## Brown University and Applied Mathematics

R G D Richardson wrote the paper 'Applied Mathematics and the Present Crisis' which was published in

*Amer. Math. Monthly***50**(7) (1943), 415-423. In this paper he discusses the deficiency in research in applied mathematics in America, he looks at the reasons for this, and points to World War II as making people realise the problem. He looks at the situation nationally and how over one hundred mathematicians have temporally left their teaching positions to undertake research with military applications. At the end of the paper he describes the developments that had been introduced at Brown University, largely at his initiative, to help address the problem. We give a modified version of this below:**New developments at Brown University.**

As a modest contribution to the amelioration of the situation, Brown University inaugurated in June, 1941 a program of Advanced Instruction and Research in Mechanics, which is now in its seventh term. This effort is supported by the Engineering, Science, and Management War Training program of the U. S. Office of Education and the Carnegie Corporation; there is also a liberal grant for fellowships from the Rockefeller Foundation.

For at least two or three years previous to 1941, there had been at Brown University a conviction that America could not avoid war, that physics and engineering and the underlying mathematics were bound to play a leading part in its prosecution, and that steps should be taken to strengthen one of the weakest links in the American scientific chain. The immediate stimulus of this enterprise was, however, the Fry report. This 1940 report on mathematics in industry was made by Thornton C Fry of the Bell Telephone Laboratories and prepared under the auspices of the Committee on Survey of Research in Industry. This report had wide circulation and has evoked strong expressions of approval.

It is instructive to consider the original objectives of this effort. To be sure, these at the moment are to a considerable extent obscured by the fact that the onset of war has made it essential that the program for the bulk of the participants should be abbreviated and speeded up. Among the basic ideas originally laid down were the improved recruitment and training of applied mathematicians and a stimulation of the interest in applied mathematics among mathematicians and engineers. The primary object was the enlisting of very high grade men and giving them thorough and deep training for careers as teachers of applied mathematics, that training to include practical experience in experimental sciences. This would involve three or four years of graduate study of which perhaps one year would be in practical work. An original subsidiary aim, thrust more prominently into the foreground by the war, was the preparation of a small number of persons for employment as mathematicians in industry and government agencies. From this group a smaller number can be expected to extend the frontiers of knowledge by new developments arising out of the practical problems on which they work. This latter phase of the plan is proving to have real significance in the progress of American science.

During the first session of the program, the University appointed an Evaluating Committee to consider the problem from a national standpoint. The report of this committee, with Marston Morse as chairman, reinforced the report of Fry and made important constructive suggestions for remedying the situation. It was pointed out that the critical situation called for something more than the ordinary evolution of educational methods in this sector. Since this report was written, America has entered the war and the recommendations of the committee would doubtless now be sharpened and intensified. Its main recommendations have been followed.

The main group of courses is centred around Mechanics, which term includes advanced work in fluid dynamics, elasticity, plasticity, aerodynamics, theory of vibrations, theory of structures, and so forth. Other fields of applied mathematics are being included from time to time.

The staff of half a dozen or more is recruited from the ablest men available. The average number of students in attendance has been in excess of fifty, the enrolment in the summer session being greater than that during the academic year. One quarter were already in possession of the doctorate. The clientele ranges from students who have just completed their undergraduate training in mathematics, physics, or engineering to mature men who wish to change their fields of research from pure to applied mathematics. Of the 200 who have enrolled, 40 have gone into research in government agencies concerned with aeronautics, ship construction, gun construction, radar, etc.; 20 are engaged in re- search in industries connected with the war; 10 have special assignments in connection with the armed forces; 25 are continuing as engineers in industry; the remainder are instructors and graduate students in universities.

More than 25 research papers have been completed and others are under way; some deal with immediate practical problems which have arisen in the prosecution of the war, while others are of a more fundamental character. As a significant feature of the program, a limited number of research problems are being investigated for government agencies and war industries.

Besides the instruction in lectures and seminars, there have been numerous single talks and short series of lectures by visiting experts, as well as conferences on topics of current research interest (Non-Linear Mechanics, Ballistics, etc.). As a by-product of the instruction, the School has mimeographed ten series of lectures which, without any advertising, have been widely distributed to industries and universities. Some of the lectures have been put into book form and others will be eventually. Such treatises will prove to be of real significance to future progress in their respective fields. The School is cooperating in preparing a resume of some of the excellent recent work of the Russians in the field of Mechanics; this will probably be published soon by the Taylor Model Basin and thus made available to engineers.

The founding of a new journal devoted to research involving advanced mathematical treatment of engineering problems was deemed necessary. Working with representatives of journals in allied fields, a group of leaders has inaugurated the

*Quarterly of Applied Mathematics*. Brown University has made a liberal subvention; there are already eight hundred subscribers. After an initial period, it is hoped that the journal will become practically self-supporting.

The experiment at Brown University is a lively one; it has already evoked much interest, and it permits a hope that it will prove to be a contribution to the advancement of American science.