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{{short description|French mathematician (born 1947)}}
{{Use dmy dates|date=March 2025}}

{{Infobox scientist
| name = Alain Connes
| image = Alain_Connes.jpg
| alt = Photo of the upper body of Alain Connes with vegetation, blue sky, and clouds in the background
| caption = Alain Connes in 2004
| birth_date = {{birth date and age|1947|04|01|df=y}}
| birth_place = [[Draguignan]], France
| death_date =
| death_place =
| fields = Mathematics [[Particle physics]]
| workplaces = [[Collège de France]] [[IHÉS]] [[Ohio State University]] [[Vanderbilt University]]
| alma_mater = [[École Normale Supérieure]] [[Pierre and Marie Curie University]]
| thesis_title = A Classification of Factors of Type III
| thesis_year = 1973
| doctoral_advisor = [[Jacques Dixmier]]
| doctoral_students = [[Jean-Benoît Bost]] [[Georges Skandalis]]
| known_for = [[Baum–Connes conjecture]] [[Noncommutative geometry]] [[Noncommutative standard model]] [[Operator algebra]]s [[Thermal time hypothesis]]
| awards = [[Peccot Lectures|Peccot-Vimont Prize]] (1976) [[CNRS Silver Medal]] (1977) [[Ampère Prize]] (1980) [[Fields Medal]] (1982) [[Clay Research Award]] (2000) [[Crafoord Prize]] (2001) [[CNRS Gold medal]] (2004)
| website = {{URL|https://alainconnes.org/}}
| footnotes =
}}

'''Alain Connes''' ({{IPA|fr|alɛ̃ kɔn|lang}}; born 1 April 1947) is a French mathematician, known for his contributions to the study of [[operator algebra]]s and [[noncommutative geometry]]. He was a professor at the {{Lang|fr|[[Collège de France]]|italic=no}}, {{Lang|fr|[[Institut des Hautes Études Scientifiques]]|italic=no}}, [[Ohio State University]] and [[Vanderbilt University]]. He was awarded the [[Fields Medal]] in 1982.<ref>{{Cite web |last1=O'Connor |first1=John |last2=Robertson |first2=Edmund |author-link2=Edmund F. Robertson |title=Alain Connes |url=https://mathshistory.st-andrews.ac.uk/Biographies/Connes/ |access-date=2023-05-19 |website=[[MacTutor History of Mathematics archive]] |language=en}}</ref><ref name=":0">{{Cite web |last=Jackson |first=Allyn |date=2021 |title=Interview with Alain Connes |url=https://celebratio.org/Connes_A/article/842/ |access-date=2023-05-18 |website=[[Celebratio Mathematica]] |language=en}}</ref><ref name=":1">{{Cite journal |last1=Skandalis |first1=Georges |author-link=Georges Skandalis |last2=Goldstein |first2=Catherine |author-link2=Catherine Goldstein |date=2007 |title=An interview with Alain Connes, part I |url=https://ems.press/content/serial-issue-files/13664 |journal=EMS Newsletter |publisher=[[European Mathematical Society]] |volume=63 |pages=25–30}}</ref><ref name=":2">{{Cite journal |last1=Skandalis |first1=Georges |author-link=Georges Skandalis |last2=Goldstein |first2=Catherine |author-link2=Catherine Goldstein |date=2008 |title=An interview with Alain Connes, part II |url=https://ems.press/content/serial-issue-files/13672 |journal=EMS Newsletter |publisher=[[European Mathematical Society]] |volume=67 |pages=29–33}}</ref>

==Career==
Alain Connes attended high school at {{Interlanguage link|Lycée Saint-Charles (Marseille)|lt=Lycée Saint-Charles|fr|Lycée Saint-Charles (Marseille)}} in Marseille, and was then a student of the [[Classe préparatoire aux grandes écoles|classes préparatoires]] in {{Interlanguage link|Lycée Thiers|lt=Lycée Thiers|fr}}. Between 1966 and 1970 he studied at [[École normale supérieure (Paris)|École normale supérieure]] in Paris, and in 1973 he obtained a PhD from [[Pierre and Marie Curie University]], under the supervision of [[Jacques Dixmier]].<ref name=":0" />

