Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. 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 sponsorship 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 currently), conferences, workshops, and summer schools.

Governance

The institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of directors that oversees and approves the committee's decisions. As of January 2015, the board is made up of members of the Clay family, whereas the advisory committee is composed of leading authorities in mathematics, namely Sir Andrew Wiles, Michael Hopkins, Carlos Kenig, Andrei Okounkov, and Simon Donaldson. Nicholas Woodhouse is the current president of CMI.

Millennium Prize Problems

The institute is best known for establishing the Millennium Prize Problems on May 24, 2000. These seven problems are considered by CMI to be "important classic questions that have resisted solution over the years." For each problem, the first person to solve it 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 23 Hilbert problems, most of which have been solved, only the Riemann hypothesis (formulated in 1859) is included in 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^[2]
• 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.

Other awards

The Clay Research Award

In recognition of major breakthroughs in mathematical research, the institute has an annual prize - the Clay Research Award. Its recipients to date are Ian Agol, Manindra Agrawal, Yves Benoist, Manjul Bhargava, Danny Calegari, Alain Connes, Nils Dencker, Alex Eskin, David Gabai, Ben Green, Larry Guth, Christopher Hacon, Richard S. Hamilton, Michael Harris, Jeremy Kahn, Nets Katz, Laurent Lafforgue, Gérard Laumon, Vladimir Markovic, James McKernan, Maryam Mirzakhani, Ngô Bảo Châu, Rahul Pandharipande, Jonathan Pila, Jean-François Quint, Peter Scholze, Oded Schramm, Stanislav Smirnov, Terence Tao, Clifford Taubes, Richard Taylor, Claire Voisin, Jean-Loup Waldspurger, Andrew Wiles, and Edward Witten.

Other activities

Besides the Millennium Prize Problems, the Clay Mathematics Institute 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 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.

• The Episode of Elementary ( Season 2, Episode 2) entitled Solve for X mentions the Clay Mathematics Institute in reference to their involvement in the P versus NP Problem.

References

1. ↑ Arthur Jaffe's first-hand account of how this Millennium Prize came about can be read in The Millennium Grand Challenge in Mathematics.
2. ↑ "Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman" (PDF) (Press release). Clay Mathematics Institute. March 18, 2010. Retrieved 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. 

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

External links

• The Clay Mathematics Institute
• The Millennium Grand Challenge in Mathematics
• The Millennium Prize Problems
• The Clay Mathematics Institute Online Library

This article incorporates material from Millennium Problems on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

Coordinates: 41°49′34.4″N 71°24′54.7″W / 41.826222°N 71.415194°W / 41.826222; -71.415194