The Scottish Book is a collection of 193 mathematical problems recorded by mathematicians meeting at the Scottish Café in Lwów, now Lviv, Ukraine. The notebook began in 1935, and its last dated contribution is from 1941. Its problems were contributed by several mathematicians, including Banach, Mazur, Steinhaus, and Ulam, rather than by Ulam alone (Ulam 1958, Mauldin 2015).
The collection includes problems in functional analysis, topology, set
theory, and geometry. Problem 19, the Ulam
floating body problem, asks whether a homogeneous convex
body floating in equilibrium in every orientation must be a closed
ball. Ryabogin (2022) answered this negatively using bodies of relative density
. The original problem statements are distinct from
the later solutions and commentaries included in Mauldin's (2015) expanded edition,
which also contains selected problems from the New Scottish Book.
The Scottish Book should also be distinguished from Ulam's (1960) A Collection of Mathematical Problems, which includes material originating both in the Scottish Book and in Ulam's later work.
