Clay Mathematics Institute
Encyclopedia
The Clay Mathematics Institute (CMI) is a private, non-profit foundation
, based in Cambridge
, Massachusetts
. 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 vision and generosity of Boston businessman Landon T. Clay
and his wife, Lavinia D. 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 each year) and an annual summer school, the proceedings of which are published jointly with the American Mathematical Society
.
, Yum-Tong Siu
, Richard Melrose, Gregory Margulis, James Carlson, and Simon Donaldson
. James Carlson is the current president of CMI.
, which were proposed in 1900, and had a substantial impact on 20th century mathematics. Of the initial twenty-three 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 by which a given solution will be measured against. The seven problems are:
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
.
, Manjul Bhargava
, Alain Connes
, Nils Dencker, Alex Eskin, Ben
Green, Christopher Hacon
, Richard Hamilton
, Michael Harris
, Laurent Lafforgue
, Ngô Bảo Châu
, Gérard Laumon
, James McKernan
, Oded Schramm
, Stanislav Smirnov
, Terence Tao
,
Richard Taylor
, Claire Voisin
, Andrew Wiles
and Edward Witten
.
.
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 also 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.
Foundation (charity)
A foundation is a legal categorization of nonprofit organizations that will typically either donate funds and support to other organizations, or provide the source of funding for its own charitable purposes....
, based in Cambridge
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
, Massachusetts
Massachusetts
The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...
. The Institute is dedicated to increasing and disseminating mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the vision and generosity of Boston businessman Landon T. Clay
Landon T. Clay
Landon T. Clay is an American businessman and founder of the Clay Institute.Clay graduated from Harvard in 1950 in English and was chair of Eaton Vance and a director of ADE Corporation.-References:...
and his wife, Lavinia D. Clay. Harvard
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
mathematician Arthur Jaffe
Arthur Jaffe
Arthur Jaffe is an American mathematical physicist and a professor at Harvard University. Born on December 22, 1937 he attended Princeton University as an undergraduate obtaining a degree in chemistry, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics...
was the first president of CMI.
While the institute is best known for its Millennium Prize Problems
Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of September 2011, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize being awarded by the institute...
, it carries out a wide range of activities, including a postdoctoral program (ten Clay Research Fellows are supported each year) and an annual summer school, the proceedings of which are published jointly with the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.
Governance
The Institute is run according to a standard structure comprising a board of directors that decides on grant-awarding and research proposals, and a scientific advisory committee that oversees and approves the board's decisions. , 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 WilesAndrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
, Yum-Tong Siu
Yum-Tong Siu
Yum-Tong Siu is the William Elwood Byerly Professor of Mathematics at Harvard University.Dr. Siu has been a prominent figure in the mathematics of several complex variables for a quarter-century. He has mastered techniques at the interfaces between complex variables, differential geometry, and...
, Richard Melrose, Gregory Margulis, James Carlson, and Simon Donaldson
Simon Donaldson
Simon Kirwan Donaldson FRS , is an English mathematician known for his work on the topology of smooth four-dimensional manifolds. He is now Royal Society research professor in Pure Mathematics and President of the Institute for Mathematical Science at Imperial College London...
. James Carlson 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 problemsHilbert's problems
Hilbert's problems form a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics...
, which were proposed in 1900, and had a substantial impact on 20th century mathematics. Of the initial twenty-three Hilbert problems, most of which have been solved, only the Riemann hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
(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 by which a given solution will be measured against. The seven problems are:
- P versus NP
- The Hodge conjectureHodge conjectureThe Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they...
- The Poincaré conjecturePoincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
- solved, by Grigori PerelmanGrigori PerelmanGrigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture... - The Riemann hypothesisRiemann hypothesisIn mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
- Yang–Mills existence and mass gapYang–Mills existence and mass gapIn mathematics, the Yang-Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute which has offered a prize of US$1,000,000 to a person solving it....
- Navier–Stokes existence and smoothness
- The Birch and Swinnerton-Dyer conjectureBirch and Swinnerton-Dyer conjectureIn mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
.
