Michael Howard Harris (born 1954) is an American mathematician known for his work in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. He is a professor of mathematics at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

and professor emeritus of mathematics at Université Paris Cité. In 2025, he was elected to the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

Early life and education

Harris was born in Kingsessing, Philadelphia, Pennsylvania and is of Jewish descent. He received his B.A. in mathematics from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

in 1973. He received his M.A. and Ph.D. in mathematics from

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

under the supervision of

Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in ...

in 1976 and 1977 respectively.

Career

Harris was a faculty member at

Brandeis University Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...

from 1977 to 1994. In 1994, he became a professor of mathematics at

Paris Diderot University Paris Diderot University, also known as Paris 7 (), was a French university located in Paris, France. It was one of the inheritors of the historic University of Paris, which was split into 13 universities in 1970. Paris Diderot merged with Pari ...

and the Institut de mathématiques de Jussieu – Paris Rive Gauche, where he has been emeritus since 2021. He became a professor of mathematics at

in 2013. He was a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

from 1983 to 1984 and in the fall of 2011. He has held visiting positions at various institutions, including Bethlehem University, the

Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

, the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...

Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...

, and the Mathematical Sciences Research Institute. His former doctoral students include Laurent Fargues and Gaëtan Chenevier. He has organized or co-organized more than 20 conferences, workshops, and special programs in his field of number theory.

Work

Research

Harris's research focuses on

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

automorphic forms In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the group action (mathematics), action of a discrete s ...

, ''L''-functions, and motives. He has developed the theory of coherent cohomology of Shimura varieties and applied it to number theoretic problems on special values of ''L''-functions, Galois representations, and the theta correspondence. His later work focuses on geometric aspects of the

Langlands program In mathematics, the Langlands program is a set of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by . It seeks to relate the structure of Galois groups in algebraic number t ...

. In 2001, Harris and Richard Taylor proved the local Langlands conjecture for GL(''n'') over a ''p''-adic

local field In mathematics, a field ''K'' is called a non-Archimedean local field if it is complete with respect to a metric induced by a discrete valuation ''v'' and if its residue field ''k'' is finite. In general, a local field is a locally compact t ...

The Sato–Tate conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.

''Mathematics without Apologies''

Harris wrote the book ''Mathematics without Apologies: Portrait of a Problematic Vocation'', published in 2015.

''Silicon Reckoner''

Since 2021, Harris has written the newsletter ''Silicon Reckoner'' exploring questions and issues related to the mechanization of mathematics and

artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

Activism

Beyond his contributions to mathematics, Michael Harris has been actively engaged in various social and political causes. Harris has also been vocal in discussions about the social responsibilities of mathematicians in general. In his essay "Do Mathematicians Have Responsibilities?" he explores the ethical implications of mathematical work and the importance of considering the societal impact of mathematical research.

Recognition

Harris received the Sophie Germain Prize (2006), the Clay Research Award (joint with Richard Taylor, 2007), the Grand Prix Scientifique de la Fondation Simone et Cino del Duca (2009), He is a two-time invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(2002, 2014). Harris was a Sloan Research Fellow (1983–1985) and a member of the

Institut Universitaire de France The Institut Universitaire de France (IUF, Academic Institute of France), is a service of the French Ministry of Higher Education that annually distinguishes a small number of university professors for their research excellence, as evidenced by t ...

(2001–2011) He has been elected a

Member of the Academia Europaea Membership of the Academia Europaea (MAE) is an award conferred by the Academia Europaea to individuals that have demonstrated "sustained academic excellence". Membership is by invitation only by existing MAE and judged during a peer review selecti ...

(2016), Fellow of the American Mathematical Society (2019), Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

(2019), and Member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

(2022).

References

External links

Michael Harris's web page
{{DEFAULTSORT:Harris, Michael 1954 births Living people 20th-century American mathematicians 21st-century American mathematicians Jewish American scientists American number theorists Harvard Graduate School of Arts and Sciences alumni Clay Research Award recipients Institute for Advanced Study visiting scholars Columbia University faculty Fellows of the American Mathematical Society Scientists from Philadelphia Members of the United States National Academy of Sciences 20th-century American Jews 21st-century American Jews Members of the American Philosophical Society