Canadian Mathematical Society
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September 16, 2003


The CMS Distinguished Service Award was created in 1995 to recognize individuals who have made sustained and significant contributions to the Canadian mathematical community and, in particular, to the Canadian Mathematical Society. William Moser is awarded the Canadian Mathematical Society 2003 Distinguished Service Award.

William Oscar James Moser was born in Winnipeg in 1927, one of the twin younger brothers of Leo Moser. His involvement in mathematics was, in some way, affected by that of his late brother Leo, a fine mathematician with similar mathematical interests, whom he has always idolized. He obtained his B.SC Hons. from the University of Manitoba and an M.A. from the University of Minnesota in 1951. He obtained his Ph.D. from the University of Toronto under the supervision of Donald Coxeter in 1955. William Moser's relations with Donald Coxeter were beyond those of a former student: during his whole life he spent many respectful hours visiting Coxeter, particularly later in Coxeter's life; some of his trips to Toronto have been only to visit Coxeter.

His first academic position - four years at the University of Saskatchewan - was followed by five years at the University of Manitoba. He spent the rest of his career at McGill University where he was Associate professor in 1964 and became Professor in 1966.  He retired from McGill University and became Professor Emeritus in 1997.

During his career William Moser published over 40 papers, mostly in classical combinatorics and also in combinatorial group theory. His first publication in 1957, a joint book With Donald Coxeter "Generators and relations for discrete groups" has been published in an unprecented number of four editions in the distinguished series Ergebnisse der Mathematik und Ihrer Grenzgebiete of Springer Verlag. The book was translated to Russian in 1980. Today, 46 years after the first edition appeared, its usefulness as the definitive handbook in the area remains undiminished. William Moser also became famous for his 1958 paper "On the number of lines determined by n points" with L.M. Kelly. Indeed the celebrated Sylvester-Gallai theorem states that given n points in the plane, not all on a line, they always determine a "simple" line, i.e., one that passes through precisely two of the points. According to Dirac's famous conjecture, there are at least n/2 such simple lines, provided that n is sufficiently large. The paper of Kelly and Moser was a breakthrough in the subject by showing that the number of simple lines is at least (3/7)n, which is sharp for n=7. Moreover, there argument holds in the projective plane without using any metric properties of the plane, which opened a completely new line of research. Willy Moser's famous problem collection RPDG=Research Problems in Discrete Geometry grew out of a list of "Poorly formulated unsolved problems in combinatorial geometry", circulated by his brother Leo at a 1963 conference in Boulder. It had an enormous effect on the field by popularizing many of its most notorious questions. Its later editions co-authored by Janos Pach reached virtually everybody interested in the subject, and is widely referenced. William Moser also has done extensive reviewing: MR, Zbl and other locations.

William Moser has an admirable record of Service to the Canadian Mathematical Society in many areas: publications, olympiads, administration. In particular he was president from 1973 to 1975. He was Editor-in-Chief of the Canadian Mathematical Bulletin from 1961 to 1970, Chairman of the Publications Committee from 1970 to 1974 and an Associate Editor of the Canadian Journal of Mathematics from 1981 to 1985.

Since the beginning of his career in 1955, William Moser has been involved with high-school/college mathematics in a variety of ways, particularly serving on committees arranging provincial mathematics competitions in Saskatchewan, Manitoba and Quebec. He was a member of the CMS Education Committee when, under the chairmanship of Lloyd Dulmage, it instituted the Canadian Mathematical Olympiad. He edited (some with Ed Barbeau) the booklets containing the problems, solutions and results of the Canadian mathematical Olympiads from 1969 to 1978. During the years 1975-1985, he, E. Barbeau and M. S. Klamkin edited five collections of problems (500 problems altogether) that the CMS printed and distributed widely. The full collection, corrected and improved, has been published by MAA in its spectrum series as 500 Mathematical Challenges in 1995. He has also taught N.S.F. Summer Institutes for High School Teachers (1959--62) and participated in the College Geometry Project (1964--68) at the University of Minnesota, making beautiful films, one about Coxeter.

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