Experimental Mathematics

Since the late 1940s when computers were introduced, they have had a profound impact on every area of scientific inquiry. While the computer's underpinnings were developed both pure mathematicians, they have seen relative little payback to their area. This has been dramatically changing since the advent of symbolic computation packages such as Maple and Mathematica. These systems have matured to a point where they are used by researchers not only for disposing of rote calculations, but as allies in the discovery process. One now can use the computer to discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, falsify conjectures, confirm analytically derived results, and --- perhaps most impressively for the purist --- suggest approaches for formal proofs. This is the thrust of experimental mathematics. It is a growing paradigm which is revolutionizing how some mathematical research is being done today.

My papers which have used the computer to discover new results follow.