Ten Problems in Experimental Mathematics

Borwein, Jonathan M. and Kapoor, Vishaal and Bailey, David H. (2006) Ten Problems in Experimental Mathematics .

Abstract

This article was stimulated by the recent SIAM “100 Digit Challenge” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent in [15] was to present ten problems that are characteristic of the sorts of problems that commonly arise in “experimental mathematics” [15][16]. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and at the same time, to present a concise account of how one combines symbolic and numeric computation, which may be termed “hybrid computation,” in the process of mathematical discovery.