My Coxeter

Cover Article
September 2024 TOC icon
Cover Article
September 2024 (Vol. 56, No. 4)

In 1984, when I was in eighth grade, I fondly remember visiting the Second-Hand Technical bookstore, a cherished shop filled with out-of-print textbooks. This bookstore was like a treasure trove for me. One day, I stumbled upon a Russian translation of “Geometry Revisited” by H. S. M. Coxeter and S. L. Greitzer. I was ecstatic to have found it, and even more thrilled when I discovered that it was available for the equivalent of just 10 cents. Even for a Soviet high school student, the price was acceptable.

As a high school student, I found “Geometry Revisited” to be highly accessible. I was excited to discover that it provided a plethora of techniques for solving complex geometry problems often encountered at Math Olympiads. However, upon delving into its contents, I soon realized that the book offered much more than just a problem-solving resource. “Geometry Revisited” completely transformed my perspective on geometry, leading me to ponder the intricate interconnections between different branches of mathematics. This newfound appreciation for the subject opened up a whole new world of understanding for me.

The authors’ intention, as stated in the preface, to combat the prevalent notion that geometry was somehow outside the mainstream of mathematics resonated deeply with me. They emphasized that geometry is not only helpful but absolutely essential for scientists and practical mathematicians, challenging the belief that analysis or set theory should overshadow it. This message struck a chord with me, especially considering the more central role that geometry played in the Soviet education system at that time, compared to the educational approach in the US. The book’s message remained remarkably relevant despite the contrasting educational systems.

I found myself deeply fascinated by the authors. After delving into additional research, I unearthed that Samuel Gleitzer played a pivotal role as one of the founding members of the American Mathematical Olympiad. Moreover, I learned that he was fervently dedicated to advocating for programs aimed at fostering the mathematical abilities of high school students throughout the United States.

I was truly captivated by the work of the second author, H.S.M. Coxeter. His name seemed to be intricately woven into my subsequent academic pursuits, whether I was delving into the complexities of Coxeter groups, analyzing Coxeter diagrams, or unravelling the intricacies of the Todd-Coxeter algorithm. His scholarly contributions were of such great magnitude that I found it remarkable that someone of such monumental importance had also taken the time to co-author an introductory textbook on geometry. In 1984, I was utterly captivated by all aspects of Coxeter, from his groundbreaking work to his captivating workplace at the University of Toronto. Although my knowledge of Canada was limited at the time, the country became synonymous with Coxeter, forever etched in my mind as an integral part of his work. While I knew essentially nothing of Coxeter as a person, I deeply admired him as a mathematician.

In 2004, I embarked on my journey at the University of Toronto, knowing that I had just missed the opportunity to meet my mathematical role model, Coxeter, who passed away in 2003 at the remarkable age of ninety-six. As I integrated into my new academic environment, I eagerly absorbed stories from my colleagues who had known him and delved into newspaper articles paying tribute to his legacy. Through these avenues, I uncovered more about Coxeter’s endearing British sense of humor, his unwavering commitment to a healthy lifestyle that clearly bore fruit, and his profound adoration for Mathematics as a whole, with a particular emphasis on Geometry. I also gained insight into his passionate mission to safeguard Classical Geometry as an integral focal point within the field of Mathematics.

And, another twenty years later, his legacy lives on. You encounter it everywhere at my University. His exquisite collection of polyhedral is showcased in the Mathematics Department. His concert piano and a famous portrait of him playing the piano as a toddler (painted by his mother) are in the Fields Institute.

But, more importantly, his legacy is cherished in our Society. Coxeter’s contributions to the CMS are numerous and influential. His significant roles included serving as the society’s seventh president from 1965 to 1967, as well as vice-president from 1963 to 1965. Additionally, he chaired the Proceedings of the First Congress, served on the Publications Committee in 1957, and was a member of the Board of Directors from 1949 to 1953 and then again from 1958 to 1965. Furthermore, he held the esteemed position of the first Editor-in-Chief of the Canadian Mathematical Journal from 1949 to 1957 and continued to contribute as a member of its editorial board from 1958 to 1975. Earlier, Coxeter served on the Journal Committee from 1945 to 1953. His involvement extended to serving on the Nominating Committee in 1953 and 1963 and the Finance Committee for one year in 1966. This extraordinary dedication and service are rightly celebrated by the Society through the establishment of the Coxeter-James Prize. Instituted in 1978, this prestigious award is presented annually to young mathematicians who have made exceptional contributions to mathematical research, in recognition of Coxeter’s enduring legacy.

I am confident that the Canadian Mathematical Society, along with the broader Canadian mathematical community, will uphold Coxeter’s legacy by perpetuating his deep affection for all areas of mathematics, and particularly his profound dedication to the study of Geometry. His relentless pursuit of excellence will undoubtedly continue to inspire and guide future generations of mathematicians like it guides me now.

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