In Praise (and Search) of J. V. Uspensky

Persi Diaconis*, Sandy Zabell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 (e.g., 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.

Original languageEnglish (US)
Pages (from-to)160-183
Number of pages24
JournalStatistical Science
Issue number1
StatePublished - 2023


  • A. A. Markov
  • Bernoulli’s theorem
  • J. V. Uspensky
  • Lexis ratio
  • Markov’s method of continued fractions
  • Russian mathematics
  • Stanford Mathematics Department
  • card shuffling
  • probability theory

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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