Physics Colloquium - Friday, March 3rd, 2006, 4:00 P.M.

E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200

Michael F. Shlesinger
Office of Naval Research

Pitfalls and Paradoxes in the History of Probability Theory

We trace the history of probability theory from the throwing of bones, sticks, and dice to modern times. Early 18th century books, Jacob Bernouill's "The Art of Conjecture" and Abraham DeMoive's "The Doctrine of Chances" were rich with new mathematics, insight and gambling odds. Progress was often made by confronting paradoxes. The first of these confused probabilities with expectations and was explained in the Pascal-Fermat letters of 1654. The St. Petersburg Paradox involved a distribution with an infinite first moment, the Bertrand paradox involved measure theory for continuous probabilities, Poisson discovered that adding random variables need not always produce the Gaussian, and Daniel Bernoulli and D'Alembert argued over the probabilities for the safety of smallpox vaccinations. Using anecdotes, we discuss these and related topics that brought us to our modern understanding of probability theory.