From 1970 to 1974 he was research fellow at the [[French National Centre for Scientific Research]] and during 1975 he held a visiting position at [[Queen's University at Kingston]] in Canada.<ref name="Alain Connes 2021">{{cite web |date=2021-04-22 |title=Curriculum Vitae |url=https://alainconnes.org/cv/ |access-date=2022-09-08 |website=Alain Connes}}</ref>

In 1976 he returned to France and worked as professor at Pierre and Marie Curie University until 1980 and at [[French National Centre for Scientific Research|CNRS]] between 1981 and 1984. Moreover, since 1979 he holds the Léon Motchane Chair at [[Institut des Hautes Études Scientifiques|IHES]].<ref>{{Cite web |title=Alain Connes, emeritus professor since 2017 |url=https://www.ihes.fr/en/professeur/alain-connes-2/ |access-date=2023-05-26 |website=[[IHES]]}}</ref> From 1984 until his retirement in 2017 he held the chair of Analysis and Geometry at [[Collège de France]].<ref name="Alain Connes 2021" /><ref>{{Cite web |date=2022-04-11 |title=Alain Connes |url=https://www.college-de-france.fr/fr/chaire/alain-connes-analyse-et-geometrie-chaire-statutaire/biography |access-date=2023-05-26 |website=[[Collège de France]] |language=fr}}</ref>

In parallel, he was awarded a distinguished professorship at [[Vanderbilt University]] between 2003 and 2012,<ref>{{Cite web |last3=Pm |first3=1:24 |date=4 September 2003 |title=World-class mathematician joins Vanderbilt faculty |url=https://news.vanderbilt.edu/2003/09/04/world-class-mathematician-joins-vanderbilt-faculty-59929/ |access-date=2023-05-18 |publisher=[[Vanderbilt University]] |language=en-US}}</ref> and at [[Ohio State University]] between 2012 and 2021.

== Research ==
Connes's main research interests revolved around [[operator algebra]]s. Besides [[noncommutative geometry]], he has applied his works in various areas of mathematics and [[number theory]], [[differential geometry]].<ref name=":0" /><ref>Alexander Hellemans, [http://www.scientificamerican.com/article.cfm?id=the-geometer-of-particle "The Geometer of Particle Physics"] '' Scientific American'', 24 July 2006</ref><ref name=":1" /><ref name=":2" /> Since the 1990s, he developed [[noncommutative geometry]].<ref>{{cite book | author = [[Sabine Hossenfelder]] | title = Lost in Math: How Beauty Leads Physics Astray | isbn=978-0465094257 | year = 2018| publisher = Basic Books }}</ref>

In his early work on [[von Neumann algebra]]s in the 1970s, he succeeded in obtaining the almost complete classification of injective [[Von Neumann algebra#Factors|factor]]s. He also formulated the [[Connes embedding problem]].

