but still primitive legends which are nevertheless pretty childish.""

From a letter by Einstein auctioned in May 2008 as described on CBC.


"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others."

(Carl Friedrich Gauss, 1777-1855)

"The difficulty lies, not in the new ideas, but in escaping the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds"

(John Maynard Keynes, 1883-1946)


"He is like the fox, who effaces his tracks in the sand with his tail."

(Niels Abel, 1802-1829)


"We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work."

(Richard Feynman, 1918-1988)

"Gauss could be a stern, demanding individual, and it is reported that this resulted in friction with two of his sons that caused them to leave Germany and come to the United States; they settled in the midwest and have descendants throughout the plains states. I was living in Greeley, Colorado, when I read this in 1972; looking in the phone book, I found a listing for a Charlotte Gauss living two blocks from my apartment! After considerable internal debate, I called her and found that she was indeed related to Gauss.

My wife, Paulette, and I visited several times with Charlotte and her sister Helen; they were bright, alert, and charming young women, ages 93 and 94, respectively. Their father, Gauss' grandson, had been a Methodist missionary to the region, and he had felt it unseemly to take pride in his famous ancestor (maybe there were some remnants of his father's feelings on leaving Germany); they were nevertheless happy to talk Gauss and their family. They showed us a baby spoon which their father had made out of a gold medal awarded to Gauss, some family papers, and a short biography of Gauss written by an aunt. I vividly remember Helen describing the reaction of one of her math teachers when he discovered he had a real, live, Gauss in his class."

(Jim Kuzmanovichi)

"Forget the 'precautionary principle.' The amount of risk to which the public should be exposed is greater than zero."

(Michael Krauss)

"Knowing things is very 20th century. You just need to be able to find things."

(Danny Hillis)

"McCain would also be wise to study the etymology of his "maverick" image. The term entered the political lexicon because of one Samuel Augustus Maverick, a land owner, legislator, and former mayor of San Antonio who was the grandfather of Maury Maverick, the famous New Dealer who described democracy as "liberty plus groceries." Samuel Maverick stubbornly refused to brand his calves and let them roam wherever they wanted. Other ranchers who encountered these free-spirited yearlings referred to them as "mavericks." Journalists later employed the term to describe politicians who bucked the party line and struck an independent course."

(John Podesta and John Halpin)

"Of course I believe in luck. How otherwise to explain the success of those you dislike?"

(Jean Cocteau)


His ambition to write may have prompted an exchange with T. S. Eliot, then in his late 50s, on the day they met in 1946, when Mr. Giroux, "just past 30," as he recalled the moment in "The Oxford Book of Literary Anecdotes," was an editor at Harcourt, Brace. "His most memorable remark of the day," Mr. Giroux said, "occurred when I asked him if he agreed with the definition that most editors are failed writers, and he replied, 'Perhaps, but so are most writers.'"

(T. S. Elliot)


" For those who had realized big losses or gains, the mania redistributed wealth. The largest honest fortune was made by Thomas Guy, a stationer turned philanthropist, who owned 54,000 of South Sea stock in April 1720 and sold it over the following six weeks for 234,000. Sir Isaac Newton, scientist, master of the mint, and a certifiably rational man, fared less well. He sold his 7,000 of stock in April for a profit of 100 percent. But something induced him to reenter the market at the top, and he lost 20,000. "I can calculate the motions of the heavenly bodies," he said, "but not the madness of people."

(Isaac Newton)


When asked about the interruptions to her career caused by three marriages and three divorces, she shrugs. "You can like 'em," she jokes about men, "but it doesn't mean you have to sample every single one."

Toward the end of the writing process, Proulx will often work 16 hours a day. "I love shaping things, pruning out the unnecessary, shaping unshapely sentences. After things are published I never read them again. I never, ever read reviews." (In the case of "Fine Just the Way It Is," that's just as well, since the reviews have been mixed.).

(Annie Proulx)

"Genetics by second nature Growing up in Arlington, Virginia, Buckler had unlimited access to a personal computer, on which he designed his own games. To him, genetics is basically life's equivalent of computer programming. "There are not many rules: You get to recombine and to mutate, but you can make incredibly complex things." Buckler laughs, giving his boyish smile: "And it's more rewarding to do genetics than programming."."

(Edward Buckler)


"Every once in while during a crisis or history-altering event, you run across a quote or an observation that sort of summarizes events on the ground, in a nutshell. Former U.S. Federal Reserve Chairman Paul Volcker articulated one such observation during a recent chat he had with PBS' Charlie Rose. "It seems to me what our nation needs is more civil engineers and electrical engineers and fewer financial engineers," Volker said."

(Joseph Lazaro)

EDITOR'S ENDNOTES "Jeffrey Lagarias (University of Michigan), Colin Mallows (Avaya Labs), and Allan Wilks (AT&T Labs-Research) submitted the following correction to their article "Beyond the Descartes Circle Theorem," which appeared in the April, 2002 issue: We have an historical and a mathematical correction. First, it has been brought to our attention that Frederick Soddy, who won a Nobel Prize in Chemistry (1921) for the discovery of isotopes, did not receive a knighthood (in the English honours list). Davies [loc. cit.] quotes a letter from his nephew, Dr. Kenneth Soddy: "He suffered a good deal of what might be termed persecution during the first World War . . . It was the recollection of these troubles that made him decline Honours later on." Besides his scientific work, Soddy loved mathematics and worked on it as a hobby. He also wrote several books setting forth unpopular economic views. Our awarding him a spurious knighthood is an example of the "Matthew effect" the phenomenon by which famous people become more famous, and less famous people become less famous. Unfortunately this error has propagated to Mumford et al. [Indra's Pearls]"

(Dan Velleman)

"Considering that past, perhaps the most incisive comment on Mr. Obama's election actually came long ago. The Rev. Dr. Martin Luther King Jr. addressed the Hawaii Legislature in 1959, two years before Mr. Obama was born in Honolulu, and declared that the civil rights movement aimed not just to free blacks but "to free the soul of America."

Mr. King ended his Hawaii speech by quoting a prayer from a preacher who had once been a slave, and it's an apt description of the idea of America today: "Lord, we ain't what we want to be; we ain't what we ought to be; we ain't what we gonna be, but, thank God, we ain't what we was."

(Nicholas Kristof)

"The collapse of communism pushed China to the center and [America] to the extreme," said Ben Simpfendorfer, chief China economist at Royal Bank of Scotland.

The Madoff affair is the cherry on top of a national breakdown in financial propriety, regulations and common sense. Which is why we don't just need a financial bailout; we need an ethical bailout. We need to re-establish the core balance between our markets, ethics and regulations. I don't want to kill the animal spirits that necessarily drive capitalism - but I don't want to be eaten by them either."

(Thomas Friedman)


"The orbit of any one planet depends on the combined motions of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect."

(Isaac Newton, 1687)


About TierneyLab

"John Tierney always wanted to be a scientist but went into journalism because its peer-review process was a great deal easier to sneak through. Now a columnist for the Science Times section, Tierney previously wrote columns for the Op-Ed page, the Metro section and the Times Magazine. Before that he covered science for magazines like Discover, Hippocrates and Science 86.

