Mark Kac

Mark Kac (August 3, 1914 – October 26, 1984) was a Polish-American mathematician known for his work in probability theory, number theory, statistical mechanics, and mathematical physics.

Born in Krzemieniec, Poland (now Ukraine), Kac received his Ph.D. from Lwów University in 1937. He emigrated to the United States in 1939 and held positions at Cornell University, Syracuse University, and the Rockefeller University, where he remained until his death.

Kac made significant contributions to diverse areas of mathematics. He is particularly well-regarded for his work on the Erdős–Kac theorem, a fundamental result in probabilistic number theory that describes the distribution of the number of distinct prime factors of an integer. His work also significantly impacted the development of the Feynman-Kac formula, which provides a probabilistic representation of solutions to certain partial differential equations.

Kac was also known for his clear and engaging writing style. He authored several influential books, including "Probability and Related Topics in Physical Science" and "Statistical Independence in Probability, Analysis and Number Theory." These works helped to popularize and develop the application of probability theory to various scientific fields. His book "Enigmas of Chance," is a collection of essays exploring probabilistic thinking.

Throughout his career, Kac received numerous awards and honors for his contributions to mathematics. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. His work continues to be highly influential in mathematical research and related fields.