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Title: Mathematics by Experiment: Plausible Reasoning in the 21st Century by Jonathan M. Borwein, David H. Bailey ISBN: 1-56881-211-6 Publisher: AK Peters Ltd Pub. Date: December, 2003 Format: Hardcover Volumes: 1 List Price(USD): $45.00 |
Average Customer Rating: 5 (1 review)
Rating: 5
Summary: A Mathematical Paradigm Shift
Comment: "Mathematics by Experiment" is a ground-breaking book about a new way of doing math that generated so much excitement it was reviewed in "Scientific American" six months before it got into print. The authors are long-time collaborators David Bailey, chief technologist in the Computational Research Department of Lawrence Berkeley National Laboratory, and Jonathan Borwein, professor of science at Simon Fraser University in Vancouver, B.C.
They write that applied mathematicians and many scientists and engineers were quick to embrace computer technology, while 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. 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.'"
Their book is 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 and Borwein, with other colleagues, were among the first to discover a number of remarkable new algorithms, among them 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, alhough that remains to be proved.
Their 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 not only explain experimental mathematics in a lively, surprisingly accessible fashion but give many engaging examples of the "new paradigm" in action.
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Title: Experimentation in Mathematics: Computational Paths to Discovery by Jonathan Borwein, David Bailey, Roland Girgensohn ISBN: 1568811365 Publisher: AK Peters Ltd Pub. Date: September, 2003 List Price(USD): $49.00 |
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Title: Mathematical Constants by Steven R. Finch, G.-C. Rota ISBN: 0521818052 Publisher: Cambridge University Press Pub. Date: 18 August, 2003 List Price(USD): $95.00 |
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Title: Mathematics in Nature : Modeling Patterns in the Natural World by John A. Adam ISBN: 0691114293 Publisher: Princeton Univ Pr Pub. Date: 10 November, 2003 List Price(USD): $39.50 |
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Title: One, True Platonic Heaven: A Scientific Fiction of the Limits of Knowledge by John L. Casti ISBN: 0309085470 Publisher: Joseph Henry Press Pub. Date: May, 2003 List Price(USD): $22.95 |
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Title: Everything and More: A Compact History of Infinity (Great Discoveries) by David Foster Wallace ISBN: 0393003388 Publisher: W.W. Norton & Company Pub. Date: October, 2003 List Price(USD): $23.95 |
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