Following this, he made contributions in [[K-theory|operator K-theory]] and [[index theory]], which culminated in the [[Baum–Connes conjecture]]. He also introduced [[cyclic homology|cyclic cohomology]] in the early 1980s as a first step in the study of [[noncommutative geometry|noncommutative differential geometry]].<ref>{{Cite journal |last=Moore |first=Calvin |author-link=Calvin C. Moore |date=1982 |title=The work of Alain Connes |url=https://www.ams.org/journals/notices/198210/198210FullIssue.pdf?cat=fullissue&trk=fullissue198210 |journal=[[Notices of the American Mathematical Society]] |volume=29 |issue=6 |pages=499–501}}</ref><ref>{{Cite journal |last=Seda |first=Anthony Karel |date=1984 |title=One aspect of the work of Alain Connes |url=https://www.irishmathsoc.org/nl11/nl11_38-48.pdf |journal=[[Irish Mathematical Society#Bulletin of the Irish Mathematical Society|Irish Mathematical Society Newsletter]] |volume=11 |pages=38–48|doi=10.33232/BIMS.0011.38.48 }}</ref><ref>{{Cite journal |last=Lesniewski |first=Andrew |date=1997 |title=Noncommutative Geometry |url=https://www.ams.org/notices/199707/lesniewski.pdf |journal=[[Notices of the American Mathematical Society]] |volume=44 |issue=7 |pages=800–805}}</ref><ref>{{Cite journal |last1=Cornelissen |first1=Gunther |last2=Landsman |first2=Klaas |last3=van Suijlekom |first3=Walter |date=2010 |title=The flashes of insight never came for free |url=https://www.nieuwarchief.nl/serie5/pdf/naw5-2010-11-4-250.pdf |journal=[[Nieuw Archief voor Wiskunde]] |volume=11 |issue=5 |pages=250–256}}</ref>

He was a member of [[Nicolas Bourbaki]].<ref>{{cite book |title=Bourbaki: a secret society of mathematicians|first=Maurice|last=Mashaal|publisher=[[American Mathematical Society]]|year=2006|page=18|isbn=978-0-8218-3967-6|url=https://books.google.com/books?id=-CXn6y_1nJ8C&pg=PA18}}</ref> Over many years, he collaborated extensively with [[Henri Moscovici]].<ref name=":0"/>

