256 BELL SYSTEM TECHNICAL JOURNAL 



In these two sections mathematics is interpreted broadly to include 

 not only the fundamental subjects, algebra, geometry, analysis, etc., 

 but also their manifestations in applied form as mechanics, elasticity, 

 electromagnetic theory, hydrodynamics, etc. Statistics, however, touches 

 industrial activity in a rather different way, and is therefore discussed 

 separately under a third heading, "Industrial Statistics and Statisticians." 



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 mathematical 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 in 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 average of a set of instru- 

 mental readings or solves a differential equation is a mathematician, there 

 are few research workers who are not. If, on the other hand, only those 

 who are primarily engaged in making additions to mathematical knowledge 

 are mathematicians, there are almost none in industry. Neither definition 

 is sound. The first is absurd ; the second not closely related to the essential 

 nature of mathematical thought. This report adopts a definition based 

 upon the character of the man's thinking rather than the ultimate use to 

 which his thinking is put. 



Some men would be called mathematicians in any man's language; 

 others physicists or engineers. These typical men are differentiated in 

 certain essential respects: 



The typical mathematician feels great confidence in a conclusion reached 

 by careful reasoning. He is not convinced to the same degree by experi- 

 mental evidence. For the typical engineer these statements may be 

 reversed. Confronted by a carefully thought-out theory which predicts a 

 certain result, and a carefully performed experiment which fails to produce 

 it, the typical mathematician asks first, "What is wrong with the experi- 

 ment?" and the typical engineer, "What is wrong with the argument?" 

 Because of this confidence in thought processes the mathematician turns 

 naturally to paper and pencil in many situations in which the engineer or 



