For over 150 years, the department of mathematics at the University of Toronto has provided one of the very best mathematics programs for undergraduates in North America and been the main training ground for Canadian mathematicians. With 43 faculty members, it is the strongest mathematics department in Canada, and it ranks among the best 15 departments in North America. Two generous donors have provided the department with endowed chairs: the Ted Mossman Chair in Mathematics and the Norman Stuart Robertson Chair in Applied Mathematics.

One measure of the stature of the department is the quality of our graduates. They gain admittance to the best graduate programs in the world, attain academic positions in Canada and beyond and are sought after by computer, financial, telecommunications and other technological industries, reflecting the importance of mathematics to advanced careers in a knowledge-based economy.

Mathematics is undergoing an explosion in new ideas and techniques, as well as in the understanding of basic mathematical structures. The discipline is also central to areas of study from economics to engineering, where it provides theoretical concepts and fundamental language. Our faculty are major players in mathematics at the international level with active research programs in analysis, applied mathematics, geometry and number theory.

The department is also a vital force in undergraduate education with more than 5,500 undergraduate students in mathematics classes across the university. Mathematics is continuously adapting its curriculum to correspond to the changing discipline and the needs of other departments for mathematics instruction. A commitment to quality teaching is also evident in the four Faculty of Arts and Science Outstanding Teaching Awards won by mathematics faculty over a six-year period.

The U of T is Canada's leading centre for research in mathematics. Our stature was a major factor in the decision of an international panel to locate the Fields Institute for Research in Mathematical Sciences at U of T. Faculty and graduate students play a leading role in many of the programs of the institute. Almost one-third of the mathematicians who are fellows of the Royal Society of Canada hold appointments in our department and one-eighth of the total national research grant budget for mathematics in Canada is awarded to our faculty members.

Faculty members include James Arthur, recently elected to the Royal Society of London and winner of the Henry Marshall Tory gold medal of the Natural Sciences and Engineering Research Council of Canada, and one of the world's foremost researchers in automorphic forms and Lie group representations. Michael Sigal in mathematical physics and Victor Ivrii in partial differential equations are changing our understanding of the behaviour of solutions of equations fundamental to physical behaviour. Arthur and Sigal are the first two winners of the Synge Prize of the Royal Society of Canada. John Friedlander's discovery that infinitely many primes can be written as the sum of a square and a fourth power is one of the striking developments of the century in this field. Edward Bierstone and Pierre Milman have provided a constructive, understandable proof of a famous theorem in algebraic geometry. The department has also attracted strong young mathematicians in such fields as geometry and geometrical physics, applied probability and partial differential equations, applied mathematics and mathematical finance. Our new young faculty members have won four prestigious Sloan Fellowships, two Premier Research Awards, and a McLean Prize.

The department of mathematics and the Fields Institute make Toronto a major centre in the international network of mathematics research. We host numerous visiting scientists and postdoctoral fellows who enrich the academic environment by bringing our graduate students and faculty in contact with mathematics around the world. Our mathematicians, in turn, regularly lecture about their research all over the globe.

Department members also serve regularly on international editorial boards and national and international academic committees. James Arthur is a trustee of the Institute for Advanced Study; Steve Halperin is a member of the selection committee (mathematical and physical sciences) for the Royal Society of Canada; Lisa Jeffrey is a council member of the Natural Sciences and Engineering Research Council of Canada (NSERC) and Catherine Sulem was chair of the NSERC grant selection committee for mathematics.

The department mounts an active program to develop and maintain connections outside the university. Faculty members play key roles in the development of Ontario curriculum, and are active in the Fields Mathematics Education Forum, which brings together high school teachers and university faculty (and was, in fact, started by the department). For high school teachers there is a super "math problems" club jointly sponsored with the Fields Institute. Finally, we have a new and rapidly developing active alumni association, with more than 100 members.