The University of Toronto Department of Mathematics is an

academic department An academic department is a division of a university or school faculty devoted to a particular academic discipline. This article covers United States usage at the university level. In the United Kingdom and other Commonwealth countries, univers ...

within the Faculty of Arts and Science at the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

. It is located at the university's main campus at the

Bahen Centre for Information Technology The Bahen Centre for Information Technology is a building at the St. George campus of the University of Toronto. It is primarily used by the Faculty of Applied Science and Engineering, the Department of Computer Science and the Department of ...

. The University of Toronto was ranked first in Canada for Mathematics in 2018 by the

QS World University Rankings ''QS World University Rankings'' is an annual publication of university rankings by Quacquarelli Symonds (QS). The QS system comprises three parts: the global overall ranking, the subject rankings (which name the world's top universities for the ...

, the

Times Higher Education World University Rankings The ''Times Higher Education World University Rankings'' (often referred to as the THE Rankings) is an annual publication of university rankings by the ''Times Higher Education'' (THE) magazine. The publisher had collaborated with Quacquarelli ...

, and the Maclean's University Rankings.

History

For most of the second half of the 19th century, the University of Toronto was the only English-language university in Canada to offer programs with specializations, one being in mathematics and

natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior throu ...

. The university launched its mathematics program in 1877, which became a model for the rest of Canada during the first half of the 20th century. The Mathematical and Physical Society was founded in 1882 as a mathematics

student society A student society, student association, university society, student club, university club, or student organization is a society or an organization, operated by students at a university or a college institution, whose membership typically consists ...

In the early 20th century, the department became the first in North American to explore the field of actuarial science. At the same time, the University of Toronto's mathematics department increasingly took the lead on mathematical research in Canada. Faculty member

John Charles Fields John Charles Fields, FRS, FRSC (May 14, 1863 – August 9, 1932) was a Canadian mathematician and the founder of the Fields Medal for outstanding achievement in mathematics. Career Born in Hamilton, Ontario, to a leather shop owner, Fields ...

, appointed professor in 1902, was perhaps the most important in developing research at Toronto. Fields organized the 1924

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 Nevanlinna Prize (to be rename ...

held in Toronto, and would later found the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

. Fields's student, Samuel Beatty, was the first mathematics

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in Canada, obtaining his degree in 1915 (Beatty would later serve as head of the mathematics department and first president of the

Canadian Mathematical Society The Canadian Mathematical Society (CMS) (french: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the ...

in 1945). In the next twenty years, Toronto was to produce eight doctorates in mathematics, two of them women. The Department's competitive mathematics team, consisting of

Irving Kaplansky Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St Andr ...

Nathan Mendelsohn Nathan Saul Mendelsohn, (April 14, 1917 – July 4, 2006) was an American-born mathematician who lived and worked in Canada. Mendelsohn was a researcher in several areas of discrete mathematics, including group theory and combinatorics. Ear ...

and John Coleman, won first place in the first year of the

William Lowell Putnam Mathematical Competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual list of mathematics competitions, mathematics competition for undergraduate college students enrolled at institutions of higher learning in th ...

in 1938. While competition rules prevented the University of Toronto from entering a team the following year, the team in won again in 1940, 1942 and 1946. Sid_Smith_Building,_University_of_Toronto

Sid_Smith_Building,_University_of_Toronto

Meanwhile, the first Canadian mathematics journal, ''

Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The ...

'', began publication by the

University of Toronto Press The University of Toronto Press is a Canadian university press founded in 1901. Although it was founded in 1901, the press did not actually publish any books until 1911. The press originally printed only examination books and the university calen ...

in 1949, with faculty members Harold Coxeter and

Gilbert de Beauregard Robinson Gilbert de Beauregard Robinson, MBE (3 June 1906 – 8 April 1992) was a Canadian mathematician most famous for his work on combinatorics and representation theory of the symmetric groups, including the Robinson-Schensted algorithm. Biograph ...

as Editor-in-Chief and Managing Editor, respectively. The department moved from

University College In a number of countries, a university college is a college institution that provides tertiary education but does not have full or independent university status. A university college is often part of a larger university. The precise usage varies ...

to Baldwin House in 1958, and then to Sidney Smith Hall upon its completion in 1961. The statistics sub-department, first established in 1947, became a separate department in 1978. The department was one of the founders of the Fields Institute for Research in Mathematical Sciences in 1991. Initially based at the

University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario Waterloo is a city in the Canadian province of Ontario. It is one of three cities in the Regional Municipality ...

