The Clay Mathematics Institute (CMI) is a private,

non-profit A nonprofit organization (NPO) or non-profit organisation, also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and operated for a collective, public or social benefit, in co ...

foundation Foundation may refer to: * Foundation (nonprofit), a type of charitable organization ** Foundation (United States law), a type of charitable organization in the U.S. ** Private foundation, a charitable organization that, while serving a good cause ...

dedicated to increasing and disseminating

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

knowledge. Formerly based in

Peterborough, New Hampshire Peterborough is a town in Hillsborough County, New Hampshire, United States. The population was 6,418 at the 2020 census. The main village, with 3,090 people at the 2020 census, is defined as the Peterborough census-designated place (CDP) and ...

, the corporate address is now in

Denver, Colorado Denver () is a consolidated city and county, the capital, and most populous city of the U.S. state of Colorado. Its population was 715,522 at the 2020 census, a 19.22% increase since 2010. It is the 19th-most populous city in the Unit ...

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

Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

, 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 Landon T. Clay (born Landon Thomas Clay, 1926 – July 29, 2017) was an American businessman and founder of the Clay Mathematics Institute. He died on July 29, 2017 at his home in Peterborough, New Hampshire. Biography Clay graduated from Harvar ...

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

mathematician

Arthur Jaffe Arthur Michael Jaffe (; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science. Education and career ...

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 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. According ...

, it carries out a wide range of activities, including 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). The ultimate goal of a postdoctoral research position is to p ...

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. , the board is made up of members of the Clay family, whereas the 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 (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He i ...

, Michael Hopkins,

Carlos Kenig Carlos Eduardo Kenig (born November 25, 1953, in Buenos Aires, Argentina) is an Argentine American mathematician and Louis Block Distinguished Service Professor in the Department of Mathematics at the University of Chicago. He is known for his wor ...

Andrei Okounkov Andrei Yuryevich Okounkov (russian: Андре́й Ю́рьевич Окунько́в, ''Andrej Okun'kov'') (born July 26, 1969) is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematic ...

, and

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, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...

. Martin R. Bridson 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 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 pro ...

, 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 ...

(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 by which a given solution will be measured against. The seven problems are: *

P versus NP The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term ''quickly'', used abov ...

* 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 conjectu ...

* The

Poincaré conjecture In the mathematics, mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the Characterization (mathematics), characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dim ...

—solved, by

Grigori Perelman Grigori Yakovlevich Perelman ( rus, links=no, Григорий Яковлевич Перельман, p=ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman, a=Ru-Grigori Yakovlevich Perelman.oga; born 13 June 1966) is a Russian mathemati ...

* The

Yang–Mills existence and mass gap The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 f ...

* 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 an ...

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, Milan) 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 Mathema ...

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

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 Crafoord Pr ...

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 contrib ...

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 t ...

, and

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...

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 Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Education and career Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and ...

Manindra Agrawal Manindra Agrawal (born 20 May 1966) is a professor at the Department of Computer Science and Engineering and the Deputy Director at the Indian Institute of Technology, Kanpur. He was also the recipient of the first Infosys Prize for Mathematics ...

, 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 Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory. Educ ...

, Nils Dencker, Alex Eskin,

David Gabai David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects. Biography David Ga ...

, Ben Green, Mark Gross,

Larry Guth Lawrence David Guth (born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. Education and career Guth graduated from Yale in 2000, with BS in mathematics. In 2005, he got his PhD in mathematics from the Massach ...

Christopher Hacon Christopher Derek Hacon (born 14 February 1970) is a mathematician with British, Italian and US nationalities. He is currently distinguished professor of mathematics at the University of Utah where he holds a Presidential Endowed Chair. His res ...

, 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 prod ...

Nets Katz Nets Hawk Katz is the IBM Professor of Mathematics at the California Institute of Technology. He was a professor of Mathematics at Indiana University Bloomington until March 2013. Katz earned a B.A. in mathematics from Rice University in 1990 at t ...

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 analysis, and in particular proved the Langlands conjectures for the automorphism ...

, 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 of ...

James McKernan James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013. Education McKernan was educated at the Campion School, Hornchurch, and Tr ...

, Jason Miller,

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

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 Rahul Pandharipande (born 1969) is a mathematician who is currently a professor of mathematics at the Swiss Federal Institute of Technology Zürich (ETH) working in algebraic geometry. His particular interests concern moduli spaces, enumerativ ...

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. Education Pila earned his bachelor's degree at ...

, Jean-François Quint,

Peter Scholze Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He ha ...

Oded Schramm Oded Schramm ( he, עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory ...

, Scott Sheffield, Bernd Siebert,

Stanislav Smirnov Stanislav Konstantinovich Smirnov (russian: Станисла́в Константи́нович Cмирно́в; born 3 September 1970) is a Russian mathematician currently working at the University of Geneva. He was awarded the Fields Medal in ...

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

Clifford Taubes Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taube ...

, Richard Taylor,

Maryna Viazovska Maryna Sergiivna Viazovska ( uk, Марина Сергіївна Вязовська, ; born 2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is full professor and Chair of Number Theory at the Institute of M ...

, Vlad Vicol,

Claire Voisin Claire Voisin (born 4 March 1962) is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and holds the chair of Algebraic Geometry at the Collège de France. Work She is noted for ...

Jean-Loup Waldspurger Jean-Loup Waldspurger (born July 2, 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal group ...

, 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 __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

, 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. Elementary episodes#Season 2 (2013–14), Season 2, Episode 2) mentions the Clay Mathematics Institute in reference to their involvement in the

P versus NP problem The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term ''quickly'', used abov ...

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