Applied Mathematics


From the summer of 1941 through the academic year 1945/6 Brown University had a Program of Advanced Instruction and Research in Mechanics.  This was the forerunner of the Graduate Division of Applied Mathematics, which was formally established by the Advisory and Executive Committee of the Corporation on May 8, 1946, and began to offer graduate courses in September 1946.  The first years of this program are described in a paper by Dean R. G. D. Richardson (American Journal of Physics 11, 67-73, 1943).  The present description draws heavily on this paper.  

Late in 1940, a committee on Survey of Research in Industry appointed by the National Research Council submitted a report to the National Resources Planning Board and President Roosevelt.  The section on Industrial Mathematics had been written by Dr. T. C. Fry, Mathematical Research Director of Bell Telephone Laboratories.  In it Dr. Fry pointed out that the need for mathematicians in industry was increasing and that there was a serious lack of university courses for graduate training of industrial mathematicians.  He also stated that management was becoming keenly alive to the importance of obtaining competent applied mathematicians to work with the scientific personnel.

To Dean Richardson, who had long felt that the applied mathematics was not adequately represented in the typical university curriculum of this country, this report provided welcome backing. With the financial support of the U. S. Office of Education, the Carnegie Foundation, and the moral support of President Wriston, he organized a 12-week summer school in 1941.  In addition to advanced graduate courses on partial different equations (J. D. Tamarkin and William Feller), advanced topics in partial diffferential equation (Stefan Bergman), fluid dynamics (Richard von Mises and K. O. Friedrichs) and elasticity (I. S. Sokolnikoff), there were research seminars in fluid mechanics and elasticity as well as single lectures and short lecture series by R. D. Courant, R. M. Foster, T. C. Fry, J. N. Goodier, R. B. Lindsay, A. I. Naidai, Hillel Poritsky, Theodore Theodorsen, S. P. Timoshenko and Norbert Wiener.  Some sixty students attended this summer school; their mathematical background ranged from that of an advanced graduate student to that of a mature mathematician.

An evaluating committee was appointed by President Wriston to study the summer experiment.  It consisted of Theodore von Karman (California Institute of Technology), Marston Morse (Institute of Advanced Studies, Princton), George P. Pegram (Columbia University) and Warren Weaver (Rockefeller Foundation).  The following passage from the report illustrates their thoughts on applied mathematics:

Thus there has been in American mathematics since 1900 a marked tendency to emphasize pure mathematics.  The success of this development is a great source of national strength and should be a cause for national pride. But it is highly unfortunate that in our enthusiasm for pure mathematics we have foolishly assumed that applied mathematics is something less attractive and less worthy.  For in the history of science it has universally been true that the "pure sciences" and the "applied sciences" have been vigorous and prosperous almost exactly to the degree that they have highly regarded each other and been concerned with each other.  It is obvious that, in the long run, pure mathematics and applied mathematics ought to be in the closest relationship of mutual respect, parallel development, and continuously stimulating interaction.

The report expressed doubts that the ordinary evolution of educational methods would remedy the situation as promptly and efficiently as was desirable, and stressed the need for a long-range program in applied mathematics to prepare teachers for scientific and engineering schools and furnish research personnel for government agencies and industry.  It encouraged Brown to continue the experiment.

William Prager and John L. Synge joined the faculty of the Program in the fall of 1941, and Leon Brillouin and Sergei A. Schelkunoff in the summer of 1942.  Whereas only about 30 students attended during the academic year 1941/42, enrollment rose to 110 in the summer of 1942, when courses were offered on three levels.  In addition to courses on the subjects treated in the previous summer session, there were courses on the theory of flight (S. Bergman), advanced dynamics (L. Brillouin), geometrical foundations of mechanics (W. Prager), plasticity (W. Prager), and electromagnetic waves (S. A. Schelkunoff).  For many courses mimeographed lecture notes were made available, which had wide distribution.

The Rockefeller Foundation supported the Program through the grant of fellowship funds, and it gathered 45 postdoctoral fellows during the summer of 1942.  The roster of fellows contained in Dean Richardson's final report to the Rockefeller Foundation (1946) makes impressive reading because so many fellows have risen to positions of eminence.

The success of the summer session of 1942 established the Program for the war years.  At the end of the war, however, when funds were no longer as readily available, a decision had to be reached on whether Brown could afford to continue the program in applied mathematics.  In a memorandum to President Wriston dated March 1, 1946, W. Prager outlined the way in which he felt the program could and should be continued.

The early program in applied mathematics focused on solid and fluid mechanics, electromagnetic theory, mathematical methods in applied physics, numerical analysis and probability theory—the principal interests of the faculty for many years. Since that time, the interests of the faculty have been extended as the Division has maintained a leading role in the development of applied mathematics.  In 1964, the Center for Dynamical Systems was established to coordinate the research of a large group of people working in ordinary and partial differential equations and their applications. More recently, strong programs of research in scientific computing and in applied probability and statistics have been established. 

Most of the above history was taken from a brochure presented at the time of the celebration of the 25th anniversary of the founding of the Division of Applied Mathematics (September 7 - 10, 1971).  Contributors were Herbert Kolsky, Philip Davis, as well as William Prager, Frederic Bisshopp, Walter Freiberger, Ulf Grenander, Jack Hale, Allen Pipkin, Lawrence Sirovich and Joseph P. LaSalle.

Historical Resources

A brief yet fascinating account of the history of applied mathematics is chronicled by Martha Mitchell in her superb collection of historical works entitled, “Encyclopedia Brunoniana."

In addition, the Division is deeply grateful for the research work of Clare Kim, a graduate from Brown University (Class of 2011) who wrote her senior thesis about the history of the Division of Applied Mathematics.  It is entitled, "Math Derived, Math Applied:  The Establishment of Brown University’s Division of Applied Mathematics, 1940-1950."

A short history of the Division of Applied Mathematics at Brown University and an oral history given by Professor Emeritus Walter Freiberger.