The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. 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.

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 September 2024, the board is made up of members of the Clay family, whereas the scientific advisory committee is composed of Simon Donaldson, Michael Hopkins, Andrei Okounkov, Gigliola Staffilani, and Andrew Wiles. Martin R. Bridson is the current president of CMI.

The Clay Mathematics Institute has announced that Ishan Levy and Mehtaab Sawhney have been awarded the 2024 Clay Research Fellowships. Both are completing their PhDs at the Massachusetts Institute of Technology and will start their five-year fellowships on July 1, 2024.

The 2024 Clay Research Conference will be held on October 2, 2024, at the Mathematical Institute, University of Oxford. The conference will be accompanied by workshops from September 30 to October 4, 2024. Notable workshops include:

• New Advances in the Langlands Program: Geometry and Arithmetic
• New Frontiers in Probabilistic and Extremal Combinatorics
• The P=W Conjecture in Non Abelian Hodge Theory

Daniel Graham from the University of Surrey won the Gold Medal for Mathematical Sciences at the 2024 STEM for Britain competition for his work on quantum authentication methods.

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 US$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.

For each problem, the Institute had a professional mathematician write up an official statement of the problem, which will be the main standard against which a given solution will be measured. 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 Michael Atiyah, Enrico Bombieri, Alain Connes, Pierre Deligne, Charles Fefferman, John Milnor, David Mumford, Andrew Wiles, and Edward Witten.

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, Tristan Buckmaster, Danny Calegari, Alain Connes, Nils Dencker, Alex Eskin, David Gabai, Ben Green, Mark Gross, Larry Guth, Christopher Hacon, Richard S. Hamilton, Michael Harris, Philip Isett, Jeremy Kahn, Nets Katz, Laurent Lafforgue, Gérard Laumon, Aleksandr Logunov, Eugenia Malinnikova, Vladimir Markovic, James McKernan, Jason Miller, Maryam Mirzakhani, Ngô Bảo Châu, Rahul Pandharipande, Jonathan Pila, Jean-François Quint, Peter Scholze, Oded Schramm, Scott Sheffield, Bernd Siebert, Stanislav Smirnov, Terence Tao, Clifford Taubes, Richard Taylor, Maryna Viazovska, Vlad Vicol, Claire Voisin, Jean-Loup Waldspurger, Andrew Wiles, Geordie Williamson, Edward Witten and Wei Zhang.

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 the postdoctoral level). CMI publications are available in PDF form at most six months after they appear in print.

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

• Official website
• The Millennium Grand Challenge in Mathematics
• Millennium Problems
• Clay Mathematics Institute Online Library Archived 2014-10-07 at the Wayback Machine

This article incorporates material from Millennium Problems on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. 41°49′34.4″N 71°24′54.7″W / 41.826222°N 71.415194°W / 41.826222; -71.415194