With your help, he's using TierneyLab to check out new research and rethink conventional wisdom about science and society. The Lab's work is guided by two founding principles:

  1. Just because an idea appeals to a lot of people doesn't mean it's wrong.
  2. But that's a good working theory.

"I don't think of myself as having gone squishy. I think of myself as having grown sober. And my conservative critics? On them, I think the most apt verdict was delivered by Niccolo Macchiavelli, 500 years ago: "This is the tragedy of man. Circumstances change, and he does not."

(David Frum)

"The late Huw Wheldon of the BBC once described to me a series, made in the early days of radio, about celebrated exiles who had lived in London. At one stage, this had involved tracking down an ancient retiree who had toiled in the British Museums reading room during the Victorian epoch. Asked if he could remember a certain Karl Marx, the wheezing old pensioner at first came up empty. But when primed with different prompts about the once-diligent attendee (monopolizing the same seat number, always there between opening and closing time, heavily bearded, suffering from carbuncles, tending to lunch in the Museum Tavern, very much interested in works on political economy), he let the fount of memory be unsealed.Oh Mr. Marx, yes, to be sure. Gave us a lot of work e did, with all is calls for books and papers. His interviewers craned forward eagerly, to hear the man say: And then one day e just stopped coming. And you know whats a funny fing, sir? A pregnant pause. Nobodys ever eard of im since! This, clearly, was one of those stubborn proletarians for the alleviation of whose false consciousness Marx had labored in vain.

(Christopher Hitchens)

Here endeth the Seder.

This year our ceremony still contains some time for reflection, and some ability to remain on the same topic for more than a minute or two. But next year, may our ceremony be faster, divided into bite-sized chunks, and with each utterance no more than 140 characters. And so we say together,


(Carl Elkin, 2009)

"If you're worried that lions are eating too many zebras, you don't say to the lions, 'You're eating too many zebras.' You have to build a fence around the lions. They're not going to build it."

(Judge Richard A. Posner)

"John Maynard Keynes wrote that ideas, "both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else." This idea popularized by Professor Singer - that we have ethical obligations that transcend our species - is one whose time appears to have come."

(Nicholas Kristof)

"Maddox was always a believer in the possibilities of science, reluctant to accept that it could cause problems as well as solve them. When a wave of environmental pessimism swept over the Western world in the early 1970s he was one of the few to resist. He published a book, The Doomsday Syndrome (1972), denouncing the gloom as overdone.
after retiring as Nature Editor he wrote a scientific tour d'horizon, What Remains to be Discovered, asserting that far from approaching the end of its glorious run, science was only just beginning to tackle a multitude of new problems. The future offered an infinity of possibilities, most of them attractive."

""6. We have a patriotic duty to stand up against Washington taxes!" Just the opposite. We have a patriotic duty to pay taxes. As multi-billionaire Warren Buffett put it, "If you stick me down in the middle of Bangladesh or Peru or someplace, you'll find out how much this talent is going to product in the wrong kind of soil. I will be struggling thirty years later. President Teddy Roosevelt made the case in 1906 when he argued in favor of continuing the inheritance tax. "The man of great wealth owes a particular obligation to the state because he derives special advantages from the mere existence of government.""

(Robert Reich)

"The most complete unfolding of his later sense of things can probably be found in a quite astonishing book-length interview published by the magazine Research as the self-standing Research No 8/9 (1984) but he remained unfailingly eloquent until the end of his life, as the interviews assembled in Conversations (2005) attest. "At times", he said in 2004, "I look around the executive housing estates of the Thames Valley and feel that [a vicious and genuinely mindless neo-fascism] is already here, quietly waiting its day, and largely unknown to itself ... What is so disturbing about the 9/11 hijackers is that they had not spent the previous years squatting in the dust on some Afghan hillside ... These were highly educated engineers and architects who had spent years sitting around in shopping malls in Hamburg and London, drinking coffee and listening to the muzak."

(The Independent)

"A heavy warning used to be given [by lecturers] that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety. Some pictures, of course, are not rigorous, but I should say most are (and I use them whenever possible myself)."

(J. E. Littlewood, 1885-1977)

"Roberts's opinion drew an incredulous dissent from Stevens, who said that the Chief Justice's words reminded him of "Anatole France's observation" that the "majestic equality" of the law forbade "rich and poor alike to sleep under bridges, to beg in the streets, and to steal their bread.""

(Jeffrey Toobin)

Assorted Americans on Paris (collected in 2003)

"France has neither winter nor summer nor morals. Apart from these drawbacks it is a fine country. France has usually been governed by prostitutes." --Mark Twain.

"I would rather have a German division in front of me than a French one behind me."---General George S. Patton. "Going to war without France is like going deer hunting without your accordion."---Secretary of Defense Donald Rumsfeld.

"We can stand here like the French, or we can do something about it."---Marge Simpson.

"As far as I'm concerned, war always means failure."---Jacques Chirac, President of France.

"As far as France is concerned, you're right."---Rush Limbaugh.

"The only time France wants us to go to war is when the German Army is sitting in Paris sipping coffee."---Regis Philbin.

"The French are a smallish, monkey-looking bunch and not dressed any better, on average, than the citizens of Baltimore.
True, you can sit outside in Paris and drink little cups of coffee, but why this is more stylish than sitting inside and drinking large glasses of whisky I don't know."---P.J O'Rourke (1989).

"You know, the French remind me a little bit of an aging actress of the 1940s who was still trying to dine out on her looks but doesn't have the face for it."---John McCain, U.S. Senator from Arizona.

"You know why the French don't want to bomb Saddam Hussein? Because he hates America, he loves mistresses, and wears a beret. He is French, people."--- Conan O'Brien.

"I don't know why people are surprised that France won't help us get Saddam out of Iraq. After all, France wouldn't help us get Hitler out of France either."---Jay Leno.

"The last time the French asked for 'more proof' it came marching into Paris under a German flag."---David Letterman

"Only thing worse than a Frenchman is a Frenchman who lives in Canada."---Ted Nugent.

"The favorite bumper sticker in Washington D.C. right now is one that says, 'First Iraq, then France.'"---Tom Brokaw.

"What do you expect from a culture and a nation that exerted more of its national will fighting against Disney World and Big Macs than the Nazis?"---Dennis Miller.

"It is important to remember that the French have always been there when they needed us."---Alan Kent.

"They've taken their own precautions against al-Qa'ida. To prepare for an attack, each Frenchman is urged to keep duct tape, a white flag, and a three-day supply of mistresses in the house."---Argus Hamilton.

"Somebody was telling me about the French Army rifle that was being advertised on eBay the other day--the description was, 'Never shot. Dropped once.'"---Rep. Roy Blunt (MO).

"The French will only agree to go to war when we've proven we've found truffles in Iraq."---Dennis Miller.

Question: What did the mayor of Paris say to the German army as they entered the city in WWII?
Answer: Table for cent milles m'sieur?

"Do you know how many Frenchmen it takes to defend Paris? It's not known, it's never been tried."---Rep. R. Blount (MO).

"Do you know it only took Germany three days to conquer France in WWII? And that's because it was raining."--John Xereas, Manager, DC Improv.

"The AP and UPI reported that the French Government announced after the London bombings that it has raised its terror alert level from Run to Hide. The only two higher levels in France are Surrender and Collaborate."

