# Clay Mathematics Institute

### From Wikipedia, the free encyclopedia

The **Clay Mathematics Institute** (**CMI**) is a private, non-profit foundation, based in Cambridge, Massachusetts. The Institute is dedicated to increasing and disseminating mathematical knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the vision and generosity of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI.

While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including a postdoctoral program (ten Clay Research Fellows are supported each year) and an annual summer school, the proceedings of which are published jointly with the American Mathematical Society.

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## [edit] Governance

The Institute is run according to a standard structure comprising a board of directors that decides on grant-awarding and research proposals, and a scientific advisory committee that oversees and approves the board's decisions. As of February, 2008, the board is made up of members of the Clay family (including Landon Clay), whereas the advisory committee is composed of leading authorities in mathematics, namely Sir Andrew Wiles, Yum-Tong Siu, Richard Melrose, Gregory Margulis, James Carlson,and Simon Donaldson. James Carlson is the current president of CMI.

## [edit] Millennium Prize Problems

The institute is best known for its establishment on May 24, 2000 of the Millennium Prize Problems. These seven problems are considered by CMI to be "important classic questions that have resisted solution over the years". The first person to solve each problem will be awarded $1,000,000 by the CMI. In announcing the prize, CMI drew a parallel to Hilbert's problems, which were proposed in 1900, and had a substantial impact on 20th century mathematics. Of the initial twenty-three Hilbert problems, most of which have been solved, only one (the Riemann hypothesis, formulated in 1859) is one of the seven Millennium Prize Problems.^{[1]}

For each problem, the Institute had a professional mathematician write up an official statement of the problem which will be the main standard by which a given solution will be measured against. The seven problems are:

- P versus NP
- The Hodge conjecture
- The Poincaré conjecture - solved, by Grigori Perelman
- The Riemann hypothesis
- Yang-Mills existence and mass gap
- Navier-Stokes existence and smoothness
- The Birch and Swinnerton-Dyer conjecture

Some of the mathematicians who were involved in the selection and presentation of the seven problems were Atiyah, Bombieri, Connes, Deligne, Fefferman, Milnor, Mumford, Wiles, and Witten.

## [edit] Other awards

### [edit] The Clay Research Award

In recognition of major breakthroughs in mathematical research, the institute has an annual prize - the Clay Research Award. It recipients to date are Manindra Agrawal, Manjul Bhargava, Alain Connes, Nils Dencker, Alex Eskin, Ben Green, Christopher Hacon, Richard Hamilton, Michael Harris,Laurent Lafforgue,Ngo Bao Chau, Gérard Laumon, James McKernan, Oded Schramm, Stanislav Smirnov, Terence Tao, Richard Taylor, Claire Voisin, Andrew Wiles, and Edward Witten.

### [edit] The Olympiad award

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The CMI also offers the Clay Olympiad Scholar Award for the most creative solution to a problem on the United States of America Mathematical Olympiad.

## [edit] Other activities

Besides the Millennium Prize Problems, the Clay Mathematics Institute also supports mathematics via the awarding of research fellowships (which range from two to five years, and are aimed at younger mathematicians), as well as shorter-term scholarships for programs, individual research, and book writing. The Institute also has a yearly Clay Research Award, recognizing major breakthroughs in mathematical research. Finally, the Institute also organizes a number of summer schools, conferences, workshops, public lectures, and outreach activities aimed primarily at junior mathematicians (from the high school to postdoctoral level). CMI publications are available in PDF form at most six months after they appear in print.

## [edit] References

**^**Arthur Jaffe's first-hand account of how this Millennium Prize came about can be read in The Millennium Grand Challenge in Mathematics

- Keith J. Devlin,
*The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time*, Basic Books (October, 2002), ISBN 0-465-01729-0.

*This article incorporates material from Millennium Problems on PlanetMath, which is licensed under the GFDL.*