Paris
Seven as yet unsolved problems that could provide keys to the mathematics of the 21st century are the focus of a millennium challenge offering millions of dollars in prizes for their resolution.
The Clay Mathematics Institute, a private foundation based in Cambridge, Massachusetts, that promotes maths, is proposing to pay $1 million for each correct answer.
The "seven problems of the millennium" were presented at a conference in Paris last week by Landon Clay, the institute's founder, and members of its scientific committee. They are Sir Andrew Wiles, who solved Fermat's last theorem in 1994 and is professor of mathematics at Princeton, Alain Connes of the College de France and the Institut des Hautes Etudes Scientifiques, and Harvard professor of mathematics, Arthur Jaffe.
The meeting, held at the College de France in Paris, marked the centenary of the second international congress of mathematicians, also held in Paris, at which German mathematician David Hilbert presented 23 unsolved problems covering all mathematical fields, which he had formulated to demonstrate the most promising avenues for 20th-century research.
The prizes will focus attention on finding answers to important classic unanswered questions.
Only one of Hilbert's original problems remains unresolved, the Riemann hypothesis, which is in the seven currently under scrutiny. Its proof would shed light on many mysteries about the distribution of prime numbers, "still regarded as the most important problem in pure mathematics", according to Professor Connes.
The other six problems are: P versus NP; the Poincare Conjecture; the Hodge Conjecture; the Birch and Swinnerton-Dyer Conjecture; the Navier-Stokes Equations; and the Yang-Mills Theory.