"The rise in the alert level was precipitated by a recent fire which destroyed France's white flag factory, effectively disabling their military."

"French Ban Fireworks at Euro Disney (AP), Paris, March 5, 2003, The French government announced today that it is imposing a ban on the use of fireworks at Euro Disney. The decision comes the day after a nightly fireworks display at the park, located just 30 miles outside of Paris, caused the soldiers at a nearby French army garrison to surrender to a group of Czech tourists."

"During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school. I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra.This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense."

(Charles Darwin)

"He made little in public of his famous grandfather, Sigmund, who in 1938 followed other members of his family in migrating to Britain beginning in 1933, the year Hitler came to power - "refugees from the Nazis before the habit caught on," as Sir Clement, a secular Jew like many in his family, said many years later. He said he remembered his grandfather, who died in London in 1939, mostly as a faltering old man with oral cancer. "He was not, to me, famous," he said, but rather "a good grandfather in that he didn't forget my birthdays."

"[He] had a testy relationship with his older brother Lucian, the artist, now 86, who is regarded by many critics as one of the greatest Realists of the past century. Late in life Sir Clement told The Observer newspaper he had no interest in reconciling with his brother. "I'm not great at forgiving," he said."If I decide I don't like someone, that's it."

(John F. Burns)

Three "laws" of prediction

  • "When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
  • "The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
  • "Any sufficiently advanced technology is indistinguishable from magic."

(Arthur C. Clarke)

"It was because Hopkins's superiors in England had so little use for him...that they encouraged him to take a position as Professor of Greek and Examiner in Classics at the Royal University of Ireland, in Dublin. This prestigious-sounding post actually involved teaching elementary Latin and grading a truly staggering number of tests: six examinations times seven hundred and fifty students, according to Hopkins, for a total of forty-five hundred papers every year.

"Such was the life of Gerard Manley Hopkins, who fortuntely was able to write a little poetry amidst all that grading. His lament about this predicament has its own poetic quality:

"From the college, he issues a series of increasingly desperate cries for help. "The melancholy I have all my life been subject to has become in late years not indeed more intense in its fits but rather more distributed, constant, and crippling."

(Adam Kirsch)

Such reversals have led the veteran Silicon Valley technology forecaster Paul Saffo to proclaim: "never mistake a clear view for a short distance."

(John Markoff)

"These aspects of exploratory experimentation and wide instrumentation originate from the philosophy of (natural) science and have not been much developed in the context of experimental mathematics. However, I claim that e.g. the importance of wide instrumentation for an exploratory approach to experiments that includes concept formation also pertain to mathematics."

(Hendrik Sorenson)

The empirical spirit on which the Western democratic societies were founded is currently under attack, and not just by such traditional adversaries as religious fundamentalists and devotees of the occult. Serious scholars claim that there is no such thing as progress and assert that science is but a collection of opinions, as socially conditioned as the weathervane world of Paris couture.

(Timothy Ferris)

"My larger target is those contemporaries who-in repeated acts of wish-fulfillment-have appropriated conclusions from the philosophy of science and put them to work in aid of a variety of social cum political causes for which those conclusions are ill adapted. Feminists, religious apologists (including "creation scientists"), counterculturalists, neo-conservatives, and a host of other curious fellow-travelers have claimed to find crucial grist for their mills in, for instance, the avowed incommensurability and underdetermination of scientific theories. The displacement of the idea that facts and evidence matter by the idea that everything boils down to subjective interests and perspectives is -- second only to American political campaigns -- the most prominent and pernicious manifestation of anti-intellectualism in our time."

(Larry Laudan)

"So to summarise, according to the citation count, in order of descent, the authors are listening to themselves, dead philosophers, other specialists in semiotic work in mathematics education research, other mathematics education research researchers and then just occasionally to social scientists but almost never to other education researchers, including mathematics teacher education researchers, school teachers and teacher educators. The engagement with Peirce is being understood primarily through personal engagements with the original material rather than as a result of working through the filters of history, including those evidenced within mathematics education research reports in the immediate area. The reports, and the hierarchy of power relations implicit in them, marginalise links to education, policy implementation or the broader social sciences."

(Tony Brown)

Enter Don Tapscott, who is looking at the challenges the digital revolution poses to the fundamental aspects of the University.

"Universities are finally losing their monopoly on higher learning", he writes. "There is fundamental challenge to the foundational modus operandi of the University - the model of pedagogy. Specifically, there is a widening gap between the model of learning offered by many big universities and the natural way that young people who have grown up digital best learn."

The old-style lecture, with the professor standing at the podium in front of a large group of students, is still a fixture of university life on many campuses. It's a model that is teacher-focused, one-way, one-size-fits-all and the student is isolated in the learning process. Yet the students, who have grown up in an interactive digital world, learn differently. Schooled on Google and Wikipedia, they want to inquire, not rely on the professor for a detailed roadmap. They want an animated conversation, not a lecture. They want an interactive education, not a broadcast one that might have been perfectly fine for the Industrial Age, or even for boomers. These students are making new demands of universities, and if the universities try to ignore them, they will do so at their peril.

Contrary to Nicholas Carr's proposition that Google is making us stupid, Tapscott counters with the following:

My research suggests these critics are wrong. Growing up digital has changed the way their minds work in a manner that will help them handle the challenges of the digital age. They're used to multi-tasking, and have learned to handle the information overload. They expect a two-way conversation. What's more, growing up digital has encouraged this generation to be active and demanding enquirers. Rather than waiting for a trusted professor to tell them what's going on, they find out on their own on everything from Google to Wikipedia."

(Don Tapscott)

Britain pays its penny to poke a stick at Susan Boyle

In one of the few commentaries written by a man, Thomas Sutcliffe at The Independent draws uncomfortable parallels with the treatment of the insane in the 18th century.

"You could pay a penny to visit Bedlam (or Bethlehem mental hospital) and chortle at the deranged. You were even allowed to poke them with a stick if they failed to caper or roar in a satisfactory way


and can ease our disquiet about the ethics of such a spectacle by reassuring ourselves that none of these people are under restraint. They choose to take part and, in so choosing, sign up to the loss of dignity that often comes with participation ... The novelty with Susan Boyle was that she sang well enough to get through to the final, elevating her from temporary comic relief into a real person whose health and well-being might arouse our protective sympathy. I doubt very much that she is the first participant to have been left in a state of anxiety by the stress and exposure of such programs, though she is probably the first person whose reaction has had any kind of widespread media coverage.

(Araminta Wordsworth)


Borwein's Five Laws of Travel

  1. 1. Distance Independence. "It is an easy 15 minute walk" covers anything from 500 to 5000 metres.
  2. 2. Time Invariance. You will learn all the relevant details of how to negotiate your host city and the like adequately, exactly twenty-four hours before your departure. This is independent of the length of your stay.
  3. 3. Universal Expressions. Beware of such expressions as they have no fixed meaning. They include: "Free Internet," "Easy Access to Beach," and "Full Continental Breakfast."
  4. 4. Travel Agents. Never travel with a travel agent who has never travelled. They will rarely make reasonable bookings and will often make infeasible ones.
  5. 5a. First Law of Directions. Never rely on oral directions given in a foreign language. All consonants sound the same after one or two city blocks, while left and right are nearly always wrong and wronger.
  6. 5b. Second law of Directions. All directions written or oral given by a host will be missing one salient detail that is so obvious to any local as to be unrememberable. This applies to geography, computer access and much else.