, the institute is now located at the University of Toronto. In 2006, the Department of Mathematics moved to the sixth floor of the

, located directly behind the Fields Institute.

Academics

Awards and medals

Of the 120 current Fellows of the

Royal Society of Canada The Royal Society of Canada (RSC; french: Société royale du Canada, SRC), also known as the Academies of Arts, Humanities and Sciences of Canada (French: ''Académies des arts, des lettres et des sciences du Canada''), is the senior national, bil ...

in the discipline of Mathematics and Computer Sciences, 21 (or 18%) are members of the University of Toronto's Department of Mathematics. A number of individuals affiliated with the department have won international prizes for their research in mathematics, including the

, the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

, the Steele Prize, the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...

, the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

, and the

Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

Rankings

In the 2018

, the University of Toronto was ranked nineteenth in the world in the subject of Mathematics. The university was ranked first in Canada for Mathematics in 2018 by the Maclean's University Rankings, the

, and the QS World University Rankings.

Notable members

Alumni

Notable alumni of the Department include Arthur Dempster,

Clifford Dowker Clifford Hugh Dowker (; March 2, 1912 – October 14, 1982) was a topologist known for his work in point-set topology and also for his contributions in category theory, sheaf theory and knot theory. Biography Clifford Hugh Dowker grew up on a smal ...

, Donald Fraser,

Walter Kohn Walter Kohn (; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998. The award recognized their contributions to the unde ...

J. Carson Mark Jordan Carson Mark (July 6, 1913 – March 2, 1997) was a Canadian-American mathematician best known for his work on developing nuclear weapons for the United States at the Los Alamos National Laboratory. Mark joined the Manhattan Project in 1945 ...

(Ph.D. 1938),

John Mighton John Mighton, OC (born October 2, 1957) is a Canadian mathematician, author, and playwright. Education and career Mighton was born in Hamilton, Ontario on and lives in Toronto, Ontario with partner Pamela Sinha and daughter Chloe. In 1998 ...

(Ph.D. 2000),

Robert Moody Robert Vaughan Moody, (; born November 28, 1941) is a Canadian mathematician. He is the co-discover of Kac–Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system. "Almost simultaneou ...

(Ph.D. 1966),

Cathleen Morawetz Cathleen Synge Morawetz (May 5, 1923 – August 8, 2017) was a Canadian mathematician who spent much of her career in the United States. Morawetz's research was mainly in the study of the partial differential equations governing fluid flow, parti ...

Gordon Slade Gordon Leigh Slade (October 9, 1904 – January 2, 1974), nicknamed Oskie, was an American professional baseball shortstop. He played six seasons in Major League Baseball (MLB) from 1930 to 1935 for the Brooklyn Robins/Dodgers, St. Louis Cardina ...

Robert Steinberg Robert Steinberg (May 25, 1922, Soroca, Bessarabia, Romania (present-day Moldova) – May 25, 2014) was a mathematician at the University of California, Los Angeles. He introduced the Steinberg representation, the Lang–Steinberg theorem, t ...

(Ph.D. 1948),

James Stewart James Maitland Stewart (May 20, 1908 – July 2, 1997) was an American actor and military pilot. Known for his distinctive drawl and everyman screen persona, Stewart's film career spanned 80 films from 1935 to 1991. With the strong morality h ...

(Ph.D. 1967), and Albert Tucker.

Current members

James Arthur James Arthur (born 2 March 1988) is an English singer and songwriter. He rose to fame after winning the ninth series of ''The X Factor'' in 2012. His debut single, a cover of Shontelle's " Impossible", was released by Syco Music after the fi ...

;

CRM-Fields-PIMS Prize The CRM-Fields-PIMS Prize is the premier Canadian research prize in the mathematical sciences. It is awarded in recognition of exceptional research achievement in the mathematical sciences and is given annually by three Canadian mathematics institu ...

