Review by Choice Review
It is at least arguable that, at the beginning of the 1990s, three of the biggest unsolved conjectures in mathematics of some vintage were Fermat's last theorem, the Poincare conjecture, and the Riemann hypothesis. Fermat has been solved (by A. Wiles, and R. Taylor and Wiles), and at this writing (June 2003), Poincare has apparently also been solved (by G. Perelman). This leaves Riemann as one of the very few problems that made Hilbert's famous list of problems for the 20th century and both Steven Smale's and the Clay Mathematics Institute's lists of problems for the 21st century. That Riemann is on all these lists is a tribute to its fundamental nature and to the contributions made by attempts to prove it. Prime Obsession, a highly nontechnical introduction to the problem and its history, is for the mathematically curious and adventurous. The mathematics is leavened with biography, history, and anecdote. Derbyshire, a mathematician and linguist, has made a serious attempt to explain a deep mathematical problem in a way that can be skimmed by mathematicians and lingered over by nonmathematicians. Notes are relegated to the end of the book, and with some effort references can be mined from the notes. ^BSumming Up: Highly recommended. General readers; lower- and upper-division undergraduates. D. Robbins Trinity College (CT)
Copyright American Library Association, used with permission.
Review by Booklist Review
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. Now two new books tackle the Riemann hypothesis. (See also Marcus Du Sautoy's Music of the Primes, reviewed on p.1435). 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. Partly a biography of Riemann, Derbyshire's work presents more technical details about the hypothesis and will probably attract math recreationists, more so than Sabbagh's book. It requires, however, only a college-prep level of knowledge because of its crystalline explanations. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it. Carrying a million-dollar bounty, the hypothesis is the most famous unsolved problem in math today, and interest in it will be both sated and stoked by these able authors. --Gilbert Taylor
From Booklist, Copyright (c) American Library Association. Used with permission.
Review by Library Journal Review
Thanks to a proof by Euclid, mathematicians have known for more than 2000 years that there is no limit to the population of prime numbers; they extend to infinity. However, work continues to be done on the distribution of the primes, and much of that work now centers on efforts to prove the Riemann hypothesis. Bernhard Riemann was a great 19th-century German mathematician who offered in an 1859 paper an admittedly unproven conjecture relating some zero values of a "zeta function" to the distribution of primes. The importance of this abstruse speculation for modern research is demonstrated in a recent online search of Mathematical Reviews for the term "Riemann hypothesis"; 1403 publications were found. Now there are three more books to add to the numerous studies. Derbyshire, a mathematician by training, a member of the Mathematical Association of America, and a novelist (Seeing Calvin Coolidge in a Dream), first takes readers through well-organized mathematical fundamentals in order to give them a good understanding of Riemann's discovery and its consequences. Interspersed with the hardcore math, other chapters profile Reimann the man and trace the history of mathematics in relation to his still-unproven hypothesis. Derbyshire shows how after 150 years, the world's greatest minds still haven't found a solution. Because this book does not sugarcoat complex ideas, readers lacking at least college-level math will be hard-pressed to understand some parts. Still, this volume is highly recommended for academic and larger public libraries as an excellent introduction for nonspecialists. Du Sautoy is the only professional research mathematician among these three authors, but he does not confront his readers with very many equations or other bits of mathematical apparatus. Instead, he offers nicely done verbal descriptions of the essence of the hypothesis and the efforts to prove it. Like Derbyshire, he intersperses items from math history and from the work and interactions of current researchers. Du Sautoy's book has much to offer for most academic and public libraries, especially to readers of very limited math background. Sabbagh (A Rum Affair) has written several books on a variety of topics, not all science-related. His latest emphasizes anecdotes from contemporary mathematicians who have studied Riemann's hypothesis. Indeed, he pays so much attention to a particularly idiosyncratic mathematician, ignored by the two other authors, that in his quest for human-interest material, he seems to lose sight of serious mathematical issues. Sabbagh's discussion of the actual mathematics is not so well organized, and much of it is relegated to a series of appendixes. His book is most useful in giving readers a feel for how research mathematicians live, work, and interrelate in the 21st century. Only libraries seeking comprehensive coverage of mathematics will need to get the Sabbagh work.-Jack W. Weigel, Ann Arbor, MI (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
(c) Copyright Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