(Jonathan Borwein)

"And yet since truth will sooner come out of error than from confusion."

(Francis Bacon, 1561-1626)

"In closing, I offer two examples from economics of what I hope to have said. Marx said that quantitative differences become qualitative ones, but a dialogue in Paris in the 1920's sums it up even more clearly:
FITZGERALD: The rich are different from us.
HEMINGWAY: Yes, they have more money."

(Phillip Anderson)

"Who ever became more intelligent," Godel answered, "by reading Voltaire?"

"Only fables," he said, "present the world as it should be and as if it had meaning."

(Kurt Godel)

"In all likelihood, our post-modern habit of viewing science as only a paradigm would evaporate if we developed appendicitis. We should look for a medically trained surgeon who knew what an appendix was, where it was, and how to cut it out without killing us. Likewise, we should be happy to debate the essentially fictive nature of, let us say, Newton's Laws of Gravity unless and until someone threatened to throw us out of a top-storey window. Then the law of gravity would seem very real indeed."

(A. N. Wilson)

"Philosophical theses may still be churned out about it,

but the question of nonconstructive existence proofs or the heinous sins committed with the axiom of choice arouses little interest in the average mathematician. Like Ol' Man River, mathematics just keeps rolling along and produces at an accelerating rate "200,000 mathematical theorems of the traditional handcrafted variety ... annually." Although sometimes proofs can be mistaken---sometimes spectacularly---and it is a matter of contention as to what exactly a "proof" is---there is absolutely no doubt that the bulk of this output is correct (though probably uninteresting) mathematics."

(Richard C. Brown)

A QUOTE BY ALBERT EINSTEIN When Paul Newman died, they said how great he was but they failed to mention he considered himself Jewish (born half-Jewish).

When Helen Suzman (who fought apartheid and helped Nelson Mandela) died recently, they said how great she was, but they failed to mention she was Jewish.

On the other side of the equation, when Ivan Boesky or Andrew Fastow or Bernie Madoff committed fraud, almost every article mentioned they were Jewish.

However, when Ken Lay, Jeff Skilling, Martha Stewart, Randy Cunningham, Gov. Edwards, Conrad Black, Senator Keating, Gov Ryan, and Gov Blagojevich messed up; no one reported what religion or denomination they were, because they were not Jewish.

All of this leads to a famous Einstein quote: In 1921, Albert Einstein presented a paper on his then-infant Theory of Relativity at the Sorbonne, the prestigious French university.

"If I am proved correct," he said,
"the Germans will call me a German,
the Swiss will call me a Swiss citizen,
and the French will call me a great scientist".

"If relativity is proved wrong,
the French will call me a Swiss,
the Swiss will call me a German,
and the Germans will call me a Jew."

(, July 2009)

It was time to leave, but not before raising one last subject. Obama started his campaign in the shadow of the Old State Capitol in Springfield, Ill., where Lincoln had delivered his famous "House Divided" speech, warning that the nation could not survive half-slave and half-free. Now, as he prepared to return to Washington, his transition team had announced plans for him to follow the last part of Lincoln's train ride to Washington before his inauguration. We wondered how Lincoln, an Illinois lawyer with little national experience, affected Obama's thoughts about his own presidency as another young Illinois lawyer with limited national experience soon to take his oath of office.

"Lincoln's my favorite president and one of my personal heroes," he answered. "I have to be very careful here that in no way am I drawing equivalence between my candidacy, my life experience, or what I face and what he went through. I just want to put that out there so you don't get a bunch of folks saying I'm comparing myself to Lincoln."

He paused. "What I admire so deeply about Lincoln -- number one, I think he's the quintessential American because he's self-made. The way Alexander Hamilton was self-made or so many of our great iconic Americans are, that sense that you don't accept limits, that you can shape your own destiny. That obviously has appeal to me, given where I came from. That American spirit is one of the things that is most fundamental to me, and I think he embodies that.

"But the second thing that I admire most in Lincoln is that there is just a deep-rooted honesty and empathy to the man that allowed him to always be able to see the other person's point of view and always sought to find that truth that is in the gap between you and me. Right? That the truth is out there somewhere and I don't fully possess it and you don't fully possess it and our job then is to listen and learn and imagine enough to be able to get to that truth.

"If you look at his presidency, he never lost that. Most of our other great presidents, there was that sense of working the angles and bending other people to their will. FDR being the classic example. And Lincoln just found a way to shape public opinion and shape people around him and lead them and guide them without tricking them or bullying them, but just through the force of what I just talked about: that way of helping to illuminate the truth. I just find that to be a very compelling style of leadership.

"It's not one that I've mastered, but I think that's when leadership is at its best."

(Barak Obama, 2008)

"Progress had always been made, but the nature of the progress could never be divulged."

(Franz Kafka)

"Bean, who had said of Monash "We do not want Australia represented by men mainly because of their ability, natural and inborn in Jews, to push themselves", conspired with Keith Murdoch to undermine Monash, and have him removed from the command of the Australian Corps. They misled Prime Minister Billy Hughes into believing that senior officers were opposed to Monash. Hughes arrived at the front before the Battle of Hamel prepared to replace Monash, but after consulting with senior officers, and after seeing the superb power of planning and execution displayed by Monash, he changed his mind."


"Almodovar was vague, saying, "Everything that isn't autobiographical is plagiarism.""

(Lynn Hirschberg)

"As Aldous Huxley opined, the strict materialist cannot yet derive Shakespeare from the advanced biochemistry of mutton."

(Richard Gallagher)

Understanding Human Origins

"Responding to a question about his soon-to-be-published On the Origin of Species, Charles Darwin wrote in 1857 to Alfred Russel Wallace, "You ask whether I shall discuss 'man'; I think I shall avoid the whole subject, as so surrounded with prejudices, though I freely admit that it is the highest and most interesting problem for the naturalist." Only some 14 years later, in The Descent of Man, did Darwin address this "highest problem" head-on: There, he presciently remarked in his introduction that "It has often and confidently been asserted, that man's origin can never be known: but ... it is those who know little, and not those who know much, who so positively assert that this or that problem will never be solved by science."

(Bruce Alberts)

"One mathematician rushes into the office of another and says 'Have you got a minute? I am a bit stuck on this problem. You see ... [goes on for many minutes explaining details] ... ah! Thanks very much!' and leaves; the colleague has said nothing, and has not needed to say anything. This behaviour is quite typical."

(John Mason)


"In Farrell v. Burke, Sotomayor, resisting the temptation to wax about the First Amendment, chose simply to include the following exchange from the testimony of a police officer who had charged a convicted sex offender for violating the terms of his probation by possessing obscene materials:

MR. NATHANSON: Are you saying, for example, that that condition of parole would prohibit Mr. Farrell from possessing, say, Playboy magazine?
P.O. BURKE: Yes.
MR. NATHANSON: Are you saying that that condition of parole would prohibit Mr. Farrell from possessing a photograph of Michelangelo['s] David?
P.O. BURKE: What is that?
MR. NATHANSON: Are you familiar with that sculpture?
MR. NATHANSON: If I tell you it's a large sculpture of a nude youth with his genitals exposed and visible, does that help to refresh your memory of what that is?
P.O. BURKE: If he possessed that, yes, he would be locked up for that.

