Michael Harris (mathematician)

{{Infobox scientist

| name = Michael Harris

| birth_name = Michael Howard Harris

| image =

| caption =

| birth_date = {{birth year and age|1954}}

| birth_place = Philadelphia, US

| death_date =

| death_place =

| alma_mater = Harvard University
Princeton University

| thesis_title = On p-Adic Representations Arising from Descent on Abelian Varieties

| thesis_year = 1977

| thesis_url =

| doctoral_advisor = Barry Mazur

| doctoral_students = Laurent Fargues

| known_for =

| spouse =

| field = Mathematics

| work_institutions = Columbia University
Paris Diderot University
Brandeis University

| prizes = Sophie Germain Prize (2006)
Clay Research Award (joint, 2007)
Grand Prix Scientifique de la Fondation Simone et Cino del Duca (2009)
Member of the Academia Europaea (2016)
Fellow of the American Mathematical Society (2019)
Member of the American Academy of Arts and Sciences (2019)
Member of the National Academy of Sciences (2022)

}}

Michael Howard Harris (born 1954) is an American mathematician known for his work in number theory. He is a professor of mathematics at Columbia University and professor emeritus of mathematics at Université Paris Cité. In 2025, he was elected to the American Philosophical Society.https://www.amphilsoc.org/news/aps-elects-new-members-2025

Early life and education

Harris was born in Kingsessing, Philadelphia, Pennsylvania and is of Jewish descent.{{cite book |last1=Harris |first1=Michael |title=Mathematics without Apologies: Portrait of a Problematic Vocation |date=2015 |publisher=Princeton University Press |isbn=9780691154237 |page=373}} He received his B.A. in mathematics from Princeton University in 1973.{{cite web |last1=Harris |first1=Michael |title=CV |url=http://www.math.columbia.edu/~harris/website/cv |website=Michael Harris |access-date=July 24, 2023}} He received his M.A. and Ph.D. in mathematics from Harvard University under the supervision of Barry Mazur in 1976 and 1977 respectively.{{MathGenealogy |id=22503|name=Michael Harris }}

Career

Harris was a faculty member at Brandeis University from 1977 to 1994. In 1994, he became a professor of mathematics at Paris Diderot University and the Institut de mathématiques de Jussieu – Paris Rive Gauche, where he has been emeritus since 2021.{{cite web |title=Emérites |url=https://www.imj-prg.fr/emerites/ |website=Institut de mathématiques de Jussieu – Paris Rive Gauche |publisher=Institut de mathématiques de Jussieu – Paris Rive Gauche |access-date=June 24, 2023}} He became a professor of mathematics at Columbia University in 2013.

He was a member of the Institute for Advanced Study from 1983 to 1984 and in the fall of 2011.{{cite web |title=Michael Harris |url=https://www.ias.edu/scholars/michael-harris |website=Institute for Advanced Study |date=9 December 2019 |publisher=Institute for Advanced Study |access-date=June 24, 2023}} He has held visiting positions at various institutions, including Bethlehem University, the Steklov Institute of Mathematics, the Institut des Hautes Études Scientifiques, Oxford University, 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.{{Cite web |title=Michael Harris |url=https://www.helixcenter.org/participants/michael-harris/ |access-date=2025-01-28 |website=The Helix Center |language=en-US}}

Work

=Research=

Harris's research focuses on arithmetic geometry, automorphic forms, 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 2001, Harris and Richard Taylor proved the local Langlands conjecture for GL(n) over a p-adic local field

{{Citation

| last1=Harris

| first1=Michael

| last2=Taylor

| first2=Richard

| title=The geometry and cohomology of some simple Shimura varieties

| year=2001

| publisher=Princeton University Press

| mr=1876802

| isbn= 978-0-691-09092-4

| url= https://books.google.com/books?id=IokNBAAAQBAJ

}} 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,{{Cite journal

| last=Taylor

| first=Richard

| title=Automorphy for some l-adic lifts of automorphic mod l Galois representations. II

| journal=Publ. Math. Inst. Hautes Études Sci.

| volume=108

| year=2008

| pages=183–239

| doi=10.1007/s10240-008-0015-2

| mr=2470688

| citeseerx=10.1.1.116.9791

}}{{Cite journal

| last1=Clozel

| first1=Laurent

| last2=Harris

| first2=Michael

| last3=Taylor

| first3=Richard

| title=Automorphy for some l-adic lifts of automorphic mod l Galois representations

| journal=Publ. Math. Inst. Hautes Études Sci.

