The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

knowledge. Formerly based in

Peterborough, New Hampshire Peterborough is a New England town, town in Hillsborough County, New Hampshire, Hillsborough County, New Hampshire, United States. The population was 6,418 at the 2020 United States census, 2020 census. The main village, with 3,090 people at the ...

, the corporate address is now in

Denver Denver ( ) is a List of municipalities in Colorado#Consolidated city and county, consolidated city and county, the List of capitals in the United States, capital and List of municipalities in Colorado, most populous city of the U.S. state of ...

, Colorado. CMI's scientific activities are managed from the President's office in

Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...

, 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 Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...

mathematician Arthur Jaffe was the first president of CMI. While the institute is best known for its

Millennium Prize Problems The Millennium Prize Problems are seven well-known complex mathematics, mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem ...

, it carries out a wide range of activities, including conferences, workshops, summer schools, and a

postdoctoral A postdoctoral fellow, postdoctoral researcher, or simply postdoc, is a person professionally conducting research after the completion of their doctoral studies (typically a PhD). Postdocs most commonly, but not always, have a temporary acade ...

program supporting Clay Research Fellows.

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. , the board is made up of members of the Clay family, whereas the scientific advisory committee is composed of

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth function, smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähl ...

, Michael Hopkins, Andrei Okounkov, Gigliola Staffilani,

Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Ferma ...

, and Martin R. Bridson. Bridson is the current president of CMI.

2024 updates

2024 Clay Research Fellows

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.

2024 Clay Research Conference and Workshops

The 2024 Clay Research Conference was held on October 2, 2024, at the Mathematical Institute, University of Oxford. The conference was 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

Awards and recognitions

Daniel Graham from the

University of Surrey The University of Surrey is a public research university in Guildford, Surrey, England. The university received its Royal Charter, royal charter in 1966, along with a Plate glass university, number of other institutions following recommendations ...

won the Gold Medal for Mathematical Sciences at the 2024 STEM for Britain competition for his work on quantum authentication methods.

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 US$1,000,000 by the CMI. In announcing the prize, CMI drew a parallel to

Hilbert's problems Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the pr ...

, 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 In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

(formulated in 1859) is included in the seven Millennium Prize Problems.Arthur Jaffe's first-hand account of how this Millennium Prize came about can be read i
The Millennium Grand Challenge in Mathematics
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 P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved. Here, "quickly" means an algorithm exists that ...

* The

Hodge conjecture In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. In simple terms, the Hodge conjectur ...

* The

Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured b ...

– solved, by

Grigori Perelman Grigori Yakovlevich Perelman (, ; born 13June 1966) is a Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his ...

* The

* Yang–Mills existence and mass gap * Navier–Stokes existence and smoothness * The

Birch and Swinnerton-Dyer conjecture In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory ...

Some of the mathematicians who were involved in the selection and presentation of the seven problems were

Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...

Enrico Bombieri Enrico Bombieri (born 26 November 1940) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently professor emeritus in the School of Mathematics ...

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He was a professor at the , , Ohio State University and Vanderbilt University. He was awar ...

Pierre Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoor ...

Charles Fefferman Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contribu ...

John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded th ...

, and

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

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 Manindra Agrawal (born 20 May 1966) is an Indian computer scientist and director of Indian Institute of Technology, Kanpur. He is also a professor at the Department of Computer Science and Engineering at the Indian Institute of Technology, Ka ...

, Yves Benoist,

Manjul Bhargava Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds A ...

, Tristan Buckmaster, Danny Calegari,

, Nils Dencker, Alex Eskin,

David Gabai David Gabai is an American mathematician and the Princeton University Department of Mathematics, Hughes-Rogers Professor of Mathematics at Princeton University. His research focuses on low-dimensional topology and hyperbolic geometry. Biography ...

, Ben Green, Mark Gross, Larry Guth, Christopher Hacon, Richard S. Hamilton, Michael Harris, Philip Isett,

Jeremy Kahn Jeremy Adam Kahn (born October 26, 1969) is an American mathematician. He works on hyperbolic geometry, Riemann surfaces and complex dynamics. Education Kahn grew up in New York City and attended Hunter College High School. He was a child prodi ...

, Nets Katz,

Laurent Lafforgue Laurent Lafforgue (; born 6 November 1966) is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and Mathematical analysis, analysis, and in particular proved the Langlands conjecture ...

, Gérard Laumon, Aleksandr Logunov, Eugenia Malinnikova,

Vladimir Markovic Vladimir Marković is a Professor of Mathematics at University of Oxford. He was previously the John D. MacArthur Professor at the California Institute of Technology (2013–2020) and Sadleirian Professor of Pure Mathematics at the University ...

, James McKernan, Jason Miller,

Maryam Mirzakhani Maryam Mirzakhani (, ; 12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller space, Teichmüller theory, hyperbolic geometry, ergodic the ...

Ngô Bảo Châu Ngô Bảo Châu (, born June 28, 1972) is a Vietnamese-French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad). He is the first Vie ...

, Rahul Pandharipande,

Jonathan Pila Jonathan Solomon Pila (born 1962) FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: is an Australian mathematician at the University of Oxford University of Melbourne in 1984. He was awarded ...

, Jean-François Quint, Peter Scholze, Oded Schramm, Scott Sheffield, Bernd Siebert, Stanislav Smirnov, Terence Tao, Clifford Taubes, Richard Taylor,

Maryna Viazovska Maryna Sergiivna Viazovska (, ; born 2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is a full professor and Chair of Number Theory Number theory is a branch of pure mathematics devoted primarily to ...

, Vlad Vicol, Claire Voisin, Jean-Loup Waldspurger,

, Geordie Williamson,

and Wei Zhang.

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

References

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

External links

Official website

The Millennium Grand Challenge in Mathematics

Millennium Problems

Clay Mathematics Institute Online Library
{{authority control Organizations established in 1998 Mathematical institutes Research institutes in Colorado 1998 establishments in New Hampshire Organizations based in Denver