History of Mathematics in Canada

Early Quebec History

The evolution of mathematics in New France followed closely on the heels of this newly acquired stature. Although there were no new discoveries, the quality of teaching was virtually equal to that found in colleges in France. The Jesuits founded Collège de Québec in 1635 and started to teach intermediate mathematics there in 1651. (See also Collège des Jésuites.) Until 1760 students were taught arithmetic, the rudiments of second-degree or quadratic equations, trigonometry, geometry and a little differential and integral calculus - all in one of the two final years of the eight-year course of studies. The first full professor was Martin Boutet de St-Martin. In 1678 Louis XIV appointed him to the new royal chair of mathematics and hydrography in Quebec City, his wish being that pilots for the St. Lawrence River and surveyors and cartographers be trained in the colony. (See also Cartography in Canada: 1600-1763.) The chair was not abolished until the end of the French regime.

The most celebrated appointee to this chair was Louis Jolliet, the discoverer of the Mississippi River. Soon after Jolliet's death, the chair officially passed to the Jesuits.

After the Conquest of New France (1759-60), the Collège de Québec had to close, but the Séminaire de Québec, which took over its operations, retained the same classical course structure. Encouraged by Abbé Jérôme Demers, the teaching of science and mathematics flourished, particularly around 1840. Soon, however, for sociological and religious reasons, it fell into disfavour. Even at the École polytechnique de Montreal, an engineering school founded in 1873, only intermediate mathematics was taught until 1910. It was only until 1920 that the sciences were recognized as valuable among Quebec francophones. In that year, Université Laval (Quebec City) organized its École supérieure de chimie (which became its faculty of science in 1937) and Université de Montréal established its Faculty of Science.

Early English Canada History

Nothing significant in the field of mathematics occurred in English Canada until 1855. Of the few English-language universities in Canada, only the University of Toronto offered programs with specializations, one being in mathematics and natural philosophy (the latter term signifying the physical sciences). (See also Philosophy.) However, each university had a mathematics and natural philosophy professor. Trained in Great Britain, these few professors brought with them the idea that science and technology were central to the Industrial Revolution (see Industrialization in Canada).

A Canadian scientific community thus began to take shape and the need for communication among its members was felt almost immediately. In 1856 the Canadian Journal of Science, Literature and History, published under the aegis of the Royal Canadian Institute, accepted articles on mathematics and continued to do so until 1912. Professor J. Bradford Cherriman (University of Toronto) was in charge of the section on mathematics and natural philosophy.

In the 1870s the idea arose of more specialized university studies. In 1877 the University of Toronto launched its mathematics and physics programs, which became models for the rest of Canada during the first half of the 20th century. Other universities, e.g., Queen's University, McGill University and Dalhousie University, gradually moved in the same direction. During this time, science departments were being subdivided, and by 1890 almost all universities (with the exception of McGill University) had at least one mathematics (no longer a "mathematics and natural philosophy") professor. At the same time, bursaries were offered for studies in mathematics, two each at University of Toronto and Dalhousie University.

In addition to J. Bradford Cherriman, three mathematicians merit special mention for the impetus they gave to the establishment and development of mathematics programs at their respective universities: James Loudon of University of Toronto, Alexander Johnson of McGill University and Nathan Fellowes Dupuis of Queen's University. In 1890 all were members of the Royal Society of Canada. Founded in 1882, this society was originally divided into four sections, one of which was mathematics and natural philosophy. The society reserved a place for the mathematics publications of its members in its Proceedings and Transactions, thereby offering a new means of communication for the mathematics community. In 1878 the American Journal of Mathematics was founded at Johns Hopkins University, Baltimore, followed in 1886 by the American Mathematical Society which, from 1891 on, published its Bulletin and from 1900 on, its Transactions. Canadian mathematicians contributed regularly to these journals.

Early 20th Century

The number of mathematics departments increased during the first two decades of this century, as a result of the growing importance of mathematics in professional fields (e.g., engineering). The University of Toronto was the first North American university to move into the field of actuarial science (i.e., the calculation of insurance and annuity premiums and dividends). The Canadian Institute of Actuaries, a professional society, was founded in 1907.

In 1915 the University of Toronto awarded the first Canadian doctorate in mathematics to Samuel Beatty, who later became the head of that institution's mathematics department. The University of Toronto increasingly took the lead in Canada and held it until the end of the 1950s. One of the most notable figures in the department was undoubtedly John Charles Fields, renowned for his work in algebraic functions, and one of those who managed to revive the International Congress of Mathematics, meetings of which had been suspended after the First World War. The first meeting after the war was held in Toronto in 1924. In 1936 the algebraist and geometer Harold Scott MacDonald Coxeter joined the department.

Did you know?
John Charles Fields, reacting to the lack of a Nobel Prize for the field of mathematics, began working to establish an equivalent prize. (See also Nobel Prizes and Canada.) The Fields Medal, named in his honour, is now universally recognized as the greatest honour that can be conferred on a mathematician.

