MIDDLEWARE

David Bailey, a senior scientist and applied mathematician at Lawrence Berkeley National Laboratory who has made his mark studying problems ranging from the digits of pi to the performance of supercomputers, has co-authored a pair of new books on experimental mathematics. Expected to hit the shelves later this year, the books are Mathematics by Experiment: Plausible Reasoning in the 21st Century by Jonathan M. Borwein and David H. Bailey, and Experiments in Mathematics: Computational Paths to Discovery by Borwein, Bailey and Roland Girgensohn. Bailey will give a short presentation on his book at the SC2003 conference, speaking at 1 p.m. Wednesday, Nov. 19, in the LBNL booth (R231). Also, Berkeley Lab will be holding a drawing to award two copies of the book, signed by Bailey, each day of the SC2003 exhibits – fill out a form at the LBNL booth for your chance to win a copy. The books, to be published by A K Peters, Ltd., generated an enthusiastic review in the May 2003 issue of Scientific American and is a selection of Bookspan®, a scientific book club. Bailey is well known for his work in computational mathematics and has written numerous papers on using modern computer technology in mathematical research. His best-known result in this area is a new formula for the mathematical constant pi, which was found by Bailey and two other researchers in 1996 using a computer program. He is currently the chief technologist for the Computational Research and the National Energy Research Scientific Computing Center divisions at the U.S. Department of Energy’s Berkeley Lab. In Mathematics by Experiment, Bailey and his longtime collaborator Borwein, who is a professor of science at Simon Fraser University in Vancouver, B.C., write that applied mathematicians, and many scientists and engineers, were quick to embrace computer technology. Pure mathematicians - whose field gave rise to computers in the first place, through the work of beautiful minds like Alan Turing's - were slower to see the possibilities, however. Two decades ago, when Bailey and Borwein started collaborating, “there appeared to be a widespread view in the field that ‘real mathematicians don't compute.’” These two books are testament to a paradigm shift in the making. Hardware has “skyrocketed in power and plummeted in cost,” and powerful mathematical software has come on the market. Just as important, “a new generation of mathematicians is eagerly becoming skilled at using these tools” people comfortable with the notion that “the computer provides the mathematician with a 'laboratory' in which he or she can perform experiments: analyzing examples, testing out new ideas, or searching for patterns.” In this virtual laboratory, Bailey, with Borwein and other colleagues, was among the first to discover a number of remarkable new algorithms. One of the new algorithms was an extraordinary, simple formula for finding any hexadecimal or binary digit of pi without knowing any of the preceding digits. Further research led to proof that a wide class of fundamental constants are mathematically "normal" probably including pi, although that remains to be proved. A section on “proof versus truth” is an example of the gems even a mathematical tyro can find among these equations. Bailey and Borwein don't claim computers can supply rigorous proofs; rather, the computer is a way to discover truths and avenues for approaching formal proofs. But often, the authors add, “computations constitute very strong evidence ... at least as compelling as some of the more complex formal proofs in the literature.” Drawing on their own work and that of others, Bailey and Borwein and, in the second volume, their German colleague Roland Girgensohn not only explain experimental mathematics in a lively, surprisingly accessible fashion, but give many engaging examples of the "new paradigm" in action. For those who just can't wait, what Bailey calls a “Reader's Digest version” 60 pages of “some of the more engaging material” from both volumes is freely available online at http://www.expmath.info/expbook-C.pdf, with a cornucopia of related resources at http://www.expmath.info. Prior to joining Berkeley Lab in 1998, Bailey was a computer scientist at the NASA Ames Research Center. While at NASA, he co-authored the NAS Parallel Benchmarks, which has been widely used to measure high-end scientific computer performance. He is currently heading a new eight-institution research effort, the U.S. Department of Energy’s Performance Evaluation Research Center (PERC), aimed at understanding and improving performance of scientific computations on high-end computer systems. Berkeley Lab is a U.S. Department of Energy national laboratory located in Berkeley, California. It conducts unclassified scientific research and is managed by the University of California. Visit our website at http://www.lbl.gov/.