Herbert E. Robbins; Statistician Wrote Key Math Text

Herbert E. Robbins, an influential statistician who wrote a classic text on mathematics, died Feb. 12 in Princeton, N.J. He was 86 and had esophageal cancer.

Robbins devised techniques to improve predictions by drawing on related data. Known as empirical Bayes methods, they are used to analyze census data and have proved to be important tools in understanding the results of clinical trials that lack random samples.

His best-known work was “What Is Mathematics?” which was published in 1941 and remains in print. Co-written with mathematician Richard Courant, it is considered a literate and lively survey of the mathematical world, from natural numbers to calculus, that introduced many students to mathematics.

The work won praise from Albert Einstein, who called it a “lucid representation of the fundamental concepts and methods of the whole field of mathematics.”

Although Robbins’ statistical work had real-world applications, he spent much of his time composing and contemplating solutions to mathematical puzzles that had no use beyond inducing mental strain.

One problem that he designed in the early 1930s involved proving that a set of three equations was equivalent to a Boolean algebra. It had no practical relevance and as such was the epitome of pure mathematics.

Robbins worked the problem himself for some time, then handed it to one of the last century’s most famous logicians, Albert Tarski of Stanford University. Tarski tried to solve it, included it in a book, then handed it out to graduate students and visitors. It was finally solved in 1996--by a computer--at Argonne National Laboratory in Illinois.

Robbins, who devoted much of his long career to solving similar abstractions, once commented on the frustrations of his occupation.

“Most people acquire a certain expertise, and they work in fields where their expertise can be used,” he said in an interview. “If I were a Picasso, I could wake up in the morning and say: ‘Well, I think I’ll paint a Picasso today.’ And by the end of the day I would have painted a real, genuine Picasso. . . .

“Now if I get up in the morning and say, ‘I think I’ll do something in mathematical statistics,’ at the end of the day I’ve got a wastebasket full of paper and nothing to show for it. . . . I cannot do something by willing myself to do it.”

A native of New Castle, Pa., Robbins earned his undergraduate degree in 1935 and a doctorate in mathematics in 1938, both at Harvard.

He taught at New York University and the University of North Carolina before landing at Columbia in 1953 as a professor of mathematical statistics. He remained at Columbia for three decades before retiring, then joined the faculty at Rutgers, where he taught until 1997.

He is survived by his wife, Carol, a sister, five children and two grandchildren.