In praise (and search) of J. V. Uspensky

TL;DR

This paper celebrates J. V. Uspensky's influential 1937 textbook on probability, highlighting its unique results and examples, and explores his life and lesser-known mathematical contributions to inspire modern readers.

Contribution

It introduces Uspensky's notable results and examples from his probability textbook and discusses his life and other mathematical works to increase awareness.

Findings

Uspensky's textbook contains unique results not found elsewhere.

The paper highlights Uspensky's contributions to number theory and probability.

It aims to inspire further study of Uspensky's work and life.

Abstract

The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on the same subject in the English language, together with many non-trivial examples, all clearly stated with careful proofs. We present some of Uspensky's gems to a modern audience hoping to tempt others to read Uspensky for themselves, as well as report on a few of the other mathematical topics he also wrote about (for example, his book on number theory contains early results about perfect shuffles). Uspensky led an interesting life: a member of the Russian Academy of Sciences, he spoke at the 1924 International Congress of Mathematicians in Toronto before leaving Russia in 1929 and coming to the US and Stanford. Comparatively little has been written about him in English; the second half of this paper attempts to remedy this.