# William Oscar Jules Moser

William Oscar Jules Moser , called Willy Moser , mostly quoted WOJ Moser , (born January 5, 1927 in Winnipeg , † January 28, 2009 in Montreal ) was a Canadian mathematician who studied combinatorial geometry and group theory .

Moser was the son of Austrian emigrants who immigrated to Canada before he was born in the 1920s. He studied mathematics at the University of Manitoba with a bachelor's degree in 1949 and at the University of Minnesota with a master's degree in 1951. He then went to the University of Toronto , where he received his doctorate in 1957 at HSM Coxeter . The joint book with Coxeter on combinatorial group theory emerged from parts of the dissertation. In 1955 he became an instructor and in 1957 an assistant professor at the University of Saskatchewan . In 1959 he became an associate professor at the University of Manitoba and in 1964 at McGill University , where he became professor in 1966 and retired in 1997.

With Coxeter he wrote a standard work on combinatorial group theory and he published several books on problems of discrete geometry. He dealt, among other things, with the subject of the sentence by Sylvester and Gallai . With Leroy Milton Kelly in 1958 he proved that in a plane arrangement of n points ( ), which are not all collinear, there are at least straight lines which contain exactly 2 points (and that this is also the upper bound for n = 7). An unproven guess by Gabriel Andrew Dirac states that there are at least straight lines. ${\ displaystyle n \ geq 3}$${\ displaystyle 3 \ lfloor n / 7 \ rfloor}$${\ displaystyle \ lfloor n / 2 \ rfloor}$

His brother Leo Moser was also a mathematician.

From 1973 to 1975 he was President of the Canadian Mathematical Society , whose Distinguished Service Award he received in 2003. From 1961 to 1970 he was editor of the Canadian Mathematical Bulletin and from 1981 to 1984 Associate Editor of the Canadian Journal of Mathematics.

## Fonts

• with Coxeter: Generators and relations for discrete groups, Springer Verlag 1957, 4th edition 1980
• with Peter Brass, Janos Pach: Research problems in discrete geometry, Springer 2005
• Problems on extremal properties of a finite set of points, Annals of the New York Academy of Sciences, Volume 440, 1985, pp. 52-64
• with Peter Borwein : A survey of Sylvester's problem and its generalizations, Aequationes Mathematicae, Volume 40, 1990, pp. 111-135
• On the relative widths of coverings by convex bodies, Canadian Mathematical Bulletin, Volume 1, 1958, p. 154
• Abstract definitions for the Mathieu groups and , Canadian Mathematical Bulletin, Volume 2, 1959, pp. 9-13${\ displaystyle M_ {11}}$${\ displaystyle M_ {12}}$