# 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.

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.