Still, Sotomayor ruled that Farrell had violated his parole. "Although a series of strongly worded opinions by this Court and others suggest that the term 'pornography' is unconstitutionally vague, we hold that 'Scum' falls within any reasonable definition of pornography," she wrote."

(Lauren Collins)

"And so Einstein and his new wife, Elsa, set sail in late March 1921 for their first visit to America. On the way over, Einstein tried to explain relativity to Weizmann. Asked upon their arrival whether he understood the theory, Weizmann gave a puckish reply: "Einstein explained his theory to me every day, and by the time we arrived I was fully convinced that he really understands it." "

(Walter Isaacson)

"That is a brute, cold, hard fact of the universe. When you pull the battery out of your computer, it shuts off. When you end a life, it shuts off. And I think that's just it."

(Brian Greene)


"Why can't people just have complex views about food without resorting to extremist ideas that both fit as fashions and act as cure-all's for the health of America? Eating and nutrition are complex algorithms to get right! Michael Pollan knows this, because he wrote a great book [In Defense of Food] with a great mantra-Eat food. Not too much. Mostly plants.- that stood in the middle. And guess what happened? He heard from every asshole with a fully organic nightshade garden or a meat locker of terror in their brownstone because he wasn't on one side or the other:

The adverb "mostly" has been the most controversial. It makes everybody unhappy. The meat people are really upset I'm taking a swipe at meat eating, and the vegetarians are saying, "What's with the 'mostly?' Why not go all the way?" You can't please everyone. In a way that little word is the most important. It's not all or nothing. Mostly. It's about degree."

(Foster Kamer)

"Initiations are welcome, of course, but we do not give children a high school diploma simply for showing up for school on the first day of the first grade. For the same reasons "born-again" moral characters should probably wait a similar period of time before celebrating their moral achievement or pressing their moral authority."

(Paul Churchland)


"Now my mum had no interest whatsoever in science, and I was forever trying to explain to her why, for instance, people in Australia did not fall off the other side of the world. So when I arrived at Caltech, I had an idea: plucking up my courage, I knocked on Feynman's office door and asked, nervously, whether he would write to my mum.

He did. "Dear Mrs Chown,"" he wrote. "Please ignore your son's attempts to teach you physics. Physics is not the most important thing. Love is. Richard Feynman.""

(Marcus Chown)


Serendipitous Astronomy "Many of the seminal discoveries in astronomy have been unanticipated."

"So our celestial science seems to be primarily instrument-driven, guided by unanticipated discoveries with unique telescopes and novel detection equipment. With our current knowledge, we can be certain that the observed universe is just a modest fraction of what remains to be discovered. Recent evidence for dark, invisible matter and mysterious dark energy indicate that the main ingredients of the universe remain largely unknown, awaiting future, serendipitous discoveries."

(Kenneth R. Lang)

"Even mathematics would not be entirely safe. (Apparently, in the early 1900's, one legislator in a southern state proposed a bill to redefine the value of pi as 3.3 exactly, just to tidy things up.)"

(Paul Churchland)

"The spread of information networks is forming a new nervous system for our planet.

Now, in many respects, information has never been so free. There are more ways to spread more ideas to more people than at any moment in history. And even in authoritarian countries, information networks are helping people discover new facts and making governments more accountable.

Because amid this unprecedented surge in connectivity, we must also recognize that these technologies are not an unmitigated blessing. These tools are also being exploited to undermine human progress and political rights. Just as steel can be used to build hospitals or machine guns, or nuclear power can either energize a city or destroy it, modern information networks and the technologies they support can be harnessed for good or for ill. The same networks that help organize movements for freedom also enable al-Qaida to spew hatred and incite violence against the innocent. And technologies with the potential to open up access to government and promote transparency can also be hijacked by governments to crush dissent and deny human rights.

In the last year, we've seen a spike in threats to the free flow of information. China, Tunisia, and Uzbekistan have stepped up their censorship of the internet. In Vietnam, access to popular social networking sites has suddenly disappeared. And last Friday in Egypt, 30 bloggers and activists were detained."

(Hilary Rodham Clinton)

"This is not to say that I am not interested in the quest for intelligent machines. My many exhibitions with chess computers stemmed from a desire to participate in this grand experiment. It was my luck (perhaps my bad luck) to be the world chess champion during the critical years in which computers challenged, then surpassed, human chess players. Before 1994 and after 2004 these duels held little interest. The computers quickly went from too weak to too strong. But for a span of ten years these contests were fascinating clashes between the computational power of the machines (and, lest we forget, the human wisdom of their programmers) and the intuition and knowledge of the grandmaster."

"Perhaps the current trend of many chess professionals taking up the more lucrative pastime of poker is not a wholly negative one. It may not be too late for humans to relearn how to take risks in order to innovate and thereby maintain the advanced lifestyles we enjoy. And if it takes a poker-playing supercomputer to remind us that we can't enjoy the rewards without taking the risks, so be it."

(Gary Kasparov)

The reference to Tokyo Rose was probably lost on many of Justice Stevens's readers. But the concluding sentence of what may be his last major dissent could not have been clearer.

"While American democracy is imperfect," he wrote, "few outside the majority of this court would have thought its flaws included a dearth of corporate money in politics."

(Adam Liptak)

"Only two years ago, Jobs contemptuously predicted that the Kindle would flop: "It doesn't matter how good or bad the product is," he told The New York Times, because "the fact is that people don't read anymore. Forty percent of the people in the U.S. read one book or less last year. The whole conception is flawed at the top because people don't read anymore."

(Alan Deutschman)

Cut This Story! "There's an old joke about the provincial newspaper that reports a nuclear attack on the nation's largest city under the headline "Local Man Dies in NY Nuclear Holocaust." Something similar happens at the national level, where everything is filtered through politics. ("In what was widely seen as a setback for Democrats just a year before the midterm elections, nuclear bombs yesterday obliterated seven states, five of which voted for President Obama in the last election ...")"

(Michael Kinsley)

"I started drinking the Kool-Aid so long ago that I can no longer taste it. I am sure I will continue my unbroken streak of mindless devotion to Apple and find a way to love the iPad, no matter how expensive and unnecessary it is. Knowledge of self is no fun."

(Sasha Frere-Jones)

"As Garry Trudeau (who is not on Twitter) has his Washington "journotwit" Roland Hedley tweet at the end of "My Shorts R Bunching. Thoughts?," ... "The time you spend reading this tweet is gone, lost forever, carrying you closer to death. Am trying not to abuse the privilege."

(George Packer)

"Emerson was a touchstone, and Salinger often quoted him in letters. For instance, "A man must have aunts and cousins, must buy carrots and turnips, must have barn and woodshed, must go to market and to the blacksmith's shop, must saunter and sleep and be inferior and silly." Writers, he thought, had trouble abiding by that, and he referred to Flaubert and Kafka as "two other born non-buyers of carrots and turnips."

