Hale Freeman Trotter (30 May 1931 – 17 January 2022)biographical information from ''American Men and Women of Science'', Thomson Gale 2004 was a Canadian-American mathematician, known for the Lie–Trotter product formula, the

Steinhaus–Johnson–Trotter algorithm The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M. Johnson and Hale F. Trotter that generates all of the permutations of n elements. E ...

, and the Lang–Trotter conjecture. He was born in

Kingston, Ontario Kingston is a city in Ontario, Canada. It is located on the north-eastern end of Lake Ontario, at the beginning of the St. Lawrence River and at the mouth of the Cataraqui River (south end of the Rideau Canal). The city is midway between Toro ...

. He died in Princeton, New Jersey on January 17, 2022.

Biography

The son of historian

Reginald George Trotter Reginald George Trotter, FRSC (14 July 1881– 7 April 1951) was a Canadian historian. He was the Douglas Professor in Canadian and Colonial History at Queen's University, Kingston from 1924 until his death. He was President of the Canadian Histor ...

, Hale Trotter studied at Queen's University in Kingston with bachelor's degree in 1952 and master's degree in 1953. He received in 1956 his PhD from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

under

William Feller William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Early life and education Feller was born in Zagreb to Ida Oemichen-Perc, a Croa ...

with thesis ''Convergence of semigroups of operators''. Trotter was from 1956 to 1958 at Princeton University the ''Fine Instructor'' for mathematics and from 1958 to 1960 an assistant professor at Queen's University. He was from 1962 to 1963 a visiting associate professor, from 1963 to 1969 an associate professor, and from 1969 until his retirement a full professor at Princeton University. From 1962 to 1986 he was an associate director for Princeton University's data center. Trotter's research dealt with, among other topics, probability theory, group theory computations, number theory, and knot theory. In 1963, he solved an open problem in knot theory by proving that there are non-invertible knots. At the time of his proof, all knots with up to 7 crossings were known to be invertible. Trotter described an infinite number of

pretzel knot A Pretzel knot may refer to: * Pretzel link: a concept in mathematics * Soft pretzel with garlic * Stafford knot The Stafford knot, more commonly known as the Staffordshire knot, is a distinctive three-looped knot that is the traditional symbol o ...

s that are not invertible.

Selected publications

Articles

"A property of Brownian motion paths."
Illinois journal of mathematics 2, no. 3 (1958): 425–433. *"Homology of group systems with applications to knot theory." Annals of Mathematics (1962): 464–498. *with Stephen W. Goldfeld and Richard E. Quandt: "Maximization by quadratic hill-climbing." Econometrica: Journal of the Econometric Society (1966): 541–551. *"On the norms of units in quadratic fields." Proc. Amer. Math. Soc. 22 (1969), 198–201. *"On S-equivalence of Seifert matrices." Inventiones mathematicae 20, no. 3 (1973): 173–207. *with

Serge Lang Serge Lang (; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the i ...

: "Primitive points on elliptic curves." Bull. Amer. Math. Soc. 83 (1977), 289–292. *"Eigenvalue distributions of large Hermitian matrices; Wigner's semi-circle law and a theorem of Kac, Murdock, and Szegö."

Advances in Mathematics ''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed ...

54, no. 1 (1984): 67–82.

Books

* with Richard Williamson and Richard Crowell: ''Calculus of vector functions'', Prentice-Hall 1972 * with Williamson: ''Multivariable Mathematics'', Prentice-Hall 1995 * with Serge Lang: ''Frobenius distributions in GL2-extensions: distribution of Frobenius automorphisms in GL2-extensions of the rational numbers'', Lecture Notes in Mathematics 504, Springer Verlag 1976;

References

External links

Hale Trotter, Department of Mathematics, Princeton University
*

{{DEFAULTSORT:Trotter, Hale 1931 births 2022 deaths People from Kingston, Ontario Princeton University alumni Princeton University faculty Queen's University at Kingston alumni 20th-century American mathematicians 21st-century American mathematicians 20th-century Canadian mathematicians 21st-century Canadian mathematicians Canadian emigrants to the United States