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The Riemann hypothesis: the greatest unsolved problem in mathematics. (English) Zbl 1049.01017

New York, NY: Farrar Straus & Giroux (ISBN 0-374-25007-3). viii, 304 p. (2003).
This book is not intended particularly for mathematicians, but rather, it aims to show the layman what mathematicians are like, by watching them working on one of their favourite problems. Thus the book is full of interesting stories about mathematicians, and of quotations revealing something of how they think.
Although the Riemann zeta-function is eventually “defined”, this is only after a full discussion of imaginary numbers, and how one might think about them. Inevitably the necessary over-simplifications have led to statements that are incorrect, strictly speaking. However any reader should get some idea of the Riemann hypothesis, no matter how poor their previous mathematical education. Nonetheless the book does nothing to dispel the idea that mathematics is only for the chosen few and, if anything, encourages the notion.
The human story is dominated by an account of Louis de Branges and his work on the Riemann hypothesis, to which the author devotes four chapters and an appendix. The reviewer found this rather depressing reading, and in total contrast to the the enjoyment and satisfaction most of us derive from our work.
In conclusion then, there is no real mathematics here, but the outsider will get a reasonable impression of what it is like to work on the Riemann hypothesis from this book.

MSC:

01A65 Development of contemporary mathematics
01A80 Sociology (and profession) of mathematics
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses

Biographic References:

de Branges, Louis
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