Mark Kac
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, 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.) Biography. 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. 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, Kac was able to stay in America, while his parents and brother who remained in Krzemieniec were murdered by the Germans in mass executions in  August 1942. From 1939–61 he was at Cornell University, first as an instructor, then from 1943 as assistant professor and from 1947 as full professor. 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. 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 1961 he left Cornell and went to The 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. After twenty years at Rockefeller, he moved to the University of Southern California where he spent the rest of his career. Work. 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 positive, meaning that the eigenfrequency set does not uniquely characterize the shape of a  resonator. Human rights concerns. For a number of years Kac was the co-chair of the Committee of Concerned Scientists. He was a co-author of 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.