ISI - International Statistical Institute
Newsletter Volume 25, no. 3 (75) 2001

Herbert E. Robbins (12 January 1915 - 12 February, 2001)

Herbert E. Robbins, Professor of Mathematical Statistics for more than fifty years at Columbia University, the University of North Carolina, and Rutgers University, died on February 12 in Princeton, N.J. where he had lived since 1990. He was eighty-six. He was held in awe by colleagues for his creativity, perhaps related to the irreverent sense of humour that led to acerbic questioning of dogma, both cultural and scientific. Perceived as a curmudgeon by those who would pretend to be experts, he was loved for his personal generosity to those who were eager to learn. He is credited by Jerzy Neyman, a founding figure in modern statistical theory, with two major breakthroughs in the field of mathematical statistics. His contributions were characterised by the mathematician Marc Kac as marked by power, great originality, and equally great elegance.

Left fatherless at the age of thirteen, he obtained a Bachelor's degree from Harvard in 1935 at the age of twenty and a Ph.D. in pure mathematics in 1938. Undoubtedly his best known work was the book "What is Mathematics?" co-authored with Richard Courant and published in 1941. Translated into scores of languages, the book has sold well over one hundred thousand copies. Written for a general audience, "What is Mathematics?" conveyed the beauty and intellectual excitement of Mathematics so successfully that, ever since its appearance, professional mathematicians have described it as an early inspiration in their choice of career.
His first experience teaching statistics occurred at New York University before World War II, when as a junior faculty member he was assigned to teach the course that none of his senior colleagues wanted to teach. His first research in statistics began during the war, when as a young naval officer he overheard two more senior officers discussing a problem of bombing coverage; this he proceeded to solve on the spot, only to be told that he lacked the security clearance needed to discuss the problem with those officers. After the war he assumed a position in the newly formed Statistics Department at the University of North Carolina, moving in 1953 to Columbia University, where he was the Higgins Professor of Mathematical Statistics. After retiring from full-time activity at Columbia in 1985, he became the New Jersey Professor of Mathematical Statistics at Rutgers, The State University of New Jersey, from which he retired in 1997.

Robbins' statistical research in the early 1950s spawned the subfields of Empirical Bayes Methods and of Stochastic Approximation. In his research on Empirical Bayes Methods he showed that certain problems, which usually were treated separately, could profitably be combined so that data concerning one problem provided information useful in solving the others. For example, if one is interested in predicting in a future year the number of accidents which will be incurred by automobile drivers who have not had any accident in the present year, Robbins showed under certain, plausible assumptions that a natural predictor is the number of drivers who had exactly one accident in the present year. Robbins' paper with his student Sutton Monro on Stochastic Approximation provided an analogue of an iterative method due to Isaac Newton for finding the root of a function, even when the function's equation is unknown and the evaluation of the function involves experimental error. The process they introduced has become a prototype for many iterative algorithms for on-line control of engineering systems.

Robbins also expanded the intellectual horizons of Sequential Analysis, which had begun at Columbia during World War II as part of a program to improve the quality of the large quantities of manufactured goods needed for the military effort.
During his more than fifty years of academic life, Robbins was particularly devoted to students and young colleagues, with whom he shared generously his enthusiasm for research along with his ideas. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and past president of the Institute for Mathematical Statistics. Robbins was a Guggenheim Fellow at the Institute for Advanced Study in Princeton in 1952-53 and at the Imperial College in London in 1975-76. In 1987 he received from Mayor Edward I. Koch of New York City one of the Mayor's Awards of Honour for Science and Technology, for a lifetime of contributions to the theory and applications of statistical methods.
For forty years, Herbert Robbins defined the field of Mathematical Statistics in this country and, of course, in this University. He influenced the careers, and left an indelible mark on the lives, of countless individuals, with his superb teaching, his elegant writings, his wit, his openness, his generous and liberal scientific ethos.

David Siegmund
Bruce Levin