First Clay Mathematics Institute Millennium Prize Announced
Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman
March 18, 2010. The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. The citation for the award reads:
The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.
The Millennium Prize Problems
In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.
The prizes were announced at a meeting in Paris, held on May 24, 2000 at the Collège de France. Three lectures were presented: Timothy Gowers spoke on The Importance of Mathematics; Michael Atiyah and John Tate spoke on the problems themselves.
The seven Millennium Prize Problems were chosen by the founding Scientific Advisory Board of CMI, which conferred with leading experts worldwide. The focus of the board was on important classic questions that have resisted solution for many years.
Follwing the decision of the Scientific Advisory Board, the Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to the solution of each problem.
It is of note that one of the seven Millennium Prize Problems, the Riemann hypothesis, formulated in 1859, also appears in the list of twenty-three problem discuss in the address given in Paris by David Hilbert on August 9, 1900.
The rules for the award of the prize have the endorsement of the CMI Scientific Advisory Board and the approval of the Directors. The members of these boards have the responsibility to preserve the nature, the integrity, and the spirit of this prize.
Please send inquiries regarding the Millennium Prize Problems to admin@claymath.org.
Riemann Hypothesis
Formulated in his 1859 paper, the Riemann hypothesis in effect says that the primes are distributed as regularly as possible given their seemingly random occurrence on the number line. Riemann's work gave an 'explicit' formula for the number of primes less than x in terms of the zeros of the zeta function. The first term is x/log(x). The Riemann hypothesis is equivalent to the assertion that other terms are bounded by a constant times log(x) times the square root of x. The Riemann hypothesis asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2.
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