(Lillian Ross)

"Fifth, society is too transparent. Since Watergate, we have tried to make government as open as possible. But as William Galston of the Brookings Institution jokes, government should sometimes be shrouded for the same reason that middle-aged people should be clothed. This isn't Galston's point, but I'd observe that the more government has become transparent, the less people are inclined to trust it."

(David Brooks)

"My specific aims didn't have 'discover telomerase'. I didn't even know I wanted to discover telomerase," she said."

(Elizabeth Blackburn)

"Math came naturally to Martin, and he sought sports with similar elements, anything with angles, geometry, calculations. He smacked his first pool ball the day he could see over the table. He played billiards for hours at the local senior center, and after the employees there grew tired of unlocking the door at odd times, they made him a key.

Martin idolized Ed Lukowich, a champion curler out of Calgary, Alberta. Martin loved the smooth delivery, the flawless mechanics. Lukowich wrapped math into curling's motions.

Opponents describe Martin the same way, as a master craftsman, calm, certain, a skip with all the angles, a bald man with a bald eagle's eyesight. He attacks his sport with a farmer's sensibility and a mathematician's wit."

(Greg Bishop)

"My name is Odd-Bjoern Hjelmeset. I skied the second lap and I fucked up today. I think I have seen too much porn in the last 14 days. I have the room next to Petter Northhug and every day there is noise in there. So I think that is the reason I fucked up. By the way, Tiger Woods is a really good man."

(Odd-Bjoern Hjelmeset)

"Writing in a 2005 Wired article that "new technologies redefine us," William Gibson hailed audience participation and argued that "an endless, recombinant, and fundamentally social process generates countless hours of creative product." Indeed, he said, "audience is as antique a term as record, the one archaically passive, the other archaically physical. The record, not the remix, is the anomaly today. The remix is the very nature of the digital."

To Mr. Lanier, however, the prevalence of mash-ups in today's culture is a sign of "nostalgic malaise." "Online culture," he writes, "is dominated by trivial mash-ups of the culture that existed before the onset of mash-ups, and by fandom responding to the dwindling outposts of centralized mass media. It is a culture of reaction without action."

He points out that much of the chatter online today is actually "driven by fan responses to expression that was originally created within the sphere of old media," which many digerati mock as old-fashioned and passe, and which is now being destroyed by the Internet."Comments about TV shows, major movies, commercial music releases and video games must be responsible for almost as much bit traffic as porn," Mr. Lanier writes. "There is certainly nothing wrong with that, but since the Web is killing the old media, we face a situation in which culture is effectively eating its own seed stock." "

(Michiko Kakutani)

'Bonkers' Crochet book knits up oddest title prize

"This year's Diagram Prize for oddest book title has gone to Crocheting Adventures with Hyperbolic Planes, by mathematician Daina Taimina.

The 32nd annual award, which carries no monetary reward, was announced late Friday by The Bookseller, a U.K. trade magazine.

"I've never won any prizes before. This is my first prize and it's wonderful," said Taimina, who teaches at Cornell University in Ithaca, New York.

The book details how Taimina uses crochet to create hyperbolic planes in which lines curve away from each other instead of running parallel. Her pieces look like complex flowers.

"These are two-dimensional objects which you can see only in three dimensions," explains Taimina.

Philip Stone, an editor with The Bookseller, said the professor's book won because "very simply, the title is completely bonkers."

"On the one hand you have the typically feminine, gentle and woolly world of needlework and on the other, the exciting but incredibly un-woolly world of hyperbolic geometry and negative curvature ... the two worlds collide in a captivating and quite breathtaking way," Stone said in a statement."

(CBC Arts)

"Harold Macmillan, prime minister of Britain from 1957 to 1963, used to quote the opinion of his classics tutor at Oxford: "Nothing you will learn in the course of your studies will be of the slightest possible use to you in after life, save only this: That if you work hard and diligently you should be able to detect when a man is talking rot. And that, in my view, is the main, if not the sole purpose of education." "

(Robert Fulford)

"But the Senate is supposed to be above the game, I tell him [Bob Bennett], at least in the election off-season. Richard Russell, the legendary Democrat from Georgia, had a saying ---

"I know," he said. "My father used to quote it: 'The Senate allows you two years as a statesman, two years as a politician, and two years as a demagogue.'?" He gave me a wistful look right then, and proceeded to say exactly what I'd been thinking. "And that's actually changed. You're now a demagogue the full six years."

(Jennifer Senior)


A. "I do! But I know what you're talking about. Whenever you say you're a physicist, there's a certain fraction of people who immediately go, "Oh, I hated physics in high school." That's because of the terrible influence of high school physics. Because of it, most people think physics is all about inclined planes and force-vector diagrams. One of the tragedies of our educational system is that we've taken this incredibly interesting subject - how the universe works - and made it boring."

(Sean Carroll)

"Je n'ai fait celle-ci plus longue que parceque je n'ai pas eu le loisir de la faire plus courte. (I have only made this letter so long because I did not had time to make it shorter.)"

(Blaise Pascal)

"What has happened? I once heard a seminar given by Grothendieck, which was described as "A telegram from Grothendieck to Serre." This should not happen."

(John Wermer)

"In the realm of practical politics, two things must happen - both of which are likely. There must be one more General Election to disillusion Labour optimists as to the measure of their political strength, standing by themselves. But equally on our side there must be a certain change.

The Liberal Party is divided between those who, if the choice be forced upon them, would vote Conservative, and those who, in the same circumstances, would vote Labour. Historically, and on grounds of past service, each section has an equal claim to call itself Liberal. Nevertheless, I think that it would be for the health of the party if all those who believe, with Mr. Winston Churchill and Sir Alfred Mond, that the coming political struggle is best described as Capitalism versus Socialism, and, thinking in these terms, mean to die in the last ditch for Capitalism, were to leave us.

The brains and character of the Conservative Party have always been recruited from the Liberals, and we must not grudge them the excellent material with which, in accordance with our historic mission, we are now preserving them from intellectual starvation. It is much better that the Conservative Party should be run by honest and intelligent ex-Liberals, who have grown too old and tough for us, than by Die-Hards. Possibly the Liberal Party cannot serve the State in any better way than by supplying Conservative Governments with Cabinets, and Labour Governments with ideas,"

(J. M. Keynes)

" "One of the things we will be doing is taking apart the timekeepers Harrison made, which can give us an alternative version of the story. If you look inside the first clock, it quickly becomes clear that several people were involved in making it. Clearly this wasn't just about a lone genius working by himself," Mr Dunn said.

As for the Board, longitude was not its only scientific success. It was also involved in stimulating interest in other fields of research, such as the expeditions of Captain Cook, which led to the discovery of Australia, the invention of the sextant, the global survey of geomagnetism, the building of the first overseas astronomical observatory and the search for a North-West passage.

Professor Schafer said that we live in a culture were we prefer to see success as the achievement of a unique author rather than the fruits of collective action. Yet without the board, British science could have been very different today.

"Essentially the Board represents the germs of our national science policy," Professor Schafer said. "State-backed science is still an issue which matters a lot now, whether it's on stem cell research or climate change. We don't know whether to trust it, and we don't know how to respond when scientists and the state fall out.

