Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics.

JOHN DERBYSHIRE

Nearly 150 years ago, Bernhard Riemann posed a deceptively simple question to his peers at the Berlin Academy: Is there a general rule for figuring out how many prime numbers there are up to a given number? Three years ago, the Clay Institute agreed to award a million dollars to the person who can prove Riemann's hypothesis, which states that there is such a general rule. Derbyshire provides the historical background of the Riemann hypothesis and, for mathematically inclined readers, details of efforts to prove it so far. He also explains the impact that any solution to this problem will have on cryptography and other areas. Alternating between telling Riemann's life story and presenting a mathematical primer on the elements of his hypothesis, Derbyshire elegantly explores a vexing topic. Joseph Henry Pr, 2003, 422 p., b&w plates, hardcover, $27.95.