# Jonathan M. Borwein

# Commemorative Conference

## 25—29 September, 2017

# ◄Number Theory, Special Functions and Pi►

10^{11}-step random walk using the digits of pi.

The theme "Number Theory, Special Functions and Pi" will be devoted to Jon
Borwein's many contributions to these areas. Jon was fascinated by the
constant pi = 3.14159... and gave many talks on properties of pi and
algorithms for computing it. Because pi occurs naturally in so many branches
of mathematics, it is possible to elucidate the connections between these
branches by studying pi. Jon promoted mathematics to a general audience by
his popular talks and articles on "Pi Day", March 14th. At a deeper level,
the book "Pi and the AGM" by Jon and Peter Borwein considers elliptic
integrals, the arithmetic-geometric mean iteration, theta functions, modular
equations, transcendence results, and the complexity of evaluating algebraic
and elementary functions, all in the context of pi. Jon made some beautiful
pictures by using the digits of pi to generate pseudo-random walks. One of
his last papers was concerned with whether the first ten trillion (10^{13})
decimal digits of pi failed a certain statistical test for randomness. He
concluded that, contrary to a recent claim in the literature, they did not.

## Speakers

- Prof. Richard Brent (keynote speaker)
- Prof. Bruce Berndt
- Dr Michael Coons
- Prof. Karl Dilcher
- David Harvey
- Dr Mumtaz Hussain
- Dr Tim Trudgian