Mathematical Experiments and Experimental Mathematics

This article introduces the emerging field of experimental mathematics by surveying just a few of its motivations, methods, results, and implications. Over the last two decades the field has matured and is growing steadily in prominence, as evidenced by a journal dedicated to experimental mathematics, several books devoted to the field, many online resources, and regular conferences. Although there is some resistance in segments of the broader mathematics community to this nascent field, the resistance is focused on one of its more extreme contentions. Regardless of how experimental you like your mathematics to be, making students aware of a more empirical approach to mathematics could have motivational and pedagogical advantages. Much of experimental mathematics can be loosely described as messing around-an activity at which many students excel if given a chance. Building on this native inclination, rather than restraining it, by giving students some direction toward producing rigorous results might be the key to nurturing the next generation of experimental mathematicians.