Chaired by Richard Brent

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 (10¹³) 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.