Hale Trotter

Hale Freeman Trotter (30 May 1931 – 17 January 2022) was a Canadian-American mathematician who made important contributions to mathematics. He is best known for the Lie–Trotter product formula, which helps solve complex equations, the Steinhaus–Johnson–Trotter algorithm, used in computer science for generating permutations, and the Lang–Trotter conjecture, an open question in number theory that mathematicians continue to explore.

Trotter was born in Kingston, Ontario and later lived and worked in the United States. Throughout his career, he taught and conducted research at several universities, sharing his knowledge with many students and fellow mathematicians.

His work has had lasting effects in both pure mathematics and its applications in computing. Even after his death in Princeton, New Jersey, on January 17, 2022, Trotter's ideas continue to influence new generations of mathematicians and computer scientists.

Biography

Hale Trotter was a mathematician known for his important work in many areas of math. He studied at Queen's University and later earned his PhD from Princeton University. Trotter worked as a teacher and professor at Princeton University for many years.

Trotter made notable discoveries, including solving a problem in knot theory by proving the existence of non-invertible knots. He also described special types of knots called pretzel knots that have unique properties. His work impacted fields like probability, group theory, and number theory.

Selected publications

Hale Trotter wrote many important papers and books in mathematics. Some of his well-known works include studies on Brownian motion, homology of group systems, and eigenvalue distributions. He also co-authored textbooks on vector functions and multivariable mathematics.

His publications include:

Articles

• Trotter, H. F. (1958). "A property of Brownian motion paths". Illinois Journal of Mathematics. 2 (3): 425–433. doi:10.1215/ijm/1255454547.
• Trotter, H. F. (1962). "Homology of group systems with applications to knot theory". Annals of Mathematics. 76 (3): 464–498. doi:10.2307/1970369. JSTOR (https://www.jstor.org/stable/1970369).
• Goldfeld, Stephen M.; Quandt, Richard E.; Trotter, H. F. (1966). "Maximization by quadratic hill-climbing". Econometrica. 34 (3): 541–551. doi:10.2307/1909768. JSTOR (https://www.jstor.org/stable/1909768).
• Trotter, H. F. (1969). "On the norms of units in quadratic fields". Proceedings of the American Mathematical Society. 22 (1): 198–201. doi:10.1090/S0002-9939-1969-0244196-6.
• Trotter, H. F. (1973). "On S-equivalence of Seifert matrices". Inventiones Mathematicae. 20 (3): 173–207. Bibcode:1973InMat..20..173T. doi:10.1007/BF01394094.
• Lang, S.; Trotter, H. F. (1977). "Primitive points on elliptic curves". Bulletin of the American Mathematical Society. 83 (2): 289–292. doi:10.1090/S0002-9904-1977-14310-3.
• Trotter, H. F. (1984). "Eigenvalue distributions of large Hermitian matrices; Wigner's semi-circle law and a theorem of Kac, Murdock, and Szegö". Advances in Mathematics. 54 (1): 67–82. doi:10.1016/0001-8708(84)90037-9.

Books

• Williamson, Richard E.; Crowell, Richard H.; Trotter, Hale F. (1972). Calculus of vector functions (Second ed.). Prentice-Hall.
• Lang, Serge; Trotter, Hale Freeman (1976). Frobenius Distributions in GL2-Extensions. Lecture Notes in Mathematics. Vol. 504. Springer Verlag. doi:10.1007/BFb0082087. ISBN 978-3-540-07550-9.
• Williamson, Richard E.; Trotter, Hale F. (1995). Multivariable Mathematics. Prentice-Hall.