The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics - Hardcover

Sabbagh, Karl

Hardcover

ISBN 10: 0374250073 ISBN 13: 9780374250072

Publisher: Farrar, Straus and Giroux, 2003

Synopsis

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.

About this title

About the Author

Karl Sabbagh is the author of six books, most recently A Rum Affair (FSG, 2000). He lives near Stratford-upon-Avon in England.

Reviews

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.

Bernhard Riemann would make any list of the greatest mathematicians ever. In 1859, he proposed a formula to count prime numbers that has defied all attempts to prove it true.This new book tackles the Riemann hypothesis. Sabbagh introduces contemporary mathematicians who are working on the problem, one of whom claims, to professional skepticism, to be on the verge of vindicating the hypothesis. Another is working away in search of a single counterexample that would refute it. Such pursuits, which often consume mathematicians' entire lives, may seem incomprehensible or even pointless to the innumerate--but that's a prejudice brilliantly dispelled through Sabbagh's interviews, which are interwoven with his not overly numerical tour of the hypothesis. The drive and competitiveness of mathematicians clearly emerge from Sabbagh's narrative.

Gilbert Taylor
Copyright © American Library Association. All rights reserved

Edition details

• Publisher: Farrar, Straus and Giroux
• Publication date: 2003
• ISBN 10: 0374250073
• ISBN 13: 9780374250072
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 304