| volume=108

| year=2008

| pages=1–181

| doi=10.1007/s10240-008-0016-1

| mr=2470687

| citeseerx=10.1.1.143.9755

}}{{Citation

| last1=Harris

| first1=Michael

| last2=Shepherd-Barron

| first2=Nicholas

| last3=Taylor

| first3=Richard

| title=A family of Calabi–Yau varieties and potential automorphy

| journal=Annals of Mathematics

| year=2010

| volume=171

| issue=2

| pages=779–813

| doi=10.4007/annals.2010.171.779

| mr=2630056

| doi-access=free

}} and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.{{Cite journal

| last1=Barnet-Lamb

| first1=Thomas

| last2=Geraghty

| first2=David

| last3=Harris

| first3=Michael

| last4=Taylor

| first4=Richard

| title=A family of Calabi–Yau varieties and potential automorphy. II

| year=2011

| pages=29–98

| journal=Publ. Res. Inst. Math. Sci.

| volume=47

| issue=1

| mr=2827723

| doi=10.2977/PRIMS/31

| doi-access=free

}}

=''Mathematics without Apologies''=

Harris wrote the book Mathematics without Apologies: Portrait of a Problematic Vocation, published in 2015.{{cite book | last=Harris | first=Michael | title=Mathematics without apologies : portrait of a problematic vocation | publisher=Princeton University Press | date=2015 | isbn=978-1-4008-5202-4 | oclc=900080550}}{{cite web|author=McCleary, John|date=November 2018|url=https://www.ams.org/journals/notices/201810/rnoti-p1280.pdf|title=Review of Mathematics without Apologies: Portrait of a Problematic Vocation by Michael Harris|website=Notices of the AMS}}{{cite journal|author=Alexander, Amir|author-link=Amir Alexander|title=Mathematics: Groping in the dark for glimpses of beauty (joint review of Birth of a Theorem by Cédric Villani and Mathematics without Apologies by Michael Harris)|journal=Nature|volume=519|issue=7541|pages=31–32|date=4 March 2015|doi=10.1038/519031a|doi-access=free}} (See Cédric Villani.){{cite web|author=Hunacek, Michael|date=August 4, 2015|title=review of Mathematics without Apologies|website=MAA Reviews|url=https://www.maa.org/press/maa-reviews/mathematics-without-apologies-portrait-of-a-problematic-vocation}}

=''Silicon Reckoner''=

Since 2021, Harris has written the newsletter Silicon Reckoner exploring questions and issues related to the mechanization of mathematics and artificial intelligence.{{cite web|author=Harris, Michael|title=About Silicon Reckoner|url=https://siliconreckoner.substack.com/about}}

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.{{Cite web |title=Michael Harris {{!}} Publications |url=https://www.math.columbia.edu/~harris/website/publications |access-date=2025-01-28 |website=www.math.columbia.edu |language=en}}

Recognition

Harris received the Sophie Germain Prize (2006), the Clay Research Award (joint with Richard Taylor, 2007),{{cite web |url=http://www.gap-system.org/~history/Societies/Clay.html |title=Clay Award |access-date=2011-06-01 |url-status=dead |archive-url=https://web.archive.org/web/20120316162039/http://www.gap-system.org/~history/Societies/Clay.html |archive-date=2012-03-16 }} 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 (2002, 2014).

Harris was a Sloan Research Fellow (1983–1985) and a member of the Institut Universitaire de France (2001–2011) He has been elected a Member of the Academia Europaea (2016), Fellow of the American Mathematical Society (2019),{{cite web|url=https://www.ams.org/fellows_by_year.cgi?year=2019 |title=2019 Class of the Fellows of the AMS |website=American Mathematical Society |publisher=American Mathematical Society|access-date=June 24, 2023}} Member of the American Academy of Arts and Sciences (2019), and Member of the National Academy of Sciences (2022).{{cite web |title=Michael Harris |url=http://www.nasonline.org/member-directory/members/20054259.html |website=National Academy of Sciences |publisher=National Academy of Sciences |access-date=June 24, 2023}}