Caltech Mourns the Passing of David Wales (1939–2023)

Caltech’s mathematics professor David Wales, who spent more than 50 years at the Institute, passed away on July 17. In addition to serving on the faculty in the Division of Physics, Mathematics and Astronomy, he was also Caltech’s associate dean of students from 1976 to 1980, dean of students from 1980 to 1984, executive officer for mathematics from 1985 to 1991, and the master of student houses from 1991 to 1997. Wales retired in 2008 but remained active in math research and attended talks at Caltech.

Wales was an expert in group theory, algebraic combinatorics, and representation theory. He spent the most time on finite group theory, searching for and studying what are called simple groups. In the same way that prime numbers can be thought of as the building blocks of integers, simple groups are the building blocks of finite groups, which are those groups with a finite number of elements.

In an interview with the Caltech Heritage Project, Wales explained that “groups are algebraic constructions, which are sets with a multiplication between elements, which gives another element of the set. The multiplication has properties much like multiplication of ordinary numbers but with different rules. Certain groups are called simple. In a sense, they are the building blocks of all groups.”

“I always enjoyed talking to David over the years, and he always answered patiently a lot of questions in group theory, which is a neighboring discipline of my field of number theory,” says Dinakar Ramakrishnan, the Taussky-Todd-Lonergan Professor, Emeritus, at Caltech. “I know many people liked to talk to David to see if his work could be useful to them. David was always quite helpful to others.”

Wales was born in 1939 in Vancouver, Canada. His father was a high school physics and math teacher, and later a school principal. Wales said that his mother, who had a degree in library science, spent her time raising him and his two younger brothers, Terry and Keith.

Wales grew up during World War II and, in his Heritage Project interview, recalled how his family had to pull down blackout blinds over the windows every night. “People were afraid that the Japanese would bomb Vancouver the way they did Pearl Harbor,” he said. When the war ended in Europe, he and his family drove around town in his mother’s Model-T Ford. “There were all kinds of people in the street waving flags and shouting and cheering, so it was exciting.”

Wales earned his bachelor’s and master’s degrees from the University of British Columbia in 1961 and 1962, respectively. He earned his PhD from Harvard in 1967, studying under Richard Brauer, who was known for creating representations of finite groups. Wales joined Caltech as a Bateman Research Fellow in 1967; he became an assistant professor in 1968 and a full professor in 1977.

Wales said that one of the reasons he chose to come to Caltech was to work with the late Marshall Hall, a Caltech professor whom he called “a famous group theorist.” Wales was also drawn to the small size of Caltech and the students. “The students are extremely good, very good all around, but the very good mathematics students are excellent,” he said.

“David was a joyful person, always positive and affirming, which was very comforting for students going through a tough time,” says Kitty Cahalan, assistant director for educational outreach. “I don’t think I ever heard him say an unkind thing to or about anyone. After he retired, he and his wife Kathy were always planning their next adventure to some far-flung place in the world, neither of them the type to let the grass grow under their feet. Family was always very important to him, and Caltechers were very lucky to have him consider all of us as part of his family.”

In his early years at Caltech, Wales worked on several projects involving the representation theory of finite groups, explains Michael Aschbacher, the Shaler Arthur Hanisch Professor of Mathematics, Emeritus. “He determined the finite groups with a faithful representation of small degree. He and his students determined the simple groups whose order is divisible by just three primes.”

Aschbacher notes that Wales worked with Hall on a simple group known as the Hall-Janko group, sometimes referred to as HJ. “Wales proved the uniqueness, subject to suitable constraints, of HJ, using a pretty argument applicable to other sporadic groups,” Aschbacher says. Wales also proved the existence of another sporadic simple group, the Rudvalis group, together with the late mathematician John Conway.

In his Heritage Project interview, Wales said of his time as associate dean and dean of students: “Although things were sometimes stressful, especially the calls during the middle of the night, I really had fun with the people who I was working with and enjoyed the contact with students.” Later, as a master of student houses (a position that no longer exists), Wales was responsible for hosting social gatherings for students at Steele House.

“Steele House was a wonderful place for hosting students,” he said. “Up to around 24 people could be comfortably seated in the dining room and adjoining sun porch. We had a pool table put in the library. The biggest attraction was the real pipe organ in Steele House. There was a large room at the side of the house that held the 3,000 pipes. The organ was later removed when Steele House was converted to other uses.”

“When I came to Caltech in 1993 as director of housing, David was the master of student houses,” says Tom Mannion, senior director of student activities and programs at Caltech. “I went on many retreats with David and the RAs, and was always struck with how much he cared about our students. When David saw students, he would always ask how they were doing, and he was always ready to help. We served on the Avery House design and construction committee together and much of the design and function of the building is a result of his guidance. From wooden baseboards to faculty in residence and a truly interactive design, Avery House is a daily reminder of David’s caring for our students.”

In his spare time, Wales liked to hike in the San Gabriel and Sierra Nevada mountains. Since 2015, he had also been helping a Dutch colleague, Arjeh Cohen, translate mathematical educational materials to English.

Wales is survived by his wife, Kathy Wales, and his two children from a previous marriage, Jonathan and Jennifer.