SECTION VI 

 4. INDUSTRIAL MATHEMATICS 



By Thornton C. Fry 

 Mathematical Research Director, Bell Telephone Laboratories, New York, N. Y. 



ABSTRACT 



The report consists of three major sections. The first 

 discusses mathematical specialists in industry, calls at- 

 tention to the essentially consultative character of their 

 work, and makes some observations regarding the edu- 

 cation, employment, and supervision of this type of 

 personnel. 



The second section deals, not with the work of these 

 specialists, but with the uses to which mathematics is 

 put at the hands of industrial workers in general, the 

 various ways in which it contributes to the economy 



and effectiveness of research, and the kinds of mathe- 

 matics that are most used. A number of illustrations 

 are given, together with brief surveys of the utilization 

 of mathematics in four important industries : commimi- 

 cations, electrical manufacturing, petroleum, and air- 

 craft. 



The third section is devoted to statistics, which 

 touches industrial life at rather different points;, and 

 hence could not conveniently be included in the gen- 

 eral discussion. 



Introduction 



Mathematical technique is used in some form in most 

 research and development activities, but the men who 

 use these techiiiques would not usually be called 

 mathematicians. 



Mathematicians also play an important role in in- 

 dustrial research, but their services are of a special 

 character and do not touch the development program 

 at nearly so many points. 



Because of this contrast between the ubiquity of 

 mathematics and the fewness of the mathematicians, 

 this report is divided into sharply differentiated parts. 

 Under "Mathematicians in Industry" an attempt is 

 made to explain what sort of service may be expected 

 of industrial mathematicians, and to develop some 

 principles of primary importance in employing and man- 

 aging them. An attempt is also made to appraise future 

 demand for men of this type, and to discuss the sources 

 from which they can be drawn. Under "Mathematics 

 in Industry" appear brief surveys of the extent and 

 character of the utilization of mathematics in a few 

 special hadustrics, and examples of specific problems 

 in the solution of which mathematical methods have 

 been necessary or advantageous. 



In these two sections mathematics is interpreted 

 broadly to include not only the fundamental subjects, 

 algebra, geometry, analysis, etc., but also their mani- 

 festations in applied form as mechanics, elasticity, 

 electromagnetic theory, hydrodynamics, etc. Statis- 

 tics, however, touches industrial activity in a rather 

 268 



different way, and is therefore discussed separately 

 under a third heading, "Statistics in Industry." 



One observation which will be made in more detail 

 later is worthy of mention here, because of the present 

 and prospective scarcity of suitably trained industrial 

 mathematicians. Though the United States holds a 

 position of outstanding leadership in pure mathematics, 

 there is no school which provides an adequate mathe- 

 matical training for the student who wishes to use the 

 subject in the field of industrial applications rather than 

 to cultivate it as an end in itself. Both science generally, 

 and its industrial applications m particular, would 

 be advanced if a group of suitable teachers were brought 

 together in an institution where there was also a strong 

 interest in the basic sciences and in engineering. 



Mathematicians in Industry 

 What is a Mathematician? 



If every man who now and then computes the aver- 

 age of a set of instrumental readings or solves a differ- 

 ential equation is a mathematician, there are few re- 

 search workers who are not. If, on the other hand, 

 only those who are primarily engaged in making addi- 

 tions to mathematical loiowledge are mathematicians, 

 there are almost none in industry. Neither definition 

 is sound. The first is absurd; the second not closely 

 related to the essential natm-e of mathematical thought. 

 This report adopts a definition based upon the charac- 

 ter of the man's thinking rather than the ultimate use 

 to which his thinking is put. 



