Mathematically or scientifically related books recommended by CARMA members.

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A beautifully crafted non-technical exposition of what modern physics has to offer. Chapters: The most beautiful of theories (relativity) Quanta The architecture of the cosmos Particles Grains of space (quantum gravity) Probability, time and the heat of black holes Ourselves Two memorable quotes: "you don't get anywhere by not 'wastng' time", "I distracted by schooling one learns best during vacations".

*Reviewed by BS*

A beautifully crafted non-technical exposition of the revelations modern physics has to offer. Chapters: The most beautiful of theories (relativity) Quanta The architecture of the cosmos Particles Grain of space (quantum gravity) Probability, time and the heat of black holes Ourselves Two memorable quotes: "you don't get anywhere by not 'wasting' time", "undistracted by schooling one studies best during vacations

*Reviewed by BS*

As a mathematician I have lectured on the theory of Hilbert spaces for many years and known of its relevance to Quantum Mechanics; after all their theory was formalised by von Neumann in his 1930's book on QM. However until reading Susskind's book I never properly understood the essence of the connection. It is a beautifully executed exposition penetrating to the very essence of QM, accessible to anyone with a knowledge of basic calculus and the algebra of vectors and matrices and even much of that is nicely explained.

*Reviewed by BS*

As the title suggests, Forbes and Mahon's book offers a compelling account of two of the 19th century's most influential men of science; Michael Faraday and James Clerk Maxwell. With the focus firmly centred on their electromagnetic researches, it is more a biography of their scientific endeavours than their personages though details of the later are certainly not neglected but rather crafted into the stage upon which their scientific achievements are played out.

*Reviewed by BS*

A well crafted highly enjoyable and informative read. It offers a wealth of biographical details about both men viewed against the prevailing times. An insightful analysis of their interaction during the years together at Princeton's I.A.S. is included. Both are seen as pushing the limits of what's knowable; Godel limits to formal reasoning, Einstein to physical knowledge. Godel's little known solution to the field equations of general relativity that admits' time-like' loops (time travel) and the philosophical conclusions he drew from it lend the book its title. Brailey Sims

*Reviewed by BS*

A fascinating description of the emergence and dangers of high frequency algorithmic trading. For a fuller review see <A href="http://www.financial-math.org/blog/2014/04/review-of-dark-pools-and-flash-boys/">the mathematical investor</A>.

*Reviewed by JB*

All mathematicians are, or at least should be, concerned with the precise meaning(s) of mathematical words (and symbols) and almost every mathematician we know exhibits at least a passing interest in their etymology; their derivation, when and where they originated, perhaps by whom they were first coined, and their subsequent evolution in usage and meaning. If you entertain such curiosity, then this book is almost surely for you. JMB & BS

*Reviewed by BS*

Sir Fred Hoyle was one of the mid-twentieth century's most creative and provocative astrophysicists. This often introspective autobiography is a very enjoyable read providing an insight into Fred's development, experiences, thoughts and science from early boyhood to the time of writing (seven years before his death in 2001, aged 85). Sprinkled throughout with his wry Yorkshire humour it gives a no holds barred glimpse into the academic politics of Cambridge circa the sixties, seventies and eighties and more generally of the politics of science in the UK and internationally as he encountered it. Brailey Sims

*Reviewed by BS*

Mandatory reading for any scientist who wants to write for or talk to nonspecialists. See also <a href="http://skepticalscientist.com/2012/05/15/hello-world/">http://skepticalscientist.com/2012/05/15/hello-world/</a>.

*Reviewed by JB*

I think Brooks exaggerates for effect, and, as some reviewers have noted, he indulges in (really engaging) anecdotal cherry-picking to knock down a straw-man that no scientist truly believes exists. There may be more malarkey among "paradigm" shifters, in Kuhn's sense. But, for every free radical like Einstein, Maxwell or Kary Mullis, there is a Darwin spending eight years on barnacles or worms ("it's dogged that does it") or an Andrew Wiles refusing relentlessly to give up on "normal science" in his pursuit of Fermat's last theorem.

*Reviewed by JB*

A great book about the effect of man on the ocean. Includes a brief history of the ocean's first 4.5 billion years, the history of fishing and declining catches as a result of overfishing, climate change and sea-level rise, ocean acidification, pollution by plastics and noise, fish-farming, and prospects for the future. The book is written for a general audience and is not explicitly mathematical, but the mathematically inclined reader will notice various mathematical models lurking under the surface.

*Reviewed by RPB*

A fascinating mathematical biography of David Hilbert (1862-1943), with lots of information about his contemporaries and students such as Courant, Gordan, Klein, Landau, Lewy, Lindemann, Minkowski, Noether, Ostrowski, Polya, Siegel, Weyl and the rise and fall of Gottingen as a mathematical centre. The subsequent biography "Courant" by the same author is recommended as a sequel - it gives the story of Richard Courant, first in Gottingen and then in New York and includes many of the same characters.

*Reviewed by RPB*