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An engaging, informative, and wryly humorous exploration of one of the great conundrums of all time
In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article giving an answer to a problem that had long puzzled mathematicians. But he didn’t provide a proof. In fact, he said he couldn’t prove it but he thought that his answer was “very probably” true. From the publication of that paper to the present day, the world’s mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann Hypothesis, and so great is the interest in its solution that in 2001 an American foundation put up prize money of $1 million for the first person to demonstrate that the hypothesis is correct.
The hypothesis refers to prime numbers, which are in some sense the atoms from which all other numbers are constructed, and seeks to explain where every single prime to infinity will occur. Riemann’s idea—if true—would illuminate how these numbers are distributed, and if false will throw pure mathematics into confusion.
Karl Sabbagh meets some of the world’s mathematicians who spend their lives thinking about the Riemann Hypothesis, focusing attention in particular on “Riemann’s zeros,” a series of points that are believed to lie in a straight line, though no one can prove it. Accessible and vivid, The Riemann Hypothesis is a brilliant explanation of numbers and a profound meditation on the ultimate meaning of mathematics.
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Karl Sabbagh is the author of six books, most recently A Rum Affair (FSG, 2000). He lives near Stratford-upon-Avon in England.
With Fermat's Last Theorem proved, the Riemann Hypothesis has become math's most glamorous unsolved problem, and has spawned a growing literature seeking to explain it to lay readers. Unfortunately, this curious genre is overshadowed by the fact that the hypothesis itself is incomprehensible to anyone without a Ph.D. Sabbagh, author of A Rum Affair, struggles manfully with this problem, and gives impressively lucid explanations of such preliminary subjects as prime numbers, logarithms, infinite series, algebraic equations and matrices. But even with all this background, the hypothesis remains such an opaque abstraction that, at one typically baffling juncture, the author throws up his hands and instructs readers to either "sign up for a few months of complex analysis and number theory, and then pick up the book again in a year or two" or else just "take it on trust." To help elucidate the material, Sabbagh includes many lengthy excerpts from interviews with mathematicians, who, he claims, "see truths with a clarity that is sometimes breathtaking," but these rambling, obscure commentaries ("what's going to probably happen for the real Riemann Hypothesis is there's going to be another blob and there's going to be a function that turns the blob into itself") are not necessarily very helpful. Sabbagh can be a gifted expositor of mathematics when he sticks to more tractable topics, but when it comes to the Riemann Hypothesis, he offers readers veneration instead of understanding. B&w illustrations and graphs.
Copyright 2003 Reed Business Information, Inc.
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