# Gilbert Agnew Hunt

### Quick Info

Washington D.C., USA

Princeton, New Jersey, USA

**Gilbert Hunt**was an American mathematician who worked in probability theory, Markov processes and potential theory.

### Biography

**Gilbert Hunt**'s parents were Gilbert Agnew Hunt, who was an engineer who built bridges, and his wife May Winfield. Gilbert, who was their only child, played tennis to a high standard from the time he was a young child. He grew up in Washington, D.C. where he attended primary school, then later became a pupil at Eastern High School. At age 16, while attending this school, he became a national tennis star being ranked No. 1 in national junior indoor tennis. Bob Considine, a

*Washington Post*sportswriter, wrote that Hunt was taking:-

... six majors ... [He] attacks the harpsichord armed with something more than a knowledge of chopsticks. [Young Mr Hunt] once took this column to task for printing poetry in a scrambled 'didactic hexameter' or some such heinous charge.Two years later Hunt was again ranked No. 1 in national junior indoor tennis. This was the year that he entered Massachusetts Institute of Technology, studying mathematics there from 1934 to 1936 when he decided to give up his university education to concentrate on playing tennis. However, he soon returned to his university studies, this time at George Washington University in his home town of Washington, D.C. He was awarded a bachelor's degree in mathematics in 1938, then enrolled at Brown University for postgraduate studies.

During these years, Hunt had continued his tennis career in parallel with his university studies. Among his famous victories was one in 1938 against Bobby Riggs, the No. 2 player in the United States. The

*Washington Post*reported:-

Riggs had been a 10 - 1 favourite when he took the court. But the frail Washington mathematician constantly out-manoeuvred and pressed the husky Chicago 'playboy'.In July 1939, the

*Washington Post*reported on another tennis match:-

Giddy Gilbert Hunt, George Washington University's mathematical wizard and eccentric extraordinary, forgot his cute capers long enough to come up with one of his great local tennis performances and whip Byran (Bitsy) Grant in an exhibition on Rock Creek courts.One reason that Hunt's tennis exploits gained so much publicity was that he was highly eccentric, so making a good story for the newspapers. Bob Considine, a Washington Post sportswriter, wrote frequently about Hunt, for example noting in 1939:-

He is an extraordinarily gifted mathematics scholar and teacher, but somewhere in his curious makeup is a streak of daffiness that occasionally prompts him to remove his shoes in the middle of a match, and entertain his galleries by picking up objects with his toes. This, we might add, is done with a strange faraway look in his brooding black eyes, and an air of complete detachment. But shoeless or shod, when he is hot he is the hottest thing in an otherwise cold and clammy crop of cup defenders.Hunt's studies at Brown University were interrupted in 1941 when the United States entered World War II. He was drafted into the US Army and [2]:-

... was assigned principally to the research section of the air weather service. During that time, he achieved the rank of captain and used his mathematical prowess to help develop weather forecasts to ensure the success of D-Day and the Allied invasion on the Normandy coast.Released from military service in 1946, Hunt went to Princeton where he studied for his doctorate advised by Salomon Bochner but at the same time acted as an assistant to John von Neumann at the Institute for Advanced Study. He was awarded a Ph.D. in 1948 for his thesis

*On Stationary Stochastic Processes*but continued to work for von Neumann until 1949. He then worked at Cornell University, Ithaca, New York, producing some impressive papers over the next years.

In 1951 Hunt published

*Random Fourier transforms*. Mark Kac, in a review, remarked that:-

Although the methods used are closely related to those of Paley and Zygmund they are used in a powerful way to yield a wealth of new results. ... Theorem 12, for example, contains as a special case the law of the iterated logarithm for the Wiener process. The ingenious use of ergodic theory is particularly noteworthy.He then wrote

*Changes of sign of sums of random variables*jointly with Paul Erdős which was published in 1953. In this paper Hunt gives his address both as Cornell University and as National Bureau of Standards, Los Angeles. He includes a note that:-

The preparation of this paper was sponsored (in part) by the Office of Naval Research, USN.Hunt then published

