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Mathematics occupies a privileged place among the sciences. It embodies the quintessence of human knowledge, reaching into every field of human endeavor. The frontiers of mathematical understanding evolve today in deep and unfathomable ways. Fundamental advances go hand in hand with discoveries in all fields of science. Technological applications of mathematics underpin our daily life, including our ability to communicate thanks to cryptology and coding theory, our ability to navigate and to travel, our health and well-being, our security, and they also play a central role in our economy. The evolution of mathematics will remain a central to shaping civilization.

To appreciate the scope of mathematical truth challenges the capabilities of the human mind. In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven "Millennium Prize Problems." The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI designated a

$7 million prize fundfor the solution to these problems, with$1 millionallocated to each. A leading specialist in the domain in question has formulated each problem. The rules for the award of the prize have been recommended by the Scientific Advisory Board of the CMI, and approved by the Directors.During the Millennium Meeting held on May 24, 2000 at the Collège de France, Timothy Gowers presented a lecture entitled "The Importance of Mathematics," aimed for the general public, while John Tate and Michael Atiyah spoke on the problems. One hundred years earlier, on August 8, 1900, David Hilbert delivered his famous lecture about open mathematical problems at the second International Congress of Mathematicians in Paris. This influenced our decision to announce the millennium problems as the central theme of a Paris meeting.

The members of these boards have the responsibilitiy to preserve the nature, the integrity, and the spirit of this prize.

Paris, May 24, 2000

EDITORIAL

Values of the abstract: A new set of prizes is an apt celebration of the significance and wonder to be found in pure mathematics.Nature, May 25, Volume 405, 379 (2000)."... All credit, then, to the Clay Mathematics Institute for celebrating the intrinsic value of such challenges.... It's an excellent way for a private foundation to recognize the eternal fascination that mathematics holds for people such as Hardy, and for the rest of us."

A SELECTION OF ARTICLES"Contest boasts $7m worth of problems," by Jocelyn Gecker.

Boston Globe.May 25, 2000. This Associated Press article also appeared in several hundred other US papers."Do the math - for $7 million," by Jeff McDonald,

San Diego Union - Tribune, front page, May 25, 2000."A Million-Dollar Incentive to Solve Some Real Sticklers in Math," by Charles Trueheart.

Washington Post,May 25, 2000andInternational Herald Tribune(Paris), p 1 & 6, May 26, 2000."Is That Your Final Equation?" by Charles Seife.

Science(Washington, DC. Weekly), p 1328-29, volume 288, May 26, 2000."Numbers Man,"

by Anjana Ahuja.The Times,p 5, May 31, 2000."There's gold in them there theorems" by Keay Davidson.

San Francisco Examiner.June 5, 2000 ."Mathematik für Millionen,"

Die Zeit(Hamburg, Germany), Nr. 22, Wissen p 24, 25 Mai 2000.

"Mathématiques, Enigmes du siècle," by Jean-Francois Augereau.Le Monde(Paris), p 1, 25 Mai 2000."Les sept énigmes du millénaire," by Jean-Francois Augereau

. Le Monde, p 28, 25 Mai 2000."Mathématiques: sept questions à 1 million de dollars," by Jean-Francois Augereau.

Le Monde, p 28, 25 Mai 2000."De la géométrie d'Euclide à la localisation par satellite," by Jean-Francois Augereau

. Le Monde, 25 Mai 2000."Mathematicians chase the seven million-dollar proofs," by David Dickson.

Nature,Volume 405, p 383, 25 May 2000."Le jeu des sept casse-tête."

Liberation(Paris), 25 Mai 2000."Sept problèmes de math "capitaux" qui peuvent rapporter gros." Le Bien Public (Dijon), 25 Mai 2000.

"Voulez-vous jouer avec les maths?"

Le Figaro, 25 Mai 2000."Tous les Francais ont la bosse," par Albert Ducrocq.

Le Figaro, 25 Mai 2000."Un enseignement en question," par Yves Miserey.

Le Figaro, 25 Mai 2000."les mathématiciens cherchent à sortir de leur splendide isolement." by Alain Perez.

Les Echos (Paris), 26 Mai 2000."Mathématiques l'exception française," by Jean-François Augereau.

Le Monde. 22 Julliet 2000.

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