Hale Freeman Trotter (born 30 May 1931, Kingston, Ontario) is a Canadian-American mathematician, known for the Lie-Trotter product formula, the Steinhaus–Johnson–Trotter algorithm, and the Lang-Trotter conjecture.
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 under William Feller 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 deals 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 knots that are not invertible.
- "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. doi:10.2307/1970369
- with Stephen W. Goldfeld and Richard E. Quandt: "Maximization by quadratic hill-climbing." Econometrica: Journal of the Econometric Society (1966): 541–551. doi:10.2307/1909768
- "On the norms of units in quadratic fields." Proc. Amer. Math. Soc. 22 (1969), 198–201. doi:10.1090/S0002-9939-1969-0244196-6
- "On S-equivalence of Seifert matrices." Inventiones mathematicae 20, no. 3 (1973): 173–207. doi:10.1007/BF01394094
- with Serge Lang: "Primitive points on elliptic curves." Bull. Amer. Math. Soc. 83 (1977), 289–292. doi:10.1090/S0002-9904-1977-14310-3
- "Eigenvalue distributions of large Hermitian matrices; Wigner's semi-circle law and a theorem of Kac, Murdock, and Szegö." Advances in mathematics 54, no. 1 (1984): 67–82. doi:10.1016/0001-8708(84)90037-9
- 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; Lang, Serge; Trotter, Hale (2006-11-14). 2006 edition. ISBN 9783540380948; pbk
- biographical information from American Men and Women of Science, Thomson Gale 2004
- Trotter, H. F. (1959), "On the product of semi-groups of operators", Proceedings of the American Mathematical Society, 10 (4): 545–551, doi:10.2307/2033649, ISSN 0002-9939, JSTOR 2033649, MR 0108732
- Hale Trotter at the Mathematics Genealogy Project
- Trotter, H. (1963). "Non-invertible knots exist" (PDF). Topology. 2 (4): 275–280. doi:10.1016/0040-9383(63)90011-9.