The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics

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.