set off research into spectral theory, the idea of understanding the extent to which the spectrum allows one to read back the geometry.

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.

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.

[3] 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.

[7] 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.