In the 1930s, the Polish city of Lwów was home to a brilliant school of mathematics, with luminaries such as Hugo Steinhaus, Stefan Banach, Stanislaw Mazur and Stanislaw Ulam, among many others.
The group met regularly at the Scottish Café near the university for lengthy discussions on functional analysis, topology and set theory. From 1935 onwards, they had a notebook to write down the problems discussed and their solutions. The “Scottish Book”, as it became known, is one of the most curious documents in the history of mathematics. Of the 198 mathematical problems listed in it, several played an important role in the development of mathematics, and remain sources of inspiration to this day.
Mazur liked to offer prizes for solving problems he posed. For problem 30, a small beer; already at 31, more difficult, five small beers. Many followed his example. While the awards seem simple to us, they were hard-to-access items in the Depression years.
The book was in the Scottish Café, available to everyone. But in the summer of 1939, certain that world war was imminent, Mazur insisted that it needed to be hidden so it would not go astray. He arranged with Ulam that he would be buried near the goal of a certain football court, but it appears that it was actually in Banach’s possession.
On his death, in 1945, he was found by his son, who showed him to Steinhaus. The latter made a complete copy by hand and, in 1956, sent it to Ulam, who was working at the Los Alamos laboratory in the United States. Ulam translated the book into English and made 300 copies, which he distributed to friends and universities. The first professional edition was made by Los Alamos in 1977.
By this time, the Lwów school of mathematics had ceased to exist. The Soviet (1939) and Nazi (1941) occupation had forced most of its members to flee, especially the Jews, and to continue their contribution to science far from their home country.
In 1946, Lwów was incorporated into the Soviet Republic of Ukraine, changing its name to Lviv. Today, he lives the horrors of another war, as unjustifiable as the previous one. Let’s hope it’s less destructive.
I am grateful to my colleague and friend Rogério Steffenon, a professor at Unisinos, for making me learn these stories, and for insisting that I share them.