An example of the high calibre of teaching then being provided in Toronto can be seen in the first years of the American William Lowell Putnam Mathematics Competition. Only undergraduates could participate in this competition and each university entered a team of three students. In the first year, 1938, the University of Toronto team won first place over all the North American universities. The competition rules prevented University of Toronto from entering a team the following year, but in 1940, it won again, as it did in 1942 and 1946. In the 1986 competition, teams from two Canadian universities (University of British Columbia and University of Waterloo) ranked among the top 10 (the others being the University of Harvard, Washington University in St. Louis, University of California Berkeley, Yale University, Massachusetts Institute of Technology (MIT), California Institute of Technology, Princeton University and Rice University. Since then, Canada has continued to do well in the competition, which has been dominated by Harvard University and Duke University since 1985. In 1998, University of Waterloo placed fifth, and had two students in the top 15; Simon Fraser University had one student in the top 15; Dalhousie University had one in the top 26; and University of Toronto had a three-member team that received an honourable mention.

The end of the Second World War was a turning point for mathematics in Canada. During the war Canadian mathematicians became aware of their isolation, even within Canada. If they wished to meet, they had to participate in meetings of the American Mathematical Society. They therefore organized the first Canadian mathematical congress, held in Montreal in June 1945. This very successful gathering led to the creation of the Canadian Mathematical Congress, which in 1978 changed its name to the Canadian Mathematical Society.

In 1949 the society began publishing the Canadian Journal of Mathematics, an internationally recognized publication, to which was added the Canadian Mathematical Bulletin in 1958 and the Canadian Mathematical Congress Notes in 1969. In 1950, still under the aegis of the congress, Professor R.L. Jeffery, from Queen's University, organized a Summer Research Institute in Kingston, which brought together 10 mathematicians to conduct joint research. This type of meeting proved so fruitful that summer research institutes have been held annually in some universities.

Late 20th Century

In the 1950s mathematics departments developed very quickly. Toronto lost its leadership, not because its quality of teaching had declined, but because departments in other Canadian universities had improved - a case of students surpassing their teachers.

Graduate studies burgeoned everywhere. Because of the development of statistics, operations research and computer science, industry showed increasing interest in mathematics graduates. However, forecasts of major increases in the student population in the 1960s indicated that there would be a high demand for university professors. With the launching of the first Sputnik by the USSR in 1957, mathematics once again found itself in the public eye, and the "New Math" movement began. In the same year, the National Research Council of Canada (NRC) began to give grants to mathematician-researchers and two new societies were founded: the Canadian Information Processing Society and the Canadian Operational Research Society.

The prodigious development of computer science and diversified interests among mathematicians and computer scientists later led to the subdivision of mathematics departments in almost all universities into mathematics and computer science departments, the most striking example being the creation in 1966 of the Faculty of Mathematics at the University of Waterloo, with its five constituent departments: pure mathematics, applied mathematics, combinatorics and optimization, applied analysis and computer science, and statistics.

In Quebec francophone universities returned to the Canadian mainstream around 1945 after successfully overcoming the difficulties generated by the prolonged lack of a scientific tradition in that province. By 1970 the department of mathematics at Université de Montréal had acquired an international reputation under the direction of Maurice L'Abbé, and had established a Centre recherches mathématiques, which is highly regarded internationally.

The early 1970s were truly a golden age for mathematicians in Canada. In 1961 Canadian universities had awarded 11 PhDs in mathematics; this number increased to 94 in 1973. The NRC in 1960-61 gave $87,500 for mathematics research; the figure for 1972-73 was $2,461,500. The figure in 1986-87 was $8,419,000.

The Statistical Sciences Association of Canada, later known as the Statistical Society of Canada, was founded in 1971; it publishes the Canadian Journal of Statistics. In 1973, the Canadian Society for the History and Philosophy of Mathematics began its activities. Another association, the Canadian Applied Mathematics Society, was created in 1980. It publishes Applied Mathematics Notes and sponsors Canadian Applied Mathematics Quarterly founded in 1992.

In 1991, a group of Ontario universities sponsored a second research center, the Fields Institute for Research in Mathematical Sciences. Initially in Waterloo, it is now located on the University of Toronto campus.

Today the number of members of the Canadian mathematical community has grown. The Canadian Mathematical Society, which celebrated its 50th birthday in 1995, had a membership counting 1,209 individuals and 39 institutional members in 1994. According to a survey based on papers reviewed in the international Mathematical Reviews, Canada's impact on international mathematics is now much greater that the population alone would predict (73 mathematical research papers per year per million of the population in 1990. The United States and Holland followed with 47 mathematical research papers per year per million of the population).

In 1961 there were about 250 university mathematics professors (assistant rank and higher) in Canadian universities; in 1973, about 1,300.

Canadian Mathematics Community

The Canadian mathematics community, like other scientific communities, is affected by the movement of promising graduates to the United States, a fact that further testifies to the level of excellence of instruction in Canadian departments. Mathematicians with international reputations who received their early training in Canada include Cathleen Morawetz (University of Toronto); Robert Langlands (University of British Columbia); Israel Herstein (University of Manitoba); Irving Kaplansky (University of Toronto); Louis Nirenberg (McGill University); G.F. Duff (University of Toronto); Leo Moser (University of Manitoba); W.O. Moser (University of Manitoba); Raoul Bott (McGill University).

The Canadian mathematics community faces a number of challenges. Connections seem to have been made among university departments, industry and government in such fields as statistics and computer science, where the future appears to hold promise. However, other areas of mathematics appear more sensitive to difficult economic conditions.