Strange Hypergeometric Series Evaluations, Zeta Function Formulae, and Computer Assisted Discovery

Abstract. The past 20 years has seen a dramatic re-concretization of Mathematics, in which fields such as number theory, classical analysis, and special functions have received new infusions fueled by advances in hardware, software, and algorithms. A whole new palette of tools is available to the researcher, many of which, with a little effort, can operate like extensions of the mind, greatly increasing our ability to generate examples, test hypotheses, and build intuition.

My own work has profited greatly from the use of inverse symbolic computational tools, leading to proofs of startling new hypergeometric series evaluations, and tantalizing results for multi-dimensional zeta functions which have attracted such luminaries as physicist/topologist Ed Witten and Cole-prize-winning number theorist Don Zagier. These are rich areas to explore, and much work still remains to be done. In this talk, I will give an introduction to this exciting area of research, and discuss the role that symbolic computation played in the discovery process.