"If we can find out what worked as that relationship was beginning - and why - then we will have lessons to teach from the project we are starting now." "

(Steve Connor)


"In fact, among younger listeners, the lower-quality sound might actually be preferred. Jonathan Berger, a professor of music at Stanford, said he had conducted an informal study among his students and found that, over the roughly seven years of the study, an increasing number of them preferred the sound of files with less data over the high-fidelity recordings.

"I think our human ears are fickle. What's considered good or bad sound changes over time," Mr. Berger said. "Abnormality can become a feature." "

(Joseph Flambeck)

"Canada is the linchpin of the English-speaking world. Canada, with those relations of friendly, affectionate intimacy with the United States on the one hand and with her unswerving fidelity to the British Commonwealth and the Motherland on the other, is the link which joins together these great branches of the human family, a link which, spanning the oceans, brings the continents into their true relation and will prevent in future generations any growth of division between the proud and the happy nations of Europe and the great countries which have come into existence in the New World."

(Winston Churchill)

"Dr. John Ioannides, an epidemiologist at the University of Ioannina, in Greece, has noted that four of the six most frequently cited epidemiological studies published in leading medical journals between 1990 and 2003 were later refuted. Demonstrating the malleability of data, Peter Austin, a medical statistician at the Institute for Clinical Evaluative Sciences, in Toronto, has retrospectively analyzed medical records of the more than ten million residents of Ontario. He showed that Sagittarians are thirty-eight per cent more likely to fracture an arm than people of other astrological signs, and Leos are fifteen per cent more likely to suffer a gastrointestinal hemorrhage. (Pisces were more prone to heart failure.)"

(Jerome Groopman)

"What we're experiencing is, in a metaphorical sense, a reversal of the early trajectory of civilization: We are evolving from cultivators of personal knowledge into hunters and gatherers in the electronic data forest. In the process, we seem fated to sacrifice much of what makes our minds so interesting. "

(Nicholas Carr)

'Fast entertainment' scared Wordsworth too: "A multitude of causes, unknown to former times," he wrote in 1800 in the preface to Lyrical Ballads,

"are now acting with a combined force to blunt the discriminating powers of the mind ... The most effective of these causes are the great national events which are daily taking place, and the increasing accumulation of men in cities, where the uniformity of their occupations produces a craving for extraordinary incident, which the rapid communication of intelligence hourly gratifies."

Appalled observers - Freeman is hardly the first - react to the web as Wordsworth reacted to London, with its 'endless stream of men and moving things'. London, like the internet, brought together people who used to live far apart: 'Moors, Malays, Lascars, the Tartar, the Chinese/And Negro Ladies in white muslin gowns'; London, too, presented 'sights that ape/The absolute presence of reality', from pantomimes to painted outdoor signs. The hourly craving for gossip, or news, the density of visual information, the loss of authentic and trustworthy face-to-face contact, the anonymity of modernity: for Wordsworth, they were all connected (and all to be feared).

(Stephen Burt)

A prolific writer, Edwards was actively involved in the ethical debates around IVF from the start. As early as 1971, he published a paper in Nature, still regarded as a classic, that laid out the ethical, social, and regulatory issues in human embryology. He liked taking provocative positions, if only to flush out counterarguments, Johnson says. He disagreed with the scientific community's decision to declare human cloning off-limits without discussing the potential benefits. "I've never met anyone worth cloning, including myself," Edwards once quipped. "But to him, closing the debate was the antithesis of scientific inquiry," says Johnson.

(Gretchen Vogel and Martin Enserink)

In that regard, this year's prize could be considered an anomaly. In the past, a few prizes have quickly spotlighted discoveries that upended the prevailing theory; others have recognized advances that over decades had led to ubiquitous applications. This year's prize, by contrast, honors physics that by all accounts is beautiful but not revolutionary. ""You don't need a new theory" to understand graphene, says Jeroen van den Brink, a theorist at the Institute for Materials Sciences at the Dresden University of Technology in Germany. At the same time, it celebrates the potential for applications yet to come." "Will this really come into the market?" Kim says. "I think it's really difficult to say. " Still, everyone interviewed by Science says Geim and Novoselov thoroughly deserve the prize.

The prize is also unusual because one recipient has another claim to fame. In 2000, Geim won a share of an Ig Nobel Prize, a satirical award given out by the publishers of the Annals of Improbable Research, for magnetically levitating a live frog. Geim is the first person to win both prizes. During a press conference announcing the Nobel Prize, Geim reacted with unusual candor to his latest award: " "When I got the telephone call, I thought, 'Shit!' because it is a life-changing event.

(Adrian Cho)


Cricket was the most-read story on The Australian website for 36 hours after the match. During the last session international attention was so great the enormous Bangalore-based, ESPN-backed Cricinfo web servers collapsed from exhaustion.

Anyway, there is a wise story about a war hero, philanthropist, inventor, champion athlete and all-round high achiever who has sexual congress with a goat. The man complains that no matter what he achieves he will always be known as a goat f . . .er.

Perhaps we had better get used to the ugly Aussie tag. It could be worse.

(Peter Lalor)

In the 1960s, much of economic theory strived to prove that the results from idealized classical economics still held sway as economists made their models more realistic, Diamond said at an MIT press conference after the prize was announced. He preferred to let the improved models lead where they may. "It seemed to me that a better approach was to think about real dynamics and see where they go," he says. "Maybe they go to the [classical] equilibrium solution and maybe they don't."

(Adrian Cho)

He also lashes out at scientists who fail to communicate the significance of their work in human terms, regardless of how abstract their work might be. He reads plenty of science journals, he says, but finds "a lot of the stuff impenetrable," which is ridiculous, he says. "In particular, I think one needs narrative and history to relate how things have come about and how they've happened. ... It's not sufficient just to give the result and the conclusion. Even when you are dealing with things that are unimaginably remote from human experience, I think it's important to think about them in a human way," the doctor says, with a pause. "After all, we are the ones who are midway between the atoms and the stars."

(Sonia Verma)

"The United States is the only nation in history which, miraculously, has gone directly from barbarism to degeneration without the usual interval of civilization." (George Clemenceau) ... "And Clemenceau was dealing with Wilson - what epigram would he have hung on Dubya's US?" "

(Dervla Murphy)

"... Born decided to investigate the simple ionic crystal-rock salt (sodium chloride)- using a ring model. He asked Lande to collaborate with him in calculating the forces between the lattice points that would determine the structure and stability of the crystal.

Try as they might, the mathematical expression that Born and Lande derived contained a summation of terms that would not converge. Sitting across from Born and watching his frustration, Madelung offered a solution. His interest in the problem stemmed from his own research in Goettingen on lattice energies that, six years earlier, had been a catalyst for Born and von Karman's article on specific heat. The new mathematical method he provided for convergence allowed Born and Lande to calculate the electrostatic energy between neighboring atoms (a value now known as the Madelung constant). Their result for lattice constants of ionic solids made up of light metal halides (such as sodium and potassium chloride), and the compressibility of these crystals agreed with experimental results. "

(Nancy Thorndike Greenspan)

"However he feels about his Jewish DNA, Holbrooke is held up as a compassionate Jew by countless Jewish organizations that have hailed his peace efforts. He has received prizes from the World Jewish Congress, the Anti-Defamation League, Jerusalem's Hebrew University, and Yeshiva University. "Les Gelb has this great joke that they're inventing Jewish organizations to give me awards," he says with a laugh. "Don't ask me. They invite me; I'm very proud to do it." "

(Abigail Pogrebin)

"Quality control aside, a larger question remains: Does the act of data gathering really constitute science?

