The Lviv Scottish Book continues traditions of the famous "Scottish Book" (1935-1941) – a notebook with open mathematical problems inscribed by visitors of the famous Scottish Café. The original café was reopened in May 2014 as a Restaurant “Szkocka” of the Atlas Deluxe Hotel (Shevchenka Ave, 27, Lviv, Ukraine). In “Szkocka” you can find a copy of the original Scottish Book and also The Lviv Scottish Book presented at the Opening Ceremony of the International Conference dedicated to the 120th anniversary of Kazimierz Kuratowski (27 September – 01 October 2016, Lviv, Ukraine).

As Stanisław Ulam wrote “the "Scottish Book" is an informal collection of problems in mathematics. It was begun in Lwow, in 1935. The story of the Scottish Book could also be called the "Tale of Two Coffee Houses", the Café Roma and, right next to it, the Café Szkocka, or Scottish Café. These two establishments are situated on a little square 100 or 200 yards from the University. ...
The mathematical life was very intense in Lwow. Some of us met practically every day, informally in small groups, at all times of the day to discuss problems of common interest, communicating to each other the latest work and results. Apart from the more official meetings of the local sections of the Mathematical Society (which took place Saturday evenings, almost every week!), there were frequent informal discussions mostly held in one of the coffee houses. ...
Stefan Banach used to spend hours, even days in the Café Roma, especially towards the end of the month before the university salary was paid. One day he became irritated with the credit situation at the Roma and decided to move to the Szkocka next door, a mere twenty yards away. Stożek and some chemists and physicists continued to frequent the Roma, but the Scottish Café now became the meeting place of a smaller group of mathematicians, including Banach, Mazur, myself, and occasionally some others.”

The Scottish Café was situated at Akademichna street, 27 not far from the old University building. The building no.27 with two towers, resembling Scottish castle, was built in 1909 under a project of the architect Zbigniew Brochwicz Lewiński for Emil Weksler, an entrepreneur. In 1909-1944 the ground floor was occupied by the Scottish coffeehouse.

Stanisław Ulam wrote in his memories: “How did the book come about? One day Banach decided that because we talked about so very many things, we should write the ideas down whenever possible in order not to forget them. He bought a large and well-bound notebook in which we started to enter problems. The first one bears the date July 17, 1935.
The notebook was kept at the Scottish Cafe by a waiter who knew the ritual-when Banach or Mazur came in it was sufficient to say, "The book please," and he would bring it with the cups of coffee.
As years passed, there were more and more entries by other mathematicians. The "Book" grew to become a collection of some 190 problems, of which by now, nearly fifty years later, about three-quarters have been solved.
The Scottish Book survived the war and was in Banach's possession. When Banach died in 1945, his son Stephan Banach, Jr. found it, and showed it to Steinhaus immediately after the war. Steinhaus then copied it verbatim by hand, and in 1956 sent this copy to me at Los Alamos. I translated it, and had some three hundred mimeographed copies of the translation made. I mailed these copies to various universities both here and abroad, and also to a few friends. Since then, as the book became known in mathematical circles, people kept writing to Los Alamos for copies. There were so many requests over the years that the laboratory decided in 1977 to print another edition, under the supervision of W. A. Beyer.”

The Scottish Book contains open problems posed by representatives of the Lwów School of Mathematics (S.Banach, S.Mazur, W.Orlicz, J.Schauder, H.Steinhaus, S.Ulam and others) of the interwar period. The following mathematicians inscribed open problems to The Scottish Book: Alexandroff, Auerbach, Banach, Bermant, Bogolubov, Borsuk, Eilenberg, Eidelheit, Fréchet, Infeld, Kac, Kaczmarz, Kampé de Fériet, Knaster, Kuratowski, Łomnicki, Lusternik, Marcinkiewicz, Mazur, von Neumann, Nikliborc, Offord, Orlicz, Ruziewicz, Saks, Schauder, Schreier, Sierpiński, Sobolev, Steinhaus, Sternbach, Stoilow, Szpilrajn, Ulam, Ward, Wavre, Zygmunt.

Usually, mathematicians writing problems to The Scottish Book suggested some prize (a bottle of wine, a dinner in "Szkocka", etc.) for solutions. "There is a charming story about one of the most famous of the problems in the Scottish Book which was posed by Mazur. This was problem number 153, which Mazur inserted into the Book on 6 November 1936. The problem asked (although not in these words) about the existence of Schauder bases in separable Banach spaces. As with many of the problems in the Scottish Book the proposer would offer a prize for their solution. Prizes offered included wine, spirits, or a meal in Cambridge but Mazur offered a live goose as the prize for this particular problem. Per Enflo showed in 1972 that the problem had a negative solution and, while in Warsaw lecturing on his solution, Mazur presented him with his prize, the live goose!" (S. Ulam)

After World War II, Steinhaus revived the tradition of The Scottish Book at the University of Wrocław by initiating The New Scottish Book, which can be found in the Library at the Wrocław University.

The problems posed in The Lviv Scottish Book can be found here on our site. Selected problems from The Lviv Scottish Book are copied in MathOverflow (on behalf of the user Lviv Scottish Book). MathOverflow is an online interactive platform for professional mathematicians providing convenient tools for submitting comments and solutions to mathematical problems.

We invite you to visit The Scottish Café in Lviv, where you can find The Lviv Scottish Book as well as a copy of the original Scottish Book. While reading the books and enjoying a cup of coffee, you can try to solve the open problems and write down your own mathematical problem, be sure it will find its solvers – checked!

© Web design Olena Hryniv