In Memoriam: Peter Nicholas Burgoyne (1932–2021)

To: UC Santa Cruz Community

From: Anthony Tromba, Distinguished Professor of Mathematics

Nicholas Burgoyne

Peter Nicholas Burgoyne, professor emeritus of mathematics, passed away on Tuesday, December 7, 2021. Nick, as we all called him, first came to UC Santa Cruz on sabbatical in the fall of 1967 from the University of Illinois (his second position after a stint at UC Berkeley) and obviously made a splash since he was soon made an offer to join our faculty the next year as a tenured fellow of Cowell College.

Nick was used to making splashes. When he was only 23, his 1955 McGill University M.A. thesis, Cohomology Theory in Abstract Groups, was published as a book by McGill University Press—an extraordinary achievement. At the time, he also had an interest in physics, so he decided to spend his next year at the Niels Bohr Institute in Copenhagen. There, he met the famous Princeton mathematical physicist Arthur Wightman, who was impressed enough to invite Nick back to Princeton as a graduate student.

At Princeton, Nick was made aware of the fact that, to the discomfort of many leading physicists, a fundamental theorem central to physics, the spin-statistics theorem, had not yet been rigorously established by a mathematical proof. The spin-statistics theorem implies that half-integer spin particles are subject to the Pauli exclusion principle while integer spin particles are not.

The basic building blocks of matter such as protons, neutrons, and electrons are fermions (particles with half-integer spin). Particles such as the photon are bosons (with integer spin). The Pauli exclusion principle states that two or more identical fermions cannot occupy the same quantum state simultaneously.

As a beginning Princeton graduate student, and essentially having mainly a background in group theory, Nick applied Hilbert space methods and a new theorem in quantum field theory to completely solve the problem.

At Santa Cruz, Nick returned to his first love, group theory, and the big 20th century problem of the classification of finite simple groups.

In the mid 1970s, the famous group theorist John Thompson made a conjecture called the U-Conjecture involving four properties of centralizers of involutions in finite simple groups. Nick verified these properties completely, proving Thompson’s conjecture in the most important cases.

In other work, with his student Carolyn Williamson, Nick classified all involutions and their centralizers in groups of Lie type of odd characteristic.

One can say that Nick's work as an active faculty member was primarily about studying properties of known simple groups, which of course played a vital role in the inductive proof of the historic classification of finite simple groups. Nick was also known to be extraordinarily generous with his ideas, and his mathematical work was both lucid and compelling.

In the Mathematics Department he was, for many years, the person in charge of the curriculum—both the development of new courses and the faculty teaching assignments, which he always did in a fair and judicious manner.

He was an opponent of what he saw as the extremes that some of the colleges went to in those early years, and we all knew that Nick Burgoyne was straightforward, direct, and never minced his words.

In retirement Nick remained mathematically very active, working especially with UCSC Professor Emeritus Al Kelley.

Nick Burgoyne was truly a unique person with an off-beat sense of humor who had an extraordinarily wide range of interests which he pursued throughout his life. He was first and foremost an excellent mathematician, and he was also a race car driver with an interest in biblical languages, a licensed pilot, a mountain climber, an accomplished skier, and an avid hiker who reputedly knew every trail in Yosemite.

Nick leaves behind his son Mark, daughter-in-law Aileen, former wife Christa, and two grandchildren, Sofia and Nico.