266 BELL SYSTEM TECHNICAL JOURNAL 



Historically it is easy to explain how this situation came about. Fifty 

 years ago America was so backward in the field of mathematics that there 

 was not even a national association of mathematicians. A quarter of a 

 century later it was just coming of age in mathematics and was properly, 

 if not indeed necessarily, devoting its entire attention to improving the 

 quality of instruction in the "pure" field. The first faint indications that 

 industrial mathematics might someday become a career had indeed begun 

 to appear, but they were not impressive enough to attract the attention of 

 university executives. 



Today we lead the world in pure mathematics, and perhaps also in 

 that other field of mathematics which has somehow come to be known as 

 modern physics. We have strong centers of actuarial and statistical 

 training. But in the field of applied mathematics which is the particular 

 subject of this report, we stand no further forward than at the turn of the 

 century, and far behind most European countries. 



A quarter of