Experimental Mathematics and Number Theory

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Fateman The investigators take up three tasks in experimental mathematics, which uses computers as a tool to discover and prove new mathematical results. They: (1) develop and enhance software tools to support experimental mathematics; (2) pursue additional results in recognizing constants in number theory; and (3) pursue additional proofs of normality for irrational constants. The investigator and his colleagues use computers as a tool to discover and prove new mathematical results. They have expertise both in mathematics and computer science. Recent examples of this methodology in action by members of the team include the discovery of new formulas for pi and other well-known constants, numerous results on multiple zeta constants and infinite series involving binomial coefficients, identification of constants that arise in physics and chemistry, a result on the randomness of the binary digits of pi and log(2), and a proof of normality for an uncountably infinite class of real numbers. In addition to its inherent scientific interest and potential impact on mathematical research, this type of research presents a unique opportunity to forge links to researchers in other disciplines, especially computer science and physics, and to convey the excitement of modern mathematics to the general public.