High Performance Mathematics and its Management

Seventy-five years ago Kurt Gödel overturned the mathematical apple cart: he proved it is not entirely deductive, and he held 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 lecture provides an introduction to Experimental Mathematics, its theory and its practice. I will reprise the ‘Experimental Methodology ’ that David Bailey and I—among many others—have come to practice over the past two decades, [2, 3]. 1 I will focus on the differences between Discovering Truths and Proving Theorems. We 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, [1, 4], and which prominently includes NIST’s forthcoming Digital Library of Mathematical Functions. viewable a