(1997),

(2015), Steele Prize (2017) *

Edward Barbeau Edward Barbeau is a Canadian mathematician and a Canadian Mathematical Educator. He is a Professor Emeritus at the University of Toronto Department of Mathematics. Awards * Fellowship of the Ontario Institute for Studies in Education The O ...

* Dror Bar-Natan * Edward Bierstone *

Stephen Cook Stephen Arthur Cook (born December 14, 1939) is an American-Canadian computer scientist and mathematician who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor at the Unive ...

;

Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...

(1982), CRM-Fields-PIMS Prize (1999) *

Derek Corneil Derek Gordon Corneil is a Canadian mathematician and computer scientist, a professor ''emeritus'' of computer science at the University of Toronto, and an expert in graph algorithms and graph theory. Life When he was leaving high school, Corneil ...

Chandler Davis Horace Chandler Davis (August 12, 1926 – September 24, 2022) was an American-Canadian mathematician, writer, educator, and political activist: "an internationally esteemed mathematician, a minor science fiction writer of note, and among the mos ...

* George Elliott *

John Friedlander John Friedlander is a Canadian mathematician specializing in analytic number theory. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Pennsylvania State University i ...

Lisa Jeffrey Lisa Claire Jeffrey FRSC is a Canadian mathematician, a professor of mathematics at the University of Toronto. In her research, she uses symplectic geometry to provide rigorous proofs of results in quantum field theory. Jeffrey graduated from P ...

Victor Ivrii Victor Ivrii ( rus, Виктор Яковлевич Иврий), (born 1 October 1949) is a Russian, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor a ...

Yael Karshon Yael Karshon (born 1964) is an Israeli and Canadian mathematician who has been described as "one of Canada's leading experts in symplectic geometry". She works as a professor at the University of Toronto Mississauga and Tel Aviv University . Edu ...

* Boris Khesin *

Askold Khovanskii Askold Georgievich Khovanskii (russian: Аскольд Георгиевич Хованский; born 3 June 1947, Moscow) is a Russian and Canadian mathematician currently a professor of mathematics at the University of Toronto, Canada. His area ...

* Stephen Kudla ;

(1981) * Robert McCann * Eckhard Meinrenken *

Pierre Milman Pierre D. Milman (russian: Пьер Д. Мильман), born 1945 in Odessa, is a mathematician and a professor at the University of Toronto. Milman graduated with a B.A. from the University of Moscow in 1967. He obtained his Ph.D. from the Uni ...

* Kumar Murty *

Alexander Nabutovsky Alexander Nabutovsky is a leading Canadian mathematician specializing in differential geometry, geometric calculus of variations and quantitative aspects of topology of manifolds. He is a professor at the University of Toronto Department of Ma ...

Toniann Pitassi Toniann Pitassi is a Canadian and American mathematician and computer scientist specializing in computational complexity theory. She is currently Jeffrey L. and Brenda Bleustein Professor of Engineering at Columbia University and was Bell Resear ...

* Jeremy Quastel ; Sloan Fellowship (1996–98), CRM-Fields-PIMS Prize (2018) *

Jeff Rosenthal Jeffrey Seth Rosenthal (born October 13, 1967 in Scarborough, Toronto, Scarborough, Ontario) is a Canadian statistician and nonfiction author. He is a professor in the University of Toronto's Department of Statistics, cross-appointed with Univer ...

Arul Shankar Arul Shankar is an Indian mathematician at the University of Toronto specialising in number theory; more specifically, arithmetic statistics. He received his B.Sc. (honours) in mathematics and computer science from Chennai Mathematical Institute ...

; Sloan Fellowship (2018) * Israel Sigal * Catherine Sulem *

Stevo Todorčević Stevo Todorčević ( sr-Cyrl, Стево Тодорчевић; born February 9, 1955), is a Yugoslavian mathematician specializing in mathematical logic and set theory. He holds a Canada Research Chair in mathematics at the University of Toront ...

; CRM-Fields-PIMS Prize (2012) * Jacob Tsimerman

Former members

* Frederick Atkinson , Professor (1960–2002) *

Artur Avila Artur Avila Cordeiro de Melo (born 29 June 1979) is a Brazilian and naturalized French mathematician working primarily in the fields of dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first La ...

, Visitor (2011);

(2014) * Samuel Beatty, Professor (1911–33) and Chair (1934–52) *

Richard Brauer Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular represent ...