"These people are not doing the work of scientists," said David Weinberger, a senior researcher at the Berkman Center for the Internet and Society at Harvard, who is writing a book about the changing shape of human knowledge in the online era. "They are doing the work of scientific instruments." Stephen Emmott, head of computational research at Microsoft Research, agrees that most citizen science projects tend to treat participants as high-functioning cogs in a distributed machine. "Certainly this is participatory," he said, "but is it science?"

Dr. Emmott believes that before Web users can claim the mantle of citizen scientists, they will have to be given more meaningful roles. "Participants should be able to make a genuine contribution," he said, "and get something back." "

(Alex Wright)

"I don't think we need to worry anytime soon about the machines taking over. I work in robotics, and the robots we build haven't gotten rid of people. They just make them more productive. We can relax for a few hundred years, is my guess."

(Rodney Brooks)

On the other, his judgments could be pointed: the 1970s was intellectually the bleakest decade of the century: structuralism and deconstructionism came to the fore because their "inherently difficult vocabulary had achieved a level of expressive opacity that proved irresistibly appealing to a new generation of students and their teachers."

(Geoffrey Wheatcroft)

You're a very naughty billionaire.

(Jonnie Marbles)

[O]nce we have accepted the authority of a particular scientific discipline, we cannot consistently reject its conclusions. To adapt Schopenhauer's famous remark about causality, science is not a taxi-cab that we can get in and out of whenever we like. Once we board the train of climate science, there is no alternative to taking it wherever it may go.

(Gary Cutting)

Write it down: Americans Elect. What did to books, what the blogosphere did to newspapers, what the iPod did to music, what did to pharmacies, Americans Elect plans to do to the two-party duopoly that has dominated American political life - remove the barriers to real competition, flatten the incumbents and let the people in. Watch out.

(Tom Friedman)

If there is a God, and he lacks a sense of irony, he will send Hitchens to the hottest precinct of hell. If God does have a sense of irony, Hitchens will spend eternity in a town that serves no liquor and has no library. Either way, heaven will be a less interesting place.

(Bill Keller)

Perhaps in another quarter of a century, every nation will arrive at the World Cup with a home-grown coaching team. Now is not the time to yearn for it. As the great art historian Kenneth Clark noted, internationalism is accepted unquestioningly when something really matters.

(Chris Hewitt)

"The idea of scaling down electronic circuits goes back at least to 1960, when a young electrical engineer named Douglas Engelbart spoke at a radio and electronics technical conference in Philadelphia. Dr. Engelbart had hit on the idea that shrinking the basic circuitry of the first digital computers could lead to a drastic increase in power. "Boy, are there going to be some surprises over there," he told his audience. It turned out to be an understatement"

(John Markoff)

"The historian's job is not to tell us what to think, but to tell us what he thinks, so that our own thoughts may be refined or rearranged by dint of the comparison and argument. But there is no arguing with Pevsner. The stare-you-in-the-face rigor of his systematizing intellect-those cold, clean pages with their hanging indents, their bolds and italics and SMALL-CAPS-has the effect of making what is only his taste look like the truth. One knew this abstractly, of course, before ever reading this biography; but having read the book one feels it in one's whole being-feels, moreover, that Pevsner himself wouldn't have a clue what one was talking about in criticizing him in this way. I don't for a moment think that she set out to tarnish her man, but Harries has changed the way we see him all the same. Pevsner wrote books about what men made with clay. Susie Harries has written one that proves at least a part of him was made of the same substance. "

(Christopher Bray)

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

(W.S. (Bill) Angelin)

"The theory of evolution is the fundamental backbone of all biological research," he said. "There is more evidence for evolution than there is for the theory of gravity, than the idea that things are made up of atoms, or Einstein's theory of relativity. It is the finest scientific theory ever devised."

(Vincent Cassone)

"It has been a disastrous half. His work has been far from satisfactory. His prepared stuff has been badly learnt, and several of his test pieces have been torn over; one of such pieces of prepared work scored 2 marks out of a possible 50. His other work has been equally bad, and several times he has been in trouble, because he will not listen, but will insist on doing his work in his own way. I believe he has ideas about becoming a Scientist; on his present showing this is quite ridiculous, if he can't learn simple Biological facts he would have no chance of doing the work of a Specialist, and it would be sheer waste of time, both on his part, and of those who have to teach him."

(A long dead teacher)

". . . do you not find that the prime numbers are given, if you will, too much honour, so that so much energy is wasted on them, and does this refined taste of our century not repel you?"

(Daniel Bernoulli)

Some subjects can be roughly associated with geographic locations: graph theory is a Canadian subject, singular integrals is an Argentine subject, class field theory an Austrian subject, algebraic topology an American subject, algebraic geometry an Italian subject, special functions a Wisconsin subject, point-set topology a Southern subject, probability a Russian subject.

A good test for evaluating the "pop math" books that appear with regularity on the shelves of college stores is the following: let a mathematician pick one up and note whether the text is engaging enough to sustain attention for more than ten minutes. Most likely, the book will be reshelved in disgust, after the reader verifies that its contents are the usual pap of Klein bottles, chaos, and colored pictures devoid of clear meaning.

It takes an effort that is likely to go unrewarded and unappreciated write an interesting exposition for the lay public at the cutting edge of mathematics. Most mathematicians (self-destructive and ungrateful wretches that they are, always ready to bite the hand that feeds them) turn their noses at the very thought. Little do they realize that in our science-eat-science world such expositions are the lifeline of mathematics.

When too many books are written on a subject, one of two suspicions arises: either the subject is understood and the book is easy to write---as is the case with books on real variables, convexity, projective geometry in the plane, or compact orientable surfaces. Or the subject is important, but nobody understands what is going on; such is the case with quantum field theory, the distribution of primes, pattern recognition, and cluster analysis.

(Gian-Carlo Rota)

There is charm to reading a philosopher who confesses to finding things bewildering. But I regret the appearance of this book. It will only bring comfort to creationists and fans of "intelligent design", who will not be too bothered about the difference between their divine architect and Nagel's natural providence. It will give ammunition to those triumphalist scientists who pronounce that philosophy is best pensioned off. If there were a philosophical Vatican, the book would be a good candidate for going on to the Index.

(Simon Blackburn)

For there might be perfectly good reasons why you can't imagine a solution to the problem of consciousness. As the philosopher Colin McGinn has emphasized, your very inability to imagine a solution might reflect your cognitive limitations as an evolved creature. The point is that we have no reason to believe that we, as organisms whose brains are evolved and finite, can fathom the answer to every question that we can ask. All other species have cognitive limitations, why not us? So even if matter does give rise to mind, we might not be able to understand how...

(H. Allen Orr)
Context is always important, but it's particularly important in this case. Here's the full quote from Keynes' A Tract on Monetary Reform:

"But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean is flat again." "

(Mathew O'Brien)