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How Math Explains the World    by James D. Stein order for
How Math Explains the World
by James D. Stein
Order:  USA  Can
Collins, 2008 (2008)
* * *   Reviewed by Hilary Williamson

In How Math Explains the World, James D. Stein (a math professor at California State University) offers readers an accessible 'Guide to the Power of Numbers, from Car Repair to Modern Physics'. It's an intriguing mixture of tidbits of math history (including the fact that Max Planck's younger son was executed in an attempt to assassinate Hitler, and a bio of the Mozart of Mathematics); math philosophy (the Mathematician's Job Interview is amusing as is a quote from Tom Lehrer's hilarious Nikolai Ivanovich Lobachevsky); and all kinds of math applications.

The book is organized into four sections: Describing the Universe, The Incomplete Toolbox, Information: The Goldilocks Dilemma, and The Unattainable Utopia. In his Introduction, Stein speaks of the giant strides made in twentieth century scientific developments, but also of the eye-opening and counterintuitive mathematical proofs that there are 'problems that are incapable of solution.' Stein later gets into a discussion about Learning from Impossibility and the discoveries to be made from investigations of the great problems of mathematics.

Regarding the book's contents he tells us that he has written to 'allow those who want to skip a section in which mathematics is done to do so without losing the gist of what is being said.' (I admit to skimming through the quantum mechanics discussion.) He also provides detailed notes and references at the end of each chapter, so that anyone who wants to follow up on a topic in more depth has the tools to do so.

He continues to give fascinating examples of math in action, including: how 'some problems may well be so complex that there is no perfect way to solve them' (e.g. the Short-Order Cook); the application of Heisenberg's Uncertainty Principle to the purchase of gasoline at a gas station (certainly relevant today!); the mystery of how husbands and wives respond identically to pollsters and its relation to entanglement; the incompleteness theorem and the impossibility of writing a computer program to detect all viruses; chaos theory and climate change; and (again very relevant today) mathematical assessment of voting systems.

James D. Stein's How Math Explains the World is not a light read for the layman, but it is a fascinating one for those willing to put their thinking hats on, and invest some time in it.

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