6:59 PM :: Stephen (contact)

Prime numbers and prize money. On May 24, 2000, the Clay Mathematics Institute announced a prize of $1 million to anyone who could solve one of seven famous problems in mathematics. As OxBlog reports, a new result in prime number theory may help point the way to a proof of the Riemann Hypothesis. Yet Josh Chafetz worries that this sort of prize will only delay mathematical progress--giving individual researchers an added incentive not to publish their intermediate results, for fear that another mathematician will then swoop in to complete the proof.

For my money, all sane mathematicians who thought they were within striking distance of the Riemann Hypothesis would have already gone into hiding. (Andrew Wiles, who proved Fermat's Last Theorem, was famously secretive about his work.) The Riemann Hypothesis is one of the most celebrated unproved conjectures in mathematics--it was famous enough a century ago to be included as number 8 on the list of Hilbert's problems. Anyone who solved it would have glory for the ages; the million bucks would only be gravy.

The Clay prizes were never really meant to motivate mathematicians with money. (Would the mathematical community expend substantially more effort if the prize were $1.5 million?) Instead, the prizes were meant to grab the public's attention and to focus research on certain deep questions in mathematics. Over the years, the pursuit of celebrated problems has inspired many important results and new proof techniques, not to mention generations of young mathematicians.

The Clay prizes are just one more way of speeding that process along. Not every list of problems gets a lot of press--not everybody is Hilbert--and along with the dollar signs come an awful lot of outside attention. But as with Hilbert's problems, those actually engaged in the work of seeking solutions are searching for fame, not fortune.