Mark Kac

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Polish-American Mathematician

title: "Mark Kac" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["1914-births", "1984-deaths", "20th-century-american-mathematicians", "american-people-of-polish-jewish-descent", "cornell-university-faculty", "institute-for-advanced-study-visiting-scholars", "lwów-school-of-mathematics", "members-of-the-american-philosophical-society", "people-from-kremenets", "naturalized-citizens-of-the-united-states", "polish-emigrants-to-the-united-states", "presidents-of-the-institute-of-mathematical-statistics", "probability-theorists", "mathematical-physicists", "university-of-southern-california-faculty", "mit-radiation-laboratory-people", "20th-century-american-statisticians"] description: "Polish-American Mathematician" topic_path: "science/mathematics" source: "https://en.wikipedia.org/wiki/Mark_Kac" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Polish-American Mathematician ::

::data[format=table title="Infobox scientist"]

FieldValue
nameMark Kac
imageMark_Kac.jpg
birth_date
birth_placeKrzemieniec, Russian Empire (now Ukraine)
death_date
death_placeCalifornia, U.S.
nationalityPolish
citizenshipPoland, USA
fieldMathematics
work_institutionsCornell University
Rockefeller University
University of Southern California
alma_materLwów University
doctoral_advisorHugo Steinhaus
doctoral_studentsHarry Kesten
William LeVeque
William Newcomb
Lonnie Cross
Daniel B. Ray
Murray Rosenblatt
Daniel Stroock
known_forFeynman–Kac formula
Erdős–Kac theorem
Kac–Bernstein theorem
Kac–van Moerbeke lattice
Kac's lemma
Kac process
Kac ring
Probabilistic number theory
awardsChauvenet Prize (1950, 1968)

Gibbs Lecture (1967) Birkhoff Prize (1978) | ::

| name=Mark Kac | image= Mark_Kac.jpg | birth_date = | birth_place = Krzemieniec, Russian Empire (now Ukraine) | death_date = | death_place = California, U.S. | nationality = Polish | citizenship = Poland, USA | field = Mathematics | work_institutions = Cornell University Rockefeller University University of Southern California | alma_mater = Lwów University | doctoral_advisor = Hugo Steinhaus | doctoral_students = Harry Kesten William LeVeque William Newcomb Lonnie Cross Daniel B. Ray Murray Rosenblatt Daniel Stroock | known_for = Feynman–Kac formula Erdős–Kac theorem Kac–Bernstein theorem Kac–van Moerbeke lattice Kac's lemma Kac process Kac ring Probabilistic number theory | awards = Chauvenet Prize (1950, 1968)

Gibbs Lecture (1967) 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".

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.

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.

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.

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.

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. During the 1951–1952 academic year, Kac was on sabbatical at the Institute for Advanced Study.

In 1952, Kac, with Theodore H. Berlin, introduced the spherical model of a ferromagnet, a variant of the Ising model, and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method.

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.

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. 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. He co-authored a letter which publicized the case of the scientist Vladimir Samuilovich Kislik and a letter which publicized the case of the applied mathematician Yosif Begun.

Awards and honors

::figure[src="https://upload.wikimedia.org/wikipedia/commons/8/8a/Mark_Kac_lecturing.jpg" caption="Mark Kac lecturing"] ::

Books

  • Mark Kac and Stanislaw Ulam: Mathematics and Logic: Retrospect and Prospects, Praeger, New York (1968) 1992 Dover paperback reprint.
  • Mark Kac, Statistical Independence in Probability, Analysis and Number Theory, Carus Mathematical Monographs, Mathematical Association of America, 1959.
  • 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).
  • 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.

References

References

  1. [http://www.math.rochester.edu/people/faculty/rarm/kac.html Obituary] {{Webarchive. link. (2012-02-05 in ''Rochester Democrat & Chronicle'', 11 November 1984)
  2. {{MathGenealogy
  3. Kac, Mark. (1985). "Enigmas of Chance: An Autobiography". Harper and Row.
  4. "Mark Kac".
  5. [http://www.ias.edu/people/cos/users/mkac01 Kac, Mark, Community of Scholars Profile, IAS] {{webarchive. link. (2013-02-07)
  6. Berlin, T. H.. (1952). "The spherical model of a ferromagnet". Phys. Rev..
  7. Kac, M.. (1952). "A combinatorial solution of the two-dimensional Ising model". Phys. Rev..
  8. (1986). "The contributions of Mark Kac to mathematical physics". The Annals of Probability.
  9. Cohen, E. G. D.. (April 1985). "Obituary: Mark Kac". Physics Today.
  10. Benguria, Rafael. (July 2014). "The centenary of Mark Kac (1914–1984)". IAMP News Bulletin.
  11. Gottesman, Max. (January 1980). "A legacy and a hope". Physics Today.
  12. Kac, Mark. (12 October 1984). "Yosif Begun". Science.
  13. Kac, Mark. (1947). "Random walk and the theory of Brownian motion". Amer. Math. Monthly.
  14. "Mark Kac".
  15. "Mark Kac".
  16. Kac, Mark. (1966). "Can one hear the shape of a drum?". Amer. Math. Monthly.
  17. "APS Member History".
  18. May, Kenneth O.. (Spring 1969). "Review of ''Mathematics and Logic'' by Mark Kac and Stanislaw Ulam". Isis.
  19. LeVeque, W. L.. (1960). "Review: ''Statistical independence in probability, analysis and number theory'', by Mark Kac. Carus Mathematical Monographs, no. 12". Bull. Amer. Math. Soc..
  20. Baxter, Glen. (1960). "Review: ''Probability and related topics in the physical sciences'', by Mark Kac". Bull. Amer. Math. Soc..
  21. Birnbaum, Z. W.. (1987). "Review: ''Enigmas of chance; an autobiography'', by Mark Kac". Bull. Amer. Math. Soc. (N.S.).

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1914-births1984-deaths20th-century-american-mathematiciansamerican-people-of-polish-jewish-descentcornell-university-facultyinstitute-for-advanced-study-visiting-scholarslwów-school-of-mathematicsmembers-of-the-american-philosophical-societypeople-from-kremenetsnaturalized-citizens-of-the-united-statespolish-emigrants-to-the-united-statespresidents-of-the-institute-of-mathematical-statisticsprobability-theoristsmathematical-physicistsuniversity-of-southern-california-facultymit-radiation-laboratory-people20th-century-american-statisticians