Herbert Robbins

Herbert Ellis Robbins (January 12, 1915 in New Castle, Pennsylvania – February 12, 2001 in Princeton, New Jersey) was a mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still (as of 2007^[update]) in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).

[edit] Biography

As an undergraduate, Robbins attended Harvard University, where Marston Morse influenced him to become interested in mathematics. Robbins received a doctorate from Harvard in 1938 and was an instructor at New York University from 1939 to 1941. After World War II, Robbins taught at the University of North Carolina at Chapel Hill from 1946 to 1952, then spent a year at the Institute for Advanced Study. In 1953, he became a professor of mathematical statistics at Columbia University. He retired from full-time activity at Columbia in 1985 and was then a professor at Rutgers University until his retirement in 1997.

In 1955, Robbins introduced empirical Bayes methods at the Third Berkeley Symposium on Mathematical Statistics and Probability. Robbins was also one of the inventors of the first stochastic approximation algorithm, the Robbins-Monro method, and worked on the theory of power-one tests and optimal stopping.

A theorem on graphs with an application to a problem on traffic control, American Mathematical Monthly, 46:281-283, 1939.
What is Mathematics?: An elementary approach to ideas and methods, with Richard Courant, London: Oxford University Press, 1941.
The central limit theorem for dependent random variables, with Wassily Hoeffding, Duke Mathematical Journal 15 (1948), pp. 773–780.
A stochastic approximation method, with Sutton Monro, Annals of Mathematical Statistics 22, #3 (September 1951), pp. 400–407.
An empirical Bayes approach to statistics, in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Jerzy Neyman, ed., vol. 1, Berkeley, California: University of California Press, 1956, pp. 157–163.

"The Contributions of Herbert Robbins to Mathematical Statistics", Tze Leung Lai and David Siegmund, Statistical Science 1, #2 (May 1986), pp. 276–284. Euclid
In Memoriam, ISI Newsletter 25, #3 (2001)
"What is known about Robbins' Problem?", F. Thomas Bruss, Journal of Applied Probability Volume 42, #1 (2005), pp. 108–120 Euclid
"A continuous-time approach to Robbins' problem of minimizing the expected rank", F. Thomas Bruss and Yves Coamhin Swan, Journal of Applied Probability , Volume 46 #1, 1–18, (2009).