Is That Your Final Equation?

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Math's "most wanted" problems now have prices on their heads. In Paris this week, mathematicians unveiled a list of seven of the world's most intractable math problems--and announced a prize of $1 million each for their solutions.

The proud sponsor of the biggest math prizes ever is the Clay Mathematics Institute (CMI) of Cambridge, Massachusetts. Founded 2 years ago by mutual-fund magnate Landon Clay, the institute has a substantial endowment (CMI president Arthur Jaffe wouldn't name a figure) devoted to advancing mathematical knowledge. "If next year every one of these problems were solved, it wouldn't be a problem," Jaffe says. "It would be a surprise."

Surprise is an understatement, as the seven problems are perhaps the deepest, toughest, and most important unsolved questions in all fields of mathematics. The so-called "P versus NP" problem comes from logic and computer science; the "Poincare Conjecture" is from topology, the study of shapes; problems related to the Yang-Mills and to the Navier-Stokes equations are inspired by physics; the "Birch-Swinnerton-Dyer conjecture" and "Hodge conjecture" both deal with abstract geometric ideas; and the Riemann Hypothesis is perhaps the granddaddy of all math problems, dealing with fields as diverse as prime numbers and geometry.

"It will certainly spur activity; whether it's good or bad, I don't know," says mathematician John Milnor of the State University of New York, Stony Brook. "I hope it doesn't have the effect of making mathematics as competitive as in other fields, where scientists live and die for the Nobel prize," he says. Anyone can submit a solution (see www.claymath.org), but entries must have been published in a peer-reviewed journal.

--CHARLES SEIFE

Posted in Math