*An inequality in probability theory*(1955) and a number of papers in 1956. For example

*A theorem of Élie Cartan*(1956) in which Hunt states:-

André Weil and Hopf and Samelson have given a topological proof of the following theorem of Élie Cartan. "Two maximal abelian subgroups of a compact connected Lie group G are conjugate within G." I present a simple metric proof.In

*Semigroups of measures on Lie groups*(1956), he explains:

This paper grew out of discussions with S Bochner. It would be hard now to disengage his contributions from mine. We shall characterise those families of finite positive measures on a Lie group G which are weakly continuous and form a semigroup under convolution.Also in 1956 he published

*Some theorems concerning Brownian motion*. Given a Markov process and a random time, Hunt defines a new Markov process. He writes:-

Although mathematicians use this extended Markov property, at least as a heuristic principle, I have nowhere found it discussed with rigour. We begin by proving a version for Brownian motion. Our statement has the good points that the hypotheses are easy to verify, and the proof is thoroughly elementary (it even avoids conditional probabilities), and that it holds for all processes with stationary independent increments. I have not pushed the scope of the proof to the limit ...In 1957 and 1958 he published three papers with the title

*Markov processes and potentials*. In the first of these he gave a generalization of the well known relation of Brownian motion to potentials. A review of the next one begins as follows:-

This very important and original article establishes close connections between the general theory of potential and homogeneous Markov processes.Hunt was appointed to the faculty at Princeton on 1959, teaching there until 1962 when he moved back to Cornell University. After spending the three years 1962-65 at Cornell, Hunt returned to Princeton where he taught until he retired in 1986.

Hunt was an invited speaker at the International Congress of Mathematicians held 15-22 August 1962 in Stockholm. His lecture,

*Transformation of Markov processes*, gave a direct treatment of the entrance boundary in the theory of Martin boundaries for diffusion or Markov processes. In Europe for the Congress, Hunt spent part of session 1962-63 at Orsay in France where he gave a course of lectures on

*Martingales et processus de Markov*. The notes, published in 1966, provide:-

... an introduction to the potential theory of Markov processes, a theory to which the author has been a major contributor. ... The first chapter ... includes a discussion of conditional probabilities and independence, but the main emphasis is on obtaining some of the principal properties of martingales. The second chapter deals with Markov processes, principally with stationary transition probabilities. The theorems which state that under mild assumptions on the transition probabilities and state-space the corresponding process will have nice properties, such as right sample function continuity, quasi-left continuity, and strong Markov property, are established. A proof is given of the fact that the first entrance time into an analytic set is a stopping time. In the last section potential theory is reached and some important results are proved: the completed maximum principle for potentials, balayage, and the almost-Borel measurability of excessive functions. The monograph is very readable.The 1960s, however, proved a very difficult period for Hunt. At the height of his mathematical powers, he suffered from macular degeneration and began to go blind. He could no longer play tennis, but even doing mathematics became more and more difficult as he tried to develop ways to enable him to continue his research.

Hunt married twice, and was twice divorced. His first marriage was to Mary with whom he had two children, Laurence and Margaret. His second marriage was to Helen with whom he had four children, Diana, Christopher, Lisa, and Gregory.

We have commented on Hunt's eccentric style of playing tennis. We also note that [1]:-

... he liked to play barefoot, would sometimes wear a floppy farmer's hat and, if he did not think he was playing well, would walk off the court.One of his colleagues at Princeton spoke of his wide interests [3]:-

He was very interested in all areas of mathematics, not just his own specialty. He was a Renaissance person, with a deep interest in literature and music as well as many other areas.

### References (show)

- J Holley, Gilbert Hunt Jr., 92; Math and Tennis Ace,
*Washington Post*(11 June 2008). - K MacPherson, Obituary: Gilbert Hunt - Princeton probability expert,
*University World News*(29 June 2008). - K MacPherson, Gilbert Hunt, probability expert, dies at 92,
*Princeton Weekly Bulletin***97**(29) (16 June 2008).

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update December 2008

Last Update December 2008