| Mark Kac | |
| Birth Date: | August 3, 1914 |
| Birth Place: | Krzemieniec, Russian Empire (now Ukraine) |
| Death Place: | California, U.S. |
| Nationality: | Polish |
| Citizenship: | Poland, USA |
| Field: | Mathematics |
| Alma Mater: | Lwów University |
| Doctoral Advisor: | Hugo Steinhaus |
| Known For: | Feynman–Kac formula Erdős–Kac theorem Kac–Bernstein theorem Kac's lemma Kac process Kac ring |
| Awards: | Chauvenet Prize (1950, 1968) Birkhoff Prize (1978) |
Mark Kac (; Polish: Marek Kac; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, the idea of understanding the extent to which the spectrum allows one to read back the geometry. In the end, the answer was generally "no".
He was born to a Polish-Jewish family; their town, Kremenets (Polish: "Krzemieniec"), changed hands from the Russian Empire (by then Soviet Ukraine) to Poland after the Peace of Riga, when Kac was a child.[1]
Kac completed his Ph.D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus. While there, he was a member of the Lwów School of Mathematics.
After receiving his degree, he began to look for a position abroad, and in 1938 was granted a scholarship from the Parnas Foundation, which enabled him to go work in the United States. He arrived in New York City in November 1938.[2]
With the onset of World War II in Europe, Kac was able to stay in the United States, while his parents and brother, who had remained in Kremenets, were murdered by the Nazis in mass executions in August 1942.[2]
From 1939 to 1961, Kac taught at Cornell University, an Ivy League university in Ithaca, New York, where he was first an instructor. In 1943, he was appointed an assistant professor, and he became a full professor in 1947.
While a professor at Cornell, he became a naturalized US citizen in 1943. From 1943 to 1945, he also worked with George Uhlenbeck at the MIT Radiation Laboratory.[2] During the 1951–1952 academic year, Kac was on sabbatical at the Institute for Advanced Study.[3]
In 1952, Kac, with Theodore H. Berlin, introduced the spherical model of a ferromagnet, a variant of the Ising model,[4] and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method.[5]
In 1956, he introduced a simplified mathematical model known as the Kac ring, which features the emergence of macroscopic irreversibility from completely time-symmetric microscopic laws. Using the model as an analogy to molecular motion, he provided an explanation for Loschmidt's paradox.[6]
In 1961, Kac left Cornell and went to The Rockefeller University in New York City.
He worked with George Uhlenbeck and P. C. Hemmer on the mathematics of a van der Waals gas.[7] After twenty years at Rockefeller, he moved to the University of Southern California where he spent the rest of his career.
In his 1966 article, "Can one hear the shape of the drum", Kac asked whether the geometric shape of a drum is uniquely defined by its sound. The answer was negative, meaning two different resonators can have identical set of eigenfrequencies.
Kac was the co-chair of the Committee of Concerned Scientists.[8] He co-authored a letter, which publicized the case of the scientist Vladimir Samuilovich Kislik[9] and a letter which publicized the case of the applied mathematician Yosif Begun.[10]