Donald Coxeter: The mathematical giant who inspired The Coxeter Lecture Series
Outside of academia, the name Donald Coxeter is unlikely to ring a bell. But the British-born mathematician, who spent seven decades teaching at the University of Toronto, made contributions to geometry that were so significant, he came to be known as “The Man Who Saved Geometry.” He is credited with almost singlehandedly salvaging classical geometry from an attempt to algebraecize it out of existence.
A man who could “really see things”
Coxeter’s combination of genius and elegance advanced the field and restored classical geometry to its place in the mathematical pantheon.
Coxeter groups and Coxeter diagrams, for instance, are tools for investigating symmetry — such as the symmetrical shapes generated by reflections in a kaleidoscope. As Siobhan Roberts writes in her definitive biography on Coxeter, “King of Infinite Space”:
You can think of these concepts as something like Internet plug-ins: they allow a crude operating system (the brain) to interface with a higher medium (say, four- or five-dimensional space). Significantly, they help the field of classical geometry mingle more effectively with algebra.
This link between the two fields, in particular, is notable for rescuing geometry from a 1970s coup attempt. As the legend goes, the consortium of French mathematicians who wrote a very influential series of textbooks on modern mathematics under the name Bourbaki fought to remove the use of geometric diagrams in textbooks in an attempt to preserve the “purity” of rationality. The thrust of his argument was that human visual senses are “weak” and therefore unreliable, leading to subjectivity and error.
Without reducing himself to public spectacle, Coxeter leveled his opponent with a combination of proof and diplomacy. “Everyone is entitled to their opinion,” he once said, “but Bourbaki is sadly mistaken.”
The shape of influence
Coxeter’s work on symmetry and the principles that bear his name are considered among “the pillars of mathematics” and his resurrection of pure geometry has informed an astonishing breadth of applications, including data mining, e-commerce, protein folding, cosmology, animation, and the algorithms that digitally design the shape of cars.
No statement about the man better contextualizes his impact than that of Michel Broué, the former director of l’Institut Henri Poincaré, who was genuinely astonished to learn he had been alive at the same time as such a giant.
“I thought he had lived in the nineteenth century,” Broué told filmmakers in the Coxeter documentary, “The Man Who Saved Geometry”. “His name was everywhere. He was such a legend.”
The Coxeter Lecture Series
The Fields Institute is proud of our long relationship with both the man and his legacy. Coxeter was the 1995 CRM-Fields-PIMS prize recipient and frequent visitor to the College St. building. A musician who tried his hand at composing, Coxeter’s piano (left) is now displayed in the Institute’s foyer.
Each year, Fields holds a prestigious lecture series in Coxeter’s honour. A world-renowned international mathematician is selected via scientific committee to deliver three talks that correspond to the Institute’s current thematic program. The first talk is designed for a general audience, while the remaining lectures highlight recent developments and advancements in the field of study.
Past lecturers include the luminaries Michael I. Jordan, Kenji Fukaya, Claire Voisin, Moshe Vardi, and Nicole El Karoui, just to name a few.
This year’s lecturer, Gil Kalai, from the Hebrew University of Jerusalem, will deliver three talks on recent work at the Program on Geometric Constraint, Framework Rigidity, and Distance Geometry.
A legacy in numbers
Coxeter published papers well into his 90s and long after he retired. His final keynote was delivered in Hungary when he was 95 years old — he couldn’t get clearance from his doctor or insurance company to attend, but he made the journey nonetheless. He died in 2003.
In a fame and celebrity-focused culture, it can be easy to lose focus on what motivates people pursue excellence. It’s rare to find individuals who remain entirely unaffected by the trappings of success. Coxeter inhabited a purity of calling that is rarely seen anymore.
Or, as York University’s Asia Weiss beautifully summed it up, “He had that love for geometry and when he spoke about geometry, he was shining. He was not guided by money; he was not guided by fame; he was only guided by his love.”
The Coxeter Lecture Series will be delivered by Gil Kalai between June 14-18, 2021. Register here to attend.