==Awards and honours==

Connes was awarded the [[Peccot Lectures|Peccot-Vimont Prize]] in 1976,<ref>{{Cite web |date=2022-05-11 |title=Cours et Prix Claude-Antoine Peccot |trans-title=Claude-Antoine Peccot Lectures and Prizes |url=https://www.college-de-france.fr/fr/prix/cours-et-prix-claude-antoine-peccot |access-date=2023-05-26 |website=[[College de France]] |language=fr}}</ref> the [[Ampère Prize]] in 1980, the [[Fields Medal]] in 1982,<ref name="FieldsMedal00">{{cite web |author1=Albers, Donald J. |author2=Alexanderson, G. L. |author3=Reid, Constance |date=1986 |title=International mathematical congresses. An illustrated history 1893 – 1986 |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1982/index.html#0x82496a1f_0x0005ea30 |access-date=2018-12-02 |publisher=Springer-Verlag}}</ref><ref name="FieldsMedal01">{{cite web |author=IMU Secretariat |title=Fields Medal – International Mathematical Union (IMU) |url=https://www.mathunion.org/imu-awards/fields-medal |access-date=2018-12-02 |publisher=International Mathematical Union}}</ref> the [[Clay Research Award]] in 2000<ref>{{Cite web |title=Research Awards |url=https://www.claymath.org/research |access-date=2023-05-26 |website=[[Clay Mathematics Institute]]}}</ref> and the [[Crafoord Prize]] in 2001.<ref>{{Cite web |date=2001-01-24 |title=Crafoord Prize to one of the world's foremost mathematicians |url=https://www.crafoordprize.se/news/crafoord-prize-to-one-of-the-worlds-foremost-mathematicians/ |access-date=2023-05-26 |website=[[Royal Swedish Academy of Sciences]] |language=en-GB}}</ref><ref name="CrafoordPrize00">{{cite web |date=2000 |title=Crafoord Prize Laureates |url=https://www.crafoordprize.se/prize-laureate/alain-connes/ |access-date=2018-12-02 |website=[[Royal Swedish Academy of Sciences]] }}</ref><ref>{{Cite journal |last=Holden |first=Constance |date=2001 |title=French Mathematician Wins Crafoord Prize |url=https://www.science.org/content/article/french-mathematician-wins-crafoord-prize |journal=[[Science (journal)|Science]]}}</ref> The [[CNRS|French National Centre for Scientific Research]] granted him the [[CNRS Silver Medal|silver medal]] in 1977<ref>{{Cite web |last=Burgos |first=Valérie |date=2023-01-31 |title=Médailles d'argent du CNRS 1960-2010 |trans-title=Silver medals of the CNRS 1960-2010 |url=https://comihistocnrs.hypotheses.org/2706 |access-date=2023-05-26 |website=Comité pour l'histoire du CNRS |doi=10.58079/n1ag |language=fr-FR}}</ref> and the [[CNRS Gold Medal|gold medal]] in 2004.<ref>{{Cite news |date=2004 |title=Alain Connes, mathématicien, Médaille d'or du CNRS 2004 |trans-title=Alain Connes, mathematician, Gold Medal of CNRS 2004 |url=https://archives.cnrs.fr/presse/article/582 |access-date=2023-05-26 |website=[[CNRS]] |language=fr-FR |archive-date=21 January 2023 |archive-url=https://web.archive.org/web/20230121205859/https://archives.cnrs.fr/presse/article/582 |url-status=dead }}</ref><ref>{{Cite web |date=2004 |title=Alain Connes, Médaille d'or 2004 du CNRS |trans-title=Alain Connes, 2004 Gold Medal of CNRS |url=http://www2.cnrs.fr/sites/band/fichier/or.pdf |website=[[CNRS]] |language=fr}}</ref><ref>{{Cite journal |date=2005 |title=Alain Connes: indomitable explorer |url=http://www2.cnrs.fr/sites/band/fichier/ra_2004_gb.pdf |journal=A Year at CNRS 2004 |pages=10–11}}</ref><ref>{{Cite web |last=Dumas |first=Cécile |date=2004-11-09 |title=Alain Connes, médaillé d'or du CNRS |trans-title=Alain Connes, gold medal of the CNRS |url=https://www.sciencesetavenir.fr/fondamental/alain-connes-medaille-d-or-du-cnrs_22257 |access-date=2023-05-26 |website=[[Sciences et Avenir]] |language=fr}}</ref><ref>{{Cite web |date=2005 |title=Vanderbilt math professor Alain Connes receives prestigious French science award |url=https://news.vanderbilt.edu/2005/02/16/vanderbilt-math-professor-alain-connes-receives-prestigious-french-science-award-59421/ |access-date=2023-05-26 |publisher=[[Vanderbilt University]] |language=en-US}}</ref>

He was an [[invited speaker at the International Congress of Mathematicians|invited speaker]] at the [[International Congress of Mathematicians]] in 1974 at Vancouver and in 1986 at Berkeley, and a plenary speaker at the ICM in 1978 at Helsinki.
[[File:Villeneuve-d'Ascq - IUT A - Alain Connes - 3.jpg|thumb|Alain Connes at a conference in 2012 in [[Villeneuve-d'Ascq]]]]
He was awarded [[honorary degree]]s from [[Queen's University at Kingston]] in 1979,<ref>{{Cite web |title=1858-2011 Honorary Degree Recipients |url=https://www.queensu.ca/registrar/sites/uregwww/files/uploaded_files/pdfs/HDrecipients.pdf |access-date=2023-05-26 |website=[[Queen's University at Kingston]]}}</ref> [[University of Rome Tor Vergata]] in 1997,<ref>{{Cite web |title=Lauree Honoris Causa |url=https://web.uniroma2.it/it/contenuto/lauree_honoris_causa |access-date=2023-05-26 |publisher=[[University of Rome Tor Vergata]] |language=it}}</ref> [[University of Oslo]] in 1999,<ref>{{Cite web |title=Æresdoktorer ved UiO 2000-2008 |trans-title=Honorary Doctorates UiO 2000-2008 |url=https://www.uio.no/om/tall-og-fakta/aresdoktorer/tidligere-aresdoktorer/2000-2008/ |publisher=[[Oslo University]] |language=no}}</ref> [[University of Southern Denmark]] in 2009, [[Université libre de Bruxelles]] in 2010<ref>{{Cite web |title=ULB's honorary doctorates |url=https://www.ulb.be/en/about-ulb/ulbs-honorary-doctorates |access-date=2023-05-26 |website=[[Université libre de Bruxelles]] |language=en}}</ref> and [[Fudan University|Shanghai Fudan University]] in 2017.

