Book Review: The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, Volume 50, Number 8

On May 24, 2000, the Clay Mathematics Institute (CMI), inspired by the centenary of the Hilbert Challenge and seeking to put its own stamp on the new century and perhaps beyond, announced awards of one million dollars each for solutions to seven “Millennium Prize Problems” [6]. The problems selected by the CMI were neither new nor concerned with pressing practical matters. Ordinarily the popular press would not have found them newsworthy. But, as the CMI correctly reckoned, seven million dollars concentrates the mind wonderfully. Journalists worldwide reported the story, stirring up so great an interest that the CMI website was quickly overwhelmed. It is reasonable to suppose that most of the fuss was concerned not with the zeros of the Riemann zeta function but with the zeros of the prize fund. The custom of prize problems in mathematics is an old one. The funds have variously come from governments, societies, interested amateurs, and mathematicians themselves. Among the latter, Paul Erdős is no doubt most associated with the practice of placing bounties on obstinate problems. It is reported that $10,000 was his greatest offer, $1,000 the greatest claim on his funds. Several other mathematicians have announced prizes of a comparable size. The £1,500 offered by Thwaites for the solution of the 3x + 1 problem is possibly the best known of these. In 1997 Andrew Beal, a Dallas banker with an interest in number theory, upped the stakes considerably by announcing the Beal Conjecture and Prize, worth $100,000 at the time of this writing. During a relatively brief publicity stunt, the Goldbach Conjecture carried a one million dollar price tag. There have been even more lucrative prize funds. At the time of its endowment, the purchasing power of the most famous of all mathematical prizes, the Wolfskehl Prize for the solution of Fermat’s Last Theorem, came to about 1.7 million dollars (as measured in 1997 currency) [1]. These sums for abstract problems stack up very well against the £20,000 reward (worth more than three million dollars in today’s currency) that the Parliament of England established in 1714 for the invention of the marine chronometer, an instrument Book Review