The Riemann hypothesis is a question in the field of number theory that is perhaps the most famous unsolved problem in mathematics. First posed by the great mathematician Bernhard Riemann in 1859, it has captured the imagination of generations of mathematicians. David Hilbert, one of the most important mathematicians of the early twentieth century, once said that if he could look 500 years into the future, his first question would be, "Has someone solved the Riemann hypothesis?" In 1900, at a meeting of the International Congress of Mathematicians in Paris, Hilbert placed the Riemann hypothesis on his famous list of the most important mathematics problems for the next century, a list that has set the course of twentieth-century mathematics. And in April 2000, the Clay Mathematics Institute (in Paris, as a tribute to Hilbert) announced that the Riemann hypothesis is to be one of its seven Millennium Prize Problems, whose...