Emerging Tools for Experimental Mathematics

Using mostly elementary examples, we discuss the use of some recent and emerging tools for experimental mathematics. The tools discussed include so-called \inverse symbolic computation", lattice reduction algorithms such as \LLL" and \PSLQ", and Sloane and Ploue's integer sequence lookup program. 1 Introduction and \Warm-up" If I can give an abstract proof of something, I'm reasonably happy. But if I can get a concrete, computational proof and actually produce numbers I'm much happier. I'm rather an addict of doing things on the computer, because that gives you an explicit criterion of what's going on. I have a visual way of thinking, and I'm happy if I can see a picture of what I'm working with. | John Milnor, p. 78 of Who Got Einstein's OÆce?, by Ed Regis (Addison-Wesley, 1986) 1 In this paper we discuss some interesting new tools for mathematical explorations. We will be concentrating on `computer-assisted discovery' of mathematical results, but a little `computer-assisted proof..