Experimental Mathematics in Action
This book contains material originating from a course on Experimental Mathematics in Action, organized by Jonathan Borwein in San Antonio in 2006. One of aims of the book is to defend an assertion that the statement “the real mathematicians don’t compute” is no longer valid with a new generation of mathematicians. Computer-aided research, taking advantage of modern computational packages (such as Maple or Mathematica) has its importance nowadays. The book presents several examples and methodological ways to make clear what computational or experimental mathematics is or should be. Starting with some remarks of philosophical character, the authors present many algorithms for experimental mathematics, such as high-precision arithmetic, integer relation detection, prime number computations and finding the roots of polynomials. Moreover, their aim is also to present (the slightly controversial) idea that “mathematics is done more like physics in that you come about things experimentally”. This does not mean that a mathematician should give up proving theorems; this is just a statement about how some of the mathematical facts can be discovered. The book is nicely written, with a special touch of mathematical poetry and beauty-behind-the-computation opinion. It will be appreciated not only by number theoreticians but also by anyone who does not prevent computers from entering the pure garden of mathematical delights.