# Hale Trotter

Hale Freeman Trotter, an emeritus professor of mathematics, died at 91 on January 17 at his home in Princeton, New Jersey.

“Hale was devoted to and prized teaching at all levels,” said Peter Sarnak, Princeton’s Eugene Higgins Professor of Mathematics. “His infectious positive outlook was an inspiration to all in Fine Hall, from undergraduates to his colleagues. He will be sorely missed.”

“Hale Trotter and I were great friends, and as a colleague in our math department he was one of my favorites,” said Elliott Lieb, Eugene Higgins Professor of Physics, Emeritus and an emeritus professor of mathematical physics.

Born May 30, 1931, in Kingston, Ontario, Trotter graduated with degrees in mathematics from Queen’s University, getting his B.A. in 1952 and his M.A. in 1953. He then came to Princeton, where he studied under William Feller, one 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 (Jones Hall, known then as Fine Hall). It was in this rich and exciting atmosphere that Trotter matured as a mathematician.

After completing his Ph.D. in 1956, he began his career as the Fine Instructor for Mathematics at Princeton from 1956-58. He then taught at Queen’s University from 1958-60 before returning to Princeton, where he stayed for the remainder of his career.

“Hale returned to Princeton initially to help the department adjust to the computer reality when computerization first struck so many years ago,” said Robert Gunning, a fellow graduate student with Hale at Princeton and a colleague in the math department for almost half a century. “He had worked with computers more than many others in the department, and as a very active research mathematician had a real sense of what computerization meant to the operations of the department. His was the initial step, but others in the department followed up.”

He served as department chair from 1979-82 and associate director of Princeton University’s Data Center from 1962-86. He transferred to emeritus status in 2000. Sarnak recalled that Trotter’s period as chairman “was marked by a high degree of calmness and congeniality.”

"He was always a gentle and helpful member of the mathematics department, always willing to help out whenever asked, and a delightful friend with a very Canadian sense of humor,” said Gunning.

His colleagues describe a beloved teacher, instructing both graduate and undergraduate students in a wide range of mathematical concepts. Trotter also wrote several textbooks on calculus in higher dimensions.

“Hale worked in various central areas of modern mathematics, and as a result his impact was very broad,” said Sarnak. “He was a pioneer and leader of the use of the modern computer in pure mathematics.”

He made 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.

“As a physicist, I had heard his name very early in my career,” said Lieb, who described the Trotter Product Formula as “Hale’s famous formula” and “one of the most applicable to theoretical physics to come out of pure mathematics.”

The Johnson-Trotter Algorithm, another powerful and useful tool he developed, is a technique for generating complete lists of permutations that had considerable significance. He also 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. Trotter 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.

He was predeceased by his beloved wife Kay, his brother Bernard, and his parents Reginald George Trotter and Prudence Trotter (née Fisher). He is survived by his stepson Stephen Pallrand (Rachel), stepdaughter Nannette, grandson Eli and granddaughter Cora, his sister-in-law Jean, and his brother-in-law John (Helen). Trotter was also the much-loved uncle of Rex (Eliza) and Tory (Tibor Vaghy), grand uncle of John, Thomas (Stephanie), Andrew (Annemarie), Marie, Philip, Claire, Martin, and great-grand uncle of James, Damien, Felix and Lily.

A memorial will be held at the Mather-Hodge Funeral Home in Princeton on Tuesday, May 31 between 3 and 5 p.m., with an informal service at 4 p.m. Interment will take place prior to the memorial on Sunday, May 29 at the Evergreen Cemetery in Salem, New York. In lieu of flowers, the family requests donations to the Kay and Hale Trotter Gynecologic Oncology Fund.

—Office of Communications