James Arthur

Born (1944-05-18) May 18, 1944 (age 78)
Alma materUniversity of Toronto
Yale University
Known forArthur–Selberg trace formula
Arthur conjectures
AwardsJohn L. Synge Award (1987)
Jeffery–Williams Prize (1993)
CRM-Fields-PIMS prize (1997)
Henry Marshall Tory Medal (1997)
Gerhard Herzberg Canada Gold Medal for Science and Engineering (1999)
Wolf Prize (2015)
Leroy P. Steele Prize for Lifetime Achievement (2017)
Scientific career
InstitutionsYale University
Duke University
University of Toronto
ThesisAnalysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One (1970)
Doctoral advisorRobert Langlands

James Greig Arthur CC FRSC FRS (born May 18, 1944)[1] is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor at the University of Toronto Department of Mathematics.[2]

Education and career

Born in Hamilton, Ontario, Arthur graduated from Upper Canada College in 1962,[3] received a B.Sc. from the University of Toronto in 1966, and a M.Sc. from the same institution in 1967. He received his Ph.D. from Yale University in 1970. He was a student of Robert Langlands; his dissertation was Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One.[4]

Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University in 1976. He has been a professor at the University of Toronto since 1978.[1] He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002.[5]


Arthur is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures.


Arthur was elected a Fellow of the Royal Society of Canada in 1981 and a Fellow of the Royal Society in 1992.[6][7] In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.[8] He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 2003.[9] In 2012 he became a fellow of the American Mathematical Society.[10] He was elected as a fellow of the Canadian Mathematical Society in 2019.[11]


  1. ^ a b "James Greig Arthur". International Mathematical Union. Archived from the original on 15 August 2011. Retrieved 25 April 2011.
  2. ^ "Arthur, James". University of Toronto Department of Mathematics. Retrieved November 11, 2019.
  3. ^ "UCC community members join Order of Canada". Upper Canada College. 2019-01-17. Retrieved 2019-11-19.
  4. ^ James Arthur at the Mathematics Genealogy Project
  5. ^ Institute for Advanced Study: A Community of Scholars Archived 2013-01-06 at the Wayback Machine
  6. ^ "Search Fellows". Royal Society of Canada. Retrieved September 7, 2017.
  7. ^ "James Arthur". Royal Society. Retrieved April 3, 2018.
  8. ^ Arthur, James (1998). "Towards a stable trace formula". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 507–517.
  9. ^ "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 25 April 2011.
  10. ^ "List of Fellows of the American Mathematical Society". Retrieved 3 November 2012.
  11. ^ Canadian Mathematical Society's Second Inaugural Class of Fellows Announced, Canadian Mathematical Society, retrieved 2020-01-06

Further reading