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 dedicated to increasing and disseminating mathematical 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) an ...
, 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.
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 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. , the board is made up of members of the Clay family, whereas the advisory committee is composed of Simon Donaldson, Michael Hopkins, Carlos Kenig, Andrei Okounkov, and Andrew Wiles. 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 p ...
(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 ...
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 ...
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 p ...
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
Yves Benoist is a French mathematician, known for his work on group dynamics on homogeneous spaces. He is currently a Senior Researcher (Directeur de Recherche) of CNRS at the University of Paris-Sud.
In 1990 Benoist proved a longstanding open co ...
Gérard Laumon
Gérard Laumon (; born 1952) is a French mathematician, best known for his results in number theory, for which he was awarded the Clay Research Award.
Life and work
Laumon studied at the École Normale Supérieure and Paris-Sud 11 University, Or ...
, 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 ...
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, enumerative ...
,
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
Jean-François Quint is a French mathematician, specializing in dynamical systems theory for homogeneous spaces.
He studied at the École normale supérieure de Lyon and then received his Ph.D. from École Normale Supérieure (ENS) in Paris unde ...
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 ...
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 Taub ...
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 he ...
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.
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.
References
* Keith J. Devlin, ''The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time'', Basic Books (October, 2002), .