Hale Freeman Trotter, Arts ’52, MA’53 (Mathematics), born May 30, 1931 in Kingston, Ontario, died in his ninety-first year on Jan. 17, 2022 at his home in Princeton, New Jersey. Predeceased by his beloved wife Kay, his dear brother Bernard, MA’48 (History) and parents Reginald George Trotter, (head of the Queen’s History Department until his death in 1951) and Prudence Hale (é Fisher). He will be remembered and greatly missed by his devoted stepson Stephen Pallrand (Rachel), stepdaughter Nannette, grandson Eli and granddaughter Cora, his sister-in-law Jean, and his brother-in-law John (Helen). Hale was also the much-loved uncle of Rex, Arts’73,(Eliza) and niece Victoria Vaghy, B. Mus ’75, B. Ed’77, nephew-in-law Tibor Vaghy (retired assistant professor Queen’s Music Department), grand uncle of John, Thomas (Stephanie), Andrew (Annemarie), Marie, MA ‘ 19 (English), Philip, Claire, Martin, and great-grand uncle of James, Damien, Felix and Lily.
Hale grew up in Kingston and became fascinated with mathematics, graduating with degrees in his chosen field from Queen’s (BA '52, MA’53) and Princeton (PhD ’56) where he studied under William Feller. Feller was part of a wave of European intellectuals who had fled the Nazis and settled in the United States. Princeton attracted a number of these refugees, including Albert Einstein, who had an office in the mathematics building. It was in this rich and exciting atmosphere that Hale matured as a mathematician
Joe Kohn, a fellow graduate student with Hale at Princeton and colleague in the math department for almost 40 years, recalled the first day of their graduate program at Princeton in 1953. Head of the mathematics department, Solomon Lefschetz, told the group of thirteen mathematics PhD students that they should congratulate themselves for the hard work it took to gain acceptance but that it was likely that only one of them, maybe two, would become actual mathematicians. Hale not only became a world class mathematician but made vital original contributions to the field.
Hale began his career as the Fine Instructor for Mathematics at Princeton from 1956-58. After teaching at Queen’s University as an assistant professor from 1958-60, he returned to Princeton as a visiting associate professor. Hale was appointed lecturer at Princeton in 1962, associate professor in 1963 and full professor in 1969. He was a highly respected administrator fulfilling duties as Chairman of the Mathematics Department from 1979-82 and associate director of Princeton University’s Data Center from 1962-86. He was a much-beloved teacher, instructing both graduate and undergraduate students in a wide range of mathematical concepts. Hale was always willing to take on a higher teaching load when a gap needed to be filled, such as teaching game theory for many years until a replacement could be hired. Additionally, Hale supervised graduate students and wrote several textbooks on calculus in higher dimensions.
As a mathematician Hale had a broad range of interests and impacts, starting with his thesis and work in probability and including significant contributions to group theory, knot theory, and number theory. One of his outstanding accomplishments, the Trotter Product Formula, has had a major impact on mathematical physics and on functional analysis. The Johnson-Trotter Algorithm is another powerful and useful tool he developed, a technique for generating complete lists of permutations that had considerable significance. He developed an interest in knot theory and was the first to show that there are non-invertible pretzel knots, thereby solving a long-standing topological problem. Hale had a later interest in some of the calculational aspects of number theory, developing the Lang-Trotter conjecture through his joint work with Yale mathematician Serge Lang.
Hale’s bright, serene, humorous and cheerful spirit will be remembered with great affection by his extended family, with whom he and Kay enjoyed many memorable visits during his summer holidays in Canada at their cottage on Lake Cecebe. Hale and Kay had a deep love of the arts and opera that they cheerfully shared with all. We are so grateful to his caregivers Joyce and her husband Joe, Antoinette, as well as his neighbour Bob, and to all who enabled Hale to stay in his Princeton home since Kay’s passing in 2021.