, Professor (1935–48);

(1949) *

James Colliander James Ellis Colliander (born 22 June 1967) is an American-Canadian mathematician. He is currently Professor of Mathematics at University of British Columbia and served as Director of the Pacific Institute for the Mathematical Sciences (PIMS) dur ...

, Professor (2001–2015); Sloan Fellowship (2003) * Harold Coxeter , Professor (1936–80); CRM-Fields-PIMS Prize (1995),

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...

(1997) * Arthur Dempster, Lecturer (1957–58) *

Gabriel Andrew Dirac Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian/British mathematician who mainly worked in graph theory. He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin 1964-1966. In 1952, he gave a sufficie ...

, Lecturer (1952–53) *

George Duff Captain George Duff RN (c. 1 February 1764 – 21 October 1805) was a British naval officer during the American War of Independence, the French Revolutionary Wars and the Napoleonic Wars, who was killed by a cannonball at the Battle of Trafal ...

, Professor (1952–92) and Chair (1968–75) *

, Professor (1902–32) *

Larry Guth Lawrence David Guth (born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. Education and career Guth graduated from Yale in 2000, with BS in mathematics. In 2005, he got his PhD in mathematics from the Massach ...

, Assistant Professor (2008–11);

(2015) *

Israel Halperin Israel Halperin, (January 5, 1911 – March 8, 2007) was a Canadian mathematician and social activist. Early life and education Israel Halperin was born in Toronto, Ontario, the son of Russian Jewish immigrants Solomon Halperin and Fanny Lun ...

, Professor (1966–78) *

Hans Heilbronn Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematician. Education He was born into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised ...

, Professor (1964–75) *

Leopold Infeld Leopold Infeld (20 August 1898 – 15 January 1968) was a Polish physicist who worked mainly in Poland and Canada (1938–1950). He was a Rockefeller fellow at Cambridge University (1933–1934) and a member of the Polish Academy of Sciences. Ea ...

, Professor (1938–50) *

William Kahan William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist, who received the Turing Award in 1989 for "''his fundamental contributions to numerical analysis''", was named an ACM Fellow in 1994, and inducte ...

, Professor (1963–70); Turing Award (1989) *

Cecilia Krieger Cypra Cecilia Krieger-Dunaij (9 April 1894 – 17 August 1974) was an Austro-Hungarian (more specifically, Galician)-born mathematician of Jewish ancestry who lived and worked in Canada. Krieger was the third person (and first woman) to earn a P ...

, Professor (1928–69) * George Lorentz, Assistant Professor (1950–54);

Humboldt Prize The Humboldt Prize, the Humboldt-Forschungspreis in German, also known as the Humboldt Research Award, is an award given by the Alexander von Humboldt Foundation of Germany to internationally renowned scientists and scholars who work outside of G ...

(1973) *

Louis Mordell Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

, Lecturer (1953–55);

Smith's Prize The Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the n ...

(1912),

De Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the societ ...

(1941), Sylvester Medal (1949) *

Abraham Robinson Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorpo ...

, Professor (1952–57) *

, Professor (1929–30, 1931–71) *

Ralph Gordon Stanton Ralph Gordon Stanton (21 October 1923 – 21 April 2010) was a Canadian mathematician, teacher, scholar, and pioneer in mathematics and computing education. As a researcher, he made important contributions in the area of discrete mathematics; and ...

, Assistant Professor (1950–58) * John Synge , Assistant Professor (1920–25, 1930–43) *

William Tutte William Thomas Tutte OC FRS FRSC (; 14 May 1917 – 2 May 2002) was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a majo ...

, Associate Professor (1948–62); CRM-Fields-PIMS Prize (2001) *

Maria Wonenburger María Josefa Wonenburger Planells ( Montrove, Oleiros, Galicia, July 17, 1927 – A Coruña, June 14, 2014) was a Galician mathematician who did research in the United States and Canada. She is known for her work on group theory. She was the fir ...

, Associate Professor (1962–66) * Maciej Zworski , Professor (1995–2000)

References

{{Mathematics in Canada 1877 establishments in Ontario Research institutes in Canada

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

University departments in Canada University of Toronto

History

Academics

Awards and medals

Rankings

Notable members

Alumni

Current members

Former members

See also

References