High performance mathematics and its management

Friday, December 8, 2006 - 3:00pm - 3:30pm
EE/CS 3-180
Jonathan Borwein (Dalhousie University)
Seventy-five years ago Kurt Gödel overturned the mathematical apple cart: he proved entirely deductively
that mathematics is not entirely deductive,while holding quite different ideas about legitimate
forms of mathematical reasoning: If mathematics describes an objective world just like physics, there
is no reason why inductive methods should not be applied in mathematics just the same as in physics.
(Kurt Gödel, 1951) This talk provides an introduction to Experimental Mathematics, its theory and
its practice. I will focus on the differences between Discovering Truths and Proving Theorems
and on the implications for knowledge management and communication. I shall explore various of
the computational tools available for deciding what to believe in mathematics, and-using accessible
examples-illustrate the rich experimental tool-box mathematicians now have access to. These
tools range from web-interfaces and databases to preprint repositories and digital library collections,
and prominently include NIST's forthcoming Digital Library of Mathematical Functions. In an attempt
to explain how mathematicians may use High Performance Computing (HPC) and what they
have to offer other computational scientists, I will touch upon various Computational Mathematics
Challenge Problems.