The centenary of Mark Kac ( 1914 – 1984 ) Rafael

After completing my Ph.D. in Physics at Princeton University, I obtained a postdoctoral position at Rockefeller University. In the early sixties, Detlev Bronk, who was president (1953–1968) of the then Rockefeller Institute for Medical Research hired George Uhlenbeck, Mark Kac and Theodore Berlin (1961), among others, to establish a Mathematical Physics group, and Abraham Pais (1962) to lead a group in High Energy Physics. In fact Detlev Bronk successfully made the transition from a research institute to the Rockefeller University (1965). Kenneth Case joined the Mathematical Physics group at Rockefeller in 1969, and so did James Glimm in 1974. I stayed in Kenneth Case’s Lab at Rockefeller University from 1979 to 1981. There I had the chance to work with Ken Case and Mark Kac [2], to meet many visitors in Mathematics and Physics and to enjoy the friendly atmosphere of the 14th floor of the Tower Building where the labs of Ken Case and Eddie Cohen were housed. This year marks the hundredth anniversary of the birth of Mark Kac (1914-1984), who was a prominent figure in mathematics and physics of the twentieth century, and I think it is appropriate to remember his life and work in the Bulletin of the IAMP. Mark Kac was born three weeks after the beginning of the First World War (August 16) in Krzemieniec, in Central Europe. Krzemieniec, at the foot of Mountain Bona, is a city that has belonged to different countries in recent history. Even during the early years of Mark Kac it was part of the Austro–Hungarian Empire, then part of the Russian Empire, later a Polish Territory and finally part of the Ukraine, where its is known as Kremenets). At the time of Mark Kac’s birth, Krzemieniec was part of Vohlynia, and a typical cultural city of Central Europe. The romantic Polish poet Juliusz S lowacki was born there in the early XIXth century, and a contemporary of Mark Kac, the violinist Isaac Stern was born in Krzemieniec in 1920. Although during the two World Wars suffered enormously (specially during the Holocaust in the Second World War), Krzemieniec enjoyed a quiet and stimulating atmosphere in the interbellum. In 1922, the polish leader Jósef Pi lsudski, reopened the Lyceum of Krzemieniec, who had been founded in the XIXth century under the supervision of Vilnius University. The Lyceum was closed by the Soviet occupation army in September 1939, at the beginning of the Second World War. A measure of the Lyceum reputation is the fact that it was soon known as the “Athens of Volhynia”. Mark Kac entered the Lyceum in 1925. In the summer of 1930 Kac had his first experience with research. Acquainted with the Cardano solution of the cubic equation, he wanted to find an alternative way of finding that solution. He exploited the invariance of the equation under bilinear transformations. Doing so, he found a two parameter flow of cubic equations and determined the parameters of the flow that yielded a trivial cubic, to finally determine the solution of the original equation. One can certainly repeat that procedure for the quartic as well, and use the two parameters to reduce the quartic into a quadratic in x. This