Since 1982 he has been a member of the [[French Academy of Sciences]].<ref>{{Cite web |title=Alain Connes |url=https://www.academie-sciences.fr/fr/Liste-des-membres-de-l-Academie-des-sciences-/-C/alain-connes.html |access-date=2023-05-19 |website=[[French Academy of Sciences]]}}</ref> He was elected member of several foreign academies and societies, including the [[Royal Danish Academy of Sciences and Letters]] in 1980,<ref>{{Cite web |title=Alain Connes |url=https://www.royalacademy.dk/en/Members/Connes-Alain |access-date=2023-05-19 |website=[[Royal Danish Academy of Sciences and Letters]]}}</ref> the [[Norwegian Academy of Science and Letters]] in 1983,<ref>{{Cite web |title=Utenlandske medlemmer |trans-title=Foreign members |url=https://dnva.no/medlemmer/53 |access-date=2023-05-19 |website=[[Norwegian Academy of Science and Letters]] |language=nb}}</ref> the [[American Academy of Arts and Sciences]] in 1989,<ref>{{Cite web |date=2023-02-09 |title=Alain Connes |url=https://www.amacad.org/person/alain-connes |access-date=2023-05-19 |website=[[American Academy of Arts and Sciences]] |language=en}}</ref> the [[London Mathematical Society]] in 1994,<ref>{{Cite web |title=London Mathematical Society Honorary Members |url=https://www.lms.ac.uk/sites/default/files/inline-files/HONORARY%20MEMBERS_0.pdf |website=[[London Mathematical Society]]}}</ref> the Canadian Academy of Sciences in 1995 (incorporated since 2002 in the [[Royal Society of Canada]]),<ref>{{Cite web |title=Member Directory |url=https://rsc-src.ca/en/find-rsc-member/results?combine=&first_name=&last_name=connes&current_employer=&academy_25=All&is_deceased=All |access-date=2023-05-19 |website=[[Royal Society of Canada]]}}</ref> the [[National Academy of Sciences|US National Academy of Sciences]] in 1997,<ref>{{Cite web |title=Alain Connes |url=https://www.nasonline.org/member-directory/members/3003968.html |access-date=2023-05-19 |website=[[National Academy of Sciences]]}}</ref> the [[Russian Academy of Sciences|Russian Academy of Science]] in 2003<ref>{{Cite web |title=Конн А.. – Общая информация |trans-title=Conn A. – General information |url=https://www.ras.ru/win/db/show_per.asp?P=.id-53787.ln-en |access-date=2023-05-19 |website=[[Russian Academy of Sciences]] |language=ru}}</ref> and the [[Royal Academy of Science, Letters and Fine Arts of Belgium]] in 2016.<ref>{{Cite web |title=Alain Connes |url=https://academieroyale.be/fr/l-academie-royale-classes-classe-sciences-membres-detail/relations/alain-connes/ |website=[[Royal Academy of Science, Letters and Fine Arts of Belgium]] |language=fr}}</ref>

In 2001 he received (together with his co-authors [[André Lichnerowicz]] and [[Marco Schutzenberger]]) the Peano Prize for his work ''Triangle of Thoughts.''<ref>{{Cite web |date=2015-11-03 |title=Premio Peano {{!}} Associazione Subalpina Mathesis |url=https://www.associazionesubalpinamathesis.it/premio-peano/ |access-date=2023-05-26 |language=it-IT}}</ref>

==Family==
Alain Connes is the middle-born of three sons. Both his parents lived to be 101 years old. He married in 1971.<ref name=":0"/>

