Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematicians for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann Hypothesis. They speak of it in awed terms, and consider it to be an even more difficult problem than Fermat's Last Theorem (which was finally proved by Andrew Wiles in 1995).
In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world-class mathematicians who spend their lives working on the hypothesis—many paying particular attention to "Riemann's zeros," a series of points that are believed to lie in a straight line, though no one can prove it—and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities.
Wryly humorous, lively, accessible, and comprehensive, The Riemann Hypothesis is at once a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession, and a profound meditation on the ultimate meaning of mathematics.
"[This book presents] to the non-mathematician what is indeed the greatest unsolved problem in pure mathematics, describing its history, the men who have contributed to its understanding, and their motivation for tackling it . . . Lively, full of anecdotes, and fun to read. The reader will find in [this book] a picture not only of the Riemann hypothesis, but also of the strange world of mathematicians."—Enrico Bombieri, The American Scientist
"Sabbagh is a producer and writer for the BBC, and he brings that perspective to his writing. He tells a different set of stories, sometimes looking at mathematics from the outside. His book is full of people talking about R.H.—what it means and how they think about it—and about themselves and their colleagues."—James Alexander, The New York Times Book Review
"The Riemann Hypothesis provides ample hand-holding for anyone who pales at the sight of symbols or can't quite distinguish an asymptote from a hole in the graph."—Kristin Leutwyler, Scientific American
"Gracefully written . . . The story of the search for a proof draws you along as if it were a detective thriller."—The Guardian
"Rewarding . . . [Sabbagh tells] a mathematical story in engaging human terms."—Graham Farmelo, The Sunday Telegraph
"Full of interesting stories about mathematicians, and of quotations revealing something of how they think . . . Any reader should get some idea of the Riemann hypothesis, no matter how poor their previous mathematical education . . . The outsider will get a reasonable impression of what it is like to work on the Riemann hypothesis from this book."—D. R. Heath-Brown, Mathematical Reviews
"Sabbagh hits the spot . . . The story of the quest for Riemann's proof is an insider's view of the highly competitive, fascinating world of mathematics."—John Cornwell, The Sunday Times (London)
"An engaging and often enthralling account of mathematicians and their continuing search for the holy grail of prime number theory. A pleasurable and painless read for anyone intrigued by numbers."—Ian Stewart, author of Nature's Numbers and Flatterland
"An accessible account of the problem every mathematician would most want to solve, why they would want to solve it, and why it would matter."—Keith Devlin, Stanford University, author of The Math Gene
"In the summer of 1900, the great David Hilbert, still in his thirties, stood on a rostrum in Paris and announced to the second International Congress of Mathematicians the twenty-three most intriguing 'good' problems of the day: each, if solved, would move the field on in a remarkable way. Seven were cracked shortly after, in Hilbert's lifetime. Two more, including Fermat's Last Theorem, fell in 1970 and 1996. The so-called Riemann Hypothesis, proposed by the German Georg Friedrich Bernhardt Riemann, belongs to the remainder of this extraordinary list: the tortuous, often reputation-destroying problems that have obsessed and defeated generations of the best mathematicians ever since. The Clay Institute of Mathematics has offered $1 million for the solution . . . Sabbagh introduces the theorem with deference, explains it with panache, and refers the more grossly ill-educated to the first of six patient, though sometimes rather optimistic, appendices."—Alexander Masters, The Times Literary Supplement
"Non-mathematician Sabbagh proves himself a very good listener [in these] conversations with two-dozen formidable researchers on recent developments concerning mathematics' most celebrated unsolved problem. He surmounts the dilemma of keeping neophytes engaged without making experts wince by letting experts speak for themselves; they prove both eager to and capable of making the larger world understand what they do. Though the curious, serious student who seeks to understand the Riemann hypothesis will certainly have to consult a careful, elementary monograph . . . such a book will generally offer only a view frozen in time decades ago; Sabbagh's up-to-the-minute easy read provides a pleasant foil . . . Highly recommended. General readers; lower- and upper-division undergraduates."—D. V. Feldman, University of New Hampshire, Choice