Some of the mathematicians who were involved in the selection and presentation of the seven problems were Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
, Bombieri, Connes, Deligne, Fefferman, Milnor, Mumford
David Mumford
David Bryant Mumford is an American mathematician known for distinguished 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 the National Medal of Science...
, Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
, and Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
.
The Clay Research Award
In recognition of major breakthroughs in mathematical research, the institute has an annual prize - the Clay Research Award. It recipients to date are Manindra AgrawalManindra Agrawal
Manindra Agrawal is a professor at the department of computer science and engineering and the Dean of Resource, Planning and Generation at the Indian Institute of Technology, Kanpur. He is also the recipient of the first Infosys Prize for Mathematics.-Early life:Manindra Agrawal obtained a...
, Manjul Bhargava
Manjul Bhargava
Manjul Bhargava is a Canadian-American mathematician of Indian origin. He is the R. Brandon Fradd Professor of Mathematics at Princeton University...
, Alain Connes
Alain Connes
Alain Connes is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.-Work:...
, Nils Dencker, Alex Eskin, Ben
Green, Christopher Hacon
Christopher Hacon
Christopher Derek Hacon is a mathematician with British, Italian and US nationalities. In 2009 he was awarded the Cole Prize for outstanding contribution to algebra, along with James McKernan. He was also awarded the Clay Research Award...
, Richard Hamilton
Richard Hamilton (professor)
Richard Streit Hamilton is Davies Professor of mathematics at Columbia University.He received his B.A in 1963 from Yale University and Ph.D. in 1966 from Princeton University. Robert Gunning supervised his thesis...
, Michael Harris
Michael Harris
Michael Harris is an award-winning Canadian author, investigative journalist, and radio personality who hosts an afternoon radio talk show, "Michael Harris Live", on Ottawa-based CFRA, and was a columnist for The Ottawa Sun newspaper until March 2011.Born in Toronto, Ontario, to Audrey McDonald ...
, Laurent Lafforgue
Laurent Lafforgue
Laurent Lafforgue is a French mathematician.He won 2 silver medals at International Mathematical Olympiad in 1984 and 1985....
, Ngô Bảo Châu
Ngo Bao Chau
Ngô Bảo Châu is a Vietnamese and 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 Vietnamese to receive the Fields Medal.- Biography :Chau was born in 1972, the...
, Gérard Laumon
Gérard Laumon
Gérard Laumon is a French mathematician. He studied at the École Normale Supérieure and Paris-Sud 11 University, Orsay.In 2004 Laumon and Ngô Bảo Châu received the Clay Research Award for the proof of the Langlands and Shelstad's Fundamental Lemma for unitary groups, a key component in the...
, James McKernan
James McKernan
James McKernan is a British mathematician, and a professor of mathematics at MIT in the United States.McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon.-External...
, Oded Schramm
Oded Schramm
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution and for working at the intersection of conformal field theory and probability theory.-Biography:...
, Stanislav Smirnov
Stanislav Smirnov
Stanislav Konstantinovich Smirnov is a Russian mathematician currently working at the University of Geneva, who was awarded the Fields Medal in 2010. His research focuses on the fields of complex analysis, dynamical systems and probability theory.-Career:...
, Terence Tao
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
,
Richard Taylor
Richard Taylor (mathematician)
-External links:**...
, Claire Voisin
Claire Voisin
Claire Voisin is a French professor of mathematics and director of research at the Institut de mathématiques de Jussieu at the University of Paris VI: Pierre et Marie Curie...
, Andrew Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
and Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
.
The Olympiad award
The CMI also offers the Clay Olympiad Scholar Award for the most creative solution to a problem on the United States of America Mathematical OlympiadUnited States of America Mathematical Olympiad
The United States of America Mathematical Olympiad is a high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests...
.
Other activities
Besides the Millennium Prize Problems, the Clay Mathematics Institute also supports mathematics via the awarding ofresearch 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
Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
, recognizing major breakthroughs in mathematical research. Finally, the Institute also 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.