Persi Warren Diaconis (born 1945) is one of the most remarkable and versatile mathematicians of his generation. A professor at Stanford University, he has made deep contributions to probability, combinatorics, group theory, and Bayesian statistics, often finding unexpected connections between these fields. His unusual background—he left home at fourteen to become a professional magician before returning to academia—gave him an intuitive understanding of randomness and deception that informs his mathematical work. His contributions to Bayesian statistics center on finite exchangeability, the rigorous analysis of Markov chain Monte Carlo methods, and the application of symmetry ideas to statistical inference.
From Magic to Mathematics
Diaconis was born in New York City and ran away from home at fourteen to apprentice with the magician Dai Vernon. He spent nearly a decade as a professional card magician before deciding to pursue mathematics, earning his bachelor's degree from the City College of New York and his PhD from Harvard University in 1974 under the supervision of Frederick Mosteller. His experience as a magician gave him deep practical knowledge of how humans perceive randomness and are deceived by patterns.
One of Diaconis's most celebrated results, proved with Dave Bayer in 1992, is that seven riffle shuffles are necessary and sufficient to randomize a standard deck of 52 cards. This work used the theory of random walks on groups and has direct implications for understanding the mixing times of Markov chains—a question that is critical for the convergence of MCMC algorithms in Bayesian computation.
Finite Exchangeability
While de Finetti's representation theorem applies to infinite exchangeable sequences, Diaconis has made foundational contributions to the study of finite exchangeability—the case where only a finite number of observations are exchangeable. With David Freedman, he showed that the finite version of de Finetti's theorem holds only approximately, and he characterized the extent of the approximation. This work is practically important because real datasets are always finite, and understanding the gap between finite and infinite exchangeability is essential for applying Bayesian nonparametric methods honestly.
“Our brains are just not wired to do probability problems very well.”— Persi Diaconis
Bayesian Statistics Meets Combinatorics
Diaconis has repeatedly demonstrated that deep combinatorial and algebraic structures underlie Bayesian statistical methods. His work on sufficiency, exponential families, and the role of symmetry in statistical models connects abstract algebra to practical inference. He has also contributed to the theory of Bayesian robustness, exploring how sensitive Bayesian conclusions are to the choice of prior.
Markov Chain Analysis
Diaconis's work on the rates of convergence of Markov chains has been fundamental to the theoretical foundation of MCMC methods. By developing techniques to bound mixing times using representation theory of groups, coupling arguments, and comparison methods, he has provided tools that help practitioners understand when their MCMC algorithms have run long enough—one of the central practical challenges in Bayesian computation.
Recognition and Impact
Diaconis has received the MacArthur Fellowship, the Rollo Davidson Prize, and numerous other awards. He is a member of the National Academy of Sciences and the American Philosophical Society. His ability to combine deep mathematics with vivid intuition and practical wisdom has made him one of the most admired figures in contemporary mathematics and statistics.
Born on 31 January in New York City.
Left home at fourteen to become a professional magician.
Earned bachelor's degree from City College of New York.
Received PhD from Harvard under Frederick Mosteller.
Awarded MacArthur Fellowship.
Proved with Bayer that seven shuffles suffice to randomize a deck of cards.
Joined Stanford University.