Mark Kac

Mark Kac
Born (1914-08-03)August 3, 1914
Died October 26, 1984(1984-10-26) (aged 70)
Residence USA
Citizenship Poland, USA
Nationality Polish
Fields Mathematics
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
Murray Rosenblatt
Daniel Stroock
Known for Feynman–Kac formula
Erdős–Kac theorem
Notable awards Chauvenet Prize (1950, 1968)
Birkhoff Prize (1978)

Mark Kac (/kɑːts/ KAHTS; Polish: Marek Kac; August 3, 1914 – October 26, 1984) was a Polish American mathematician. He was born to a Polish-Jewish family; their town, Kremenets (Polish: "Krzemieniec"), changed hands from the Russian Empire to Poland when Kac was a child.[1] His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. (In the end, the answer was "no", in general.)

Kac completed his Ph.D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus.[2] 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.[3]

With the onset of World War II, Kac was able to stay in America, while his parents and brother who remained in Western Ukraine were murdered by the Germans in the mass executions in Krzemieniec in August 1942.[4]

From 1939-61 he was at Cornell University, first as an instructor, then from 1943 as assistant professor and from 1947 as full professor.[5] While there, he became a naturalized US citizen in 1943. In the academic year 1951–1952 Kac was on sabbatical at the Institute for Advanced Study.[6] In 1952, Kac, with Theodore H. Berlin, introduced the spherical model of a ferromagnet (a variant of the Ising model)[7] and, with J. C. Ward, found an exact solution of the Ising model using a combinatorial method.[8] In 1961 he left Cornell and went to Rockefeller University in New York City. In the early 1960s he worked with George Uhlenbeck and P. C. Hemmer on the mathematics of a van der Waals gas.[9] After twenty years at Rockefeller University, he moved to the University of Southern California where he spent the rest of his career.


In his 1966 article with the title "Can one hear the shape of the drum" Kac asked the question whether two resonators ("drums") of different geometrical shapes can have exactly the same set of frequencies ("sound tones"). The answer was negative, meaning that the eigenfrequency set does not uniquely characterize the shape of a resonator.


Awards and honors


See also


  1. Obituary in Rochester Democrat & Chronicle, 11 November 1984
  2. Mark Kac at the Mathematics Genealogy Project
  3. 1 2 Mark Kac, Enigmas of Chance: An Autobiography, Harper and Row, New York, 1985. ISBN 0-06-015433-0
  4. M Kac, Enigmas of chance: an autobiography (California, 1987)
  5. O'Connor, John J.; Robertson, Edmund F., "Mark Kac", MacTutor History of Mathematics archive, University of St Andrews.
  6. Kac, Mark, Community of Scholars Profile, IAS
  7. Berlin, T. H.; Kac, M. (1952). "The spherical model of a ferromagnet". Phys. Rev. 86: 821–835. doi:10.1103/PhysRev.86.821.
  8. Kac, M.; Ward, J. C. (1952). "A combinatorial solution of the two-dimensional Ising model". Phys. Rev. 88: 1332–1337. Bibcode:1952PhRv...88.1332K. doi:10.1103/physrev.88.1332.
  9. Cohen, E. G. D. (April 1985). "Obituary: Mark Kac". Physics Today. 38 (4): 99–100. doi:10.1063/1.2814542.
  10. Kac, Mark (1947). "Random walk and the theory of Brownian motion". Amer. Math. Monthly. 54: 369–391. doi:10.2307/2304386.
  11. Kac, Mark (1966). "Can one hear the shape of a drum?". Amer. Math. Monthly. 73, Part II: 1–23.
  12. 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. 66 (4): 265–266. doi:10.1090/S0002-9904-1960-10459-4.
  13. Baxter, Glen (1960). "Review: Probability and related topics in the physical sciences, by Mark Kac". Bull. Amer. Math. Soc. 66 (6): 472–475. doi:10.1090/s0002-9904-1960-10500-9.
  14. Birnbaum, Z. W. (1987). "Review: Enigmas of chance; an autobiography, by Mark Kac". Bull. Amer. Math. Soc. (N.S.). 17 (1): 200–202. doi:10.1090/s0273-0979-1987-15563-7.
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