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 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 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!
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