**Elliott Montroll**'s parents were Esther Israel and Adolph Baer Montroll. Adolph was an artist who dealt in furs and together with his wife Esther provided a loving home in which Elliott grew up. They taught Elliott to read and write before he entered school for the first time at the age of five. At school he showed great initiative in designing projects for his class and, with a growing interest in chemistry, his parents allowed him to convert the basement of their home into a laboratory. There he spent long hours carrying out experiments with one of his school friends.

It was clear that given his passion for chemistry that was the subject Montroll would study at university. Indeed he entered the University of Pittsburgh in 1933, taking a chemistry course and he graduated with a B.S. in chemistry four years later. However by the time he graduated he had changed from his schoolboy ambition to become a chemist and decided to undertake research in mathematics. He registered for a Ph.D. in mathematics at the University of Pittsburgh and was awarded his doctorate in 1939. He used both his expertise in chemistry and mathematics in his thesis *Applications of the characteristic value theory of integral equations* in which he applied integral equations to the study of imperfect gases. A paper published jointly with Joseph E Mayer in 1941 *Statistical mechanics of imperfect gases* also examined ideas developing out of his thesis.

Montroll was now in the unusual position of being able to work in mathematics, physics or chemistry departments. His first appointment was as a research assistant in chemistry at Columbia University in 1939-40. It was during this time that he worked with Joseph Mayer on the techniques published in the 1941 paper mentioned above. In 1940-41 he was a Sterling Research Fellow at Yale University where his work on the Ising model of a ferromagnet led him to solve certain Markov chain problems. Following this he was a Research Associate at Cornell University in 1941-42 where he began his studies of the problem of finding the frequency spectrum of elastic vibrations in crystal lattices. During 1942-43 Montroll was an instructor in physics at Princeton University and in 1943 he married Shirley Abrams; they had ten children, five boys and five girls.

In 1943 Montroll was appointed as Head of the Mathematics Research Group at the Kellex Corporation in New York. There he worked on programs associated with the Manhattan Project, using his expertise in applying statistical mechanics to the behaviour of neutrons in a chain reaction. In 1944 he went to the Polytechnic Institute of Brooklyn, being appointed adjunct professor of chemistry, then in 1946 he returned to the University of Pittsburgh. He served as assistant professor of physics and mathematics and was promoted to associate professor in 1947. He remained at Pittsburgh until 1950 but also served as head of the Physics Branch of the Office of Naval Research in Washington, D.C., from 1948 to 1950. In 1950 he was appointed as a research fellow at the Courant Institute in New York. In 1951 he was appointed Research Professor in the Institute for Fluid Dynamics and Applied Mathematics at the University of Maryland and, given the many moves he had made, this was a period of comparative stability since he held the post until 1960. However, he also Director of its Physical Science Division of the Office of Naval Research from 1952 to 1954.

During his time at Maryland, Montroll published *Topics in statistical mechanics of interacting particles* which was 86 pages of mimeographed notes of a lecture series, written jointly with G F Newell. The object of the lectures was to study the equilibrium statistical mechanics of large systems of interacting particles. In 1953 he delivered a lecture at the symposium on special topics in applied mathematics at Northwestern University, publishing *Frequency spectrum of vibrations of a crystal lattice* in the Proceedings. This is a review of some developments in the analysis of the vibration spectrum of crystal lattices with particular emphasis on the observation that the frequency distribution function is expected to have singularities. At the Third Berkeley Symposium on Mathematical Statistics and Probability 1954-1955, Montroll gave a paper *Theory of the vibration of simple cubic lattices with nearest neighbor interactions* in which described vibrations of a cubic lattice with 1, 2, 3, and *n* dimensions where *n* is large. In 1956 he published *Random walks in multidimensional spaces, especially on periodic lattices* in which he looked at random walks on a *k*-dimensional lattice. In 1958, as consultant to General Motors Corporation, he undertook studies of traffic flow and published *Traffic dynamics: Studies in car following*.

Montroll was not someone who was happy to remain in one place for a long time and by 1960, having been at the University of Maryland for nine years, he felt it was time to move on. He wanted to move, both from Maryland and also from universities, and took a took the post of Director of General Sciences at the IBM Thomas J Watson Research Center in Yorktown Heights, New York. In 1963 he took up the position of Vice President for Research at the Institute for Defense Analysis in Washington, D.C. but by this time a return to university life looked attractive. In 1966 he was appointed Albert Einstein Professor of Physics, and the Director of the Institute for Fundamental Studies, at the University of Rochester. He remained there until he reached the retiring age of 65 when he accepted two further posts, one back at the University of Maryland and the other at the University of California, Irvine.

Some of his later work appeared in *Social dynamics and the quantifying of social forces* (1978) in which he proposed a general framework in which social and technological change can be modelled and measured. In the proceeding of the conference *Nonlinear equations in abstract spaces* held in 1977 at the University of Texas he published *On some mathematical models of social phenomena* in which he examined models for population growth and statistical models of other social phenomena.

Montroll's work led to him receiving many honours and prizes. He was elected to the National Academy of Sciences (United States) in 1969, and to the American Academy of Arts and Sciences in 1973. His work on traffic flow led to him winning (jointly) the Lanchester Prize of the Operations Research Society of America in 1959. Carey writes in [1]:-

A A Maradudin, K E Shuler and R F Wallis write in a tribute to Montroll by the University of California:-His particular genius consisted of his ability to develop elegant and powerful mathematical formulae capable of explaining complex physical and social relationships.

He died at his home from heart failure.As a person, Elliott Montroll was one of the most cheerful and imperturbable people one could ever hope to meet. He was unfailingly helpful to his colleagues, and always willing to take on tasks without first asking what was in it for him. He was truly a man about whom it can be said that no one ever uttered an unkind word and who never made an unkind remark about anyone. His universe consisted exclusively of friends and admirers.

**Article by:** *J J O'Connor* and *E F Robertson*

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