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Loving + Hating Mathematics: Challenging the Myths of Mathematical Life

Reuben Hersh and Vera John-Steiner
PRINCETON UNIVERSITY PRESS 2011, 428 PAGES
PRICE (HARDBACK) £20.95 ISBN 978-0-691-14247-0

Mathematicians are different from other people, lacking emotional complexity. Mathematics is a solitary pursuit. Mathematics is a young man’s game. Mathematics is an effective filter for higher education.

These are four myths, according to Reuben Hersh, Professor Emeritus of Mathematics at the University of New Mexico, and Vera John-Steiner, Professor Emerita of Linguistics and Education at the same university. In this book they seek to dispel these myths, principally by examining the lives of several mathematicians, from the widely known, such as Hilbert, Hardy and Littlewood, to the less widely known, but still influential, such as Julia and Raphael Robinson and Lenore Blum.

They note, early on, that, contrary to common belief, it is not the case that ‘Either you are mathematically inclined or you are not’. They give some interesting examples of the early development of different skills and capabilities exhibited by some of the top mathematical minds. For example, they contrast John Von Neumann’s prodigious ability to perform complicated numerical calculations with Roger Penrose’s initial slowness in arithmetic as a youngster. They liken Von Neumann to Mozart, whose music came with ease and fluency, and Penrose to Beethoven, with his more laboured and time-consuming approach to music.

Perhaps inevitably when dealing with some of the brightest mathematicians the anecdotes the authors recount do not always provide convincing support for their ‘myth-busting’ aim. They suggest that Wolodymir V. Petryshyn, one-time Professor at Rutgers University, killed his wife with a hammer because he discovered a mistake in his book ‘Generalized Topological Degree and Semi-Linear Equations’. His perfectionism, they suggest, drove him to insanity! They go on to note that to a fellow mathematician this is in some degree understandable! Hmm … They also tell of the French mathematician André Bloch, who won the Becquerel Prize for an important discovery in the theory of univalent analytic functions of a complex variable. Near the end of the FirstWorldWar he killed his brother, his uncle and his aunt. Declared insane he was sent to the Charenton Mental Hospital where, each day for decades, he sat in the same corner of a corridor of the hospital working on mathematical problems!

My first reaction to all this is that it does not do much to persuade me that mathematicians are terribly normal! On second thoughts though, I guess they are just saying that mathematicians are as mad as the rest of us!

The authors go on to consider gender bias in mathematics (though limited mainly to academic research mathematics and teachers) and to suggest that requiring a pass in school mathematics should not be a condition of university entry for all (non-mathematics) students.

Because the book is largely anecdotal it is difficult to know how much ‘cherry-picking’ the authors have done in their attempt to make their case. I found some of their arguments a little weak. However, taken as a glimpse into the idiosyncrasies and motivations of the lives of many research mathematicians and mathematics teachers, the book makes for a fascinating read.

Alan Stevens CMath FIMA
Mathematics Today October 2011

Loving + Hating Mathematics: Challenging the Myths of Mathematical Life can be purchased at Amazon.co.uk