AMS Nos: 97C80, 00A30, 65-01, 33F10
Key Words Experimental Mathematics, symbolic computations, number theory, special functions

Abstract. This document is an adapted selection of excerpts from two newly published books, Mathematics by Experiment: Plausible Reasoning in the 21st Century, and Experimentation in Mathematics: Computational Paths to Discovery, published by AK Peters, Natick, Massachussetts. We have gleaned from these two volumes material that explains what experimental mathematics is all about, as well as some of the more engaging examples of experimental mathematics in action.

The experimental methodology that we describe in these books provides a compelling way to generate understanding and insight; to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for both the professional researcher and the novice. We have concentrated primarily on examples from analysis and number theory, but there are numerous excursions into other areas of mathematics as well. Much of this material is gleaned from existing sources, but there is a significant amount of material that, as far as we are aware, has not yet appeared in the literature.