==Books==
* Alain Connes and [[Matilde Marcolli]], ''Noncommutative Geometry, Quantum Fields and Motives'', Colloquium Publications, [[American Mathematical Society]], 2007, {{ISBN|978-0-8218-4210-2}} [http://www.alainconnes.org/docs/bookwebfinal.pdf]
* Alain Connes, [[André Lichnerowicz]], and [[Marcel-Paul Schützenberger|Marcel-Paul Schutzenberger]], ''Triangle of Thought'', translated by Jennifer Gage, American Mathematical Society, 2001, {{ISBN|978-0-8218-2614-0}}
* [[Jean-Pierre Changeux]] and Alain Connes, ''Conversations on Mind, Matter, and Mathematics'', translated by M. B. DeBevoise, [[Princeton University Press]], 1998, {{ISBN|978-0-691-00405-1}}
* Alain Connes, ''Noncommutative Geometry'', [[Academic Press]], 1994, {{ISBN|978-0-12-185860-5}}<ref>{{cite journal|author=Segal, Irving|author-link=Irving Segal|title=Book Review: ''Noncommutative Geometry'', by Alan Connes|journal= Bulletin of the American Mathematical Society|series=New Series|year=1996|volume=33|issue=4|pages=459–465|url=https://www.ams.org/journals/bull/1996-33-04/S0273-0979-96-00687-8/S0273-0979-96-00687-8.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/journals/bull/1996-33-04/S0273-0979-96-00687-8/S0273-0979-96-00687-8.pdf |archive-date=2022-10-09 |url-status=live|doi=10.1090/s0273-0979-96-00687-8|doi-access=free}}</ref>

==See also==
* [[Bost–Connes system]]
* [[Cyclic category]]
* [[Cyclic homology]]
* [[Factor (functional analysis)]]
* [[Higgs boson]]
* [[C*-algebra]]
* [[Noncommutative quantum field theory]]
* [[M-theory]]
* [[Groupoid]]
* [[Spectral triple]]
*[[Criticism of non-standard analysis]]
* [[Riemann hypothesis]]

==References==
{{reflist}}

==External links==
{{commons category}}
{{wikiquote}}
* [http://www.alainconnes.org/ Alain Connes Official Web Site] containing [http://www.alainconnes.org/en/downloads.php downloadable papers], and his book [http://www.alainconnes.org/docs/book94bigpdf.pdf ''Non-commutative geometry''], {{isbn|0-12-185860-X}}.
* {{nlab|id=Alain+Connes|title=Alain Connes}}
* [http://resonaances.blogspot.com/2007/02/alain-connes-standard-model.html Alain Connes's Standard Model]
* An [http://www.ipm.ac.ir/ViewNewsInfo.jsp?NTID=227 interview with Alain Connes] and a [http://www.math.columbia.edu/~woit/wordpress/?p=313 discussion about it]
* {{MathGenealogy|id=34220}}
* {{Google scholar id|OMnIF4sAAAAJ}}

{{Fields medalists}}
{{Authority control}}

{{DEFAULTSORT:Connes, Alain}}
[[Category:1947 births]]
[[Category:Living people]]
[[Category:People from Draguignan]]
[[Category:20th-century French mathematicians]]
[[Category:21st-century French mathematicians]]
[[Category:French mathematical analysts]]
[[Category:Differential geometers]]
[[Category:Fields Medalists]]
[[Category:Clay Research Award recipients]]
[[Category:École normale supérieure (Paris) alumni]]
[[Category:Academic staff of the Collège de France]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Vanderbilt University faculty]]
[[Category:Foreign members of the Russian Academy of Sciences]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Members of the Norwegian Academy of Science and Letters]]
[[Category:Members of the Royal Danish Academy of Sciences and Letters]]
[[Category:London Mathematical Society]]

Alain Connes - Revision history

>An anonymous username, not my real name: /* Family */ Fixing unintelligible wording