Mark Kac

Mark Kac (Template:IPAc-en Template:Respell; 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".

Early life and education

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.<ref name="rochester">Obituary in Rochester Democrat & Chronicle, 11 November 1984</ref>

Kac completed his Ph.D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus.<ref name="mathgen">Template:MathGenealogy</ref> 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.<ref name="autobio">Template:Cite book</ref>

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.<ref name="autobio"/>

Career

Cornell University

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.<ref name="mactutor">Template:MacTutor</ref>

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.<ref name="autobio"/> During the 1951–1952 academic year, Kac was on sabbatical at the Institute for Advanced Study.<ref>Kac, Mark, Community of Scholars Profile, IAS Template:Webarchive</ref>

In 1952, Kac, with Theodore H. Berlin, introduced the spherical model of a ferromagnet, a variant of the Ising model,<ref>Template:Cite journal</ref> and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method.<ref>Template:Cite journal</ref>

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.<ref>Template:Cite journal</ref>

Rockefeller University

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.<ref>Template:Cite journal</ref> 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.

Human rights

Kac was the co-chair of the Committee of Concerned Scientists.<ref>Template:Cite journal (See pages 14–15.)</ref> He co-authored a letter which publicized the case of the scientist Vladimir Samuilovich Kislik<ref>Template:Cite journal</ref> and a letter which publicized the case of the applied mathematician Yosif Begun.<ref>Template:Cite journal</ref>

Awards and honors

• 1950 — Chauvenet Prize for 1947 expository article<ref>Template:Cite journal</ref>
• 1959 – member of the American Academy of Arts and Sciences<ref>{{#invoke:citation/CS1|citation

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• 1965 – member of the National Academy of Sciences<ref>{{#invoke:citation/CS1|citation

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• 1968 – Chauvenet Prize (and 1967 Lester R. Ford Award) for 1966 expository article<ref>Template:Cite journal</ref>
• 1969 – member of the American Philosophical Society<ref>{{#invoke:citation/CS1|citation

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• 1971 – Solvay Lecturer at Brussels
• 1980 – Fermi Lecturer at the Scuola Normale, Pisa

Books

• Mark Kac and Stanislaw Ulam: Mathematics and Logic: Retrospect and Prospects, Praeger, New York (1968)<ref>Template:Cite journal</ref> 1992 Dover paperback reprint. Template:Isbn
• Mark Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Mathematical Monographs, Mathematical Association of America, 1959.<ref>Template:Cite journal</ref>
• Mark Kac, Probability and related topics in the physical sciences. 1959 (with contributions by Uhlenbeck on the Boltzmann equation, Hibbs on quantum mechanics, and van der Pol on finite difference analogues of the wave and potential equations, Boulder Seminar 1957).<ref>Template:Cite journal</ref>
• Mark Kac, Enigmas of Chance: An Autobiography, Harper and Row, New York, 1985. Sloan Foundation Series. Published posthumously with a memoriam note by Gian-Carlo Rota.<ref>Template:Cite journal</ref> Template:Isbn

External links

• Template:MacTutor Biography
• Template:MathGenealogy
• National Academy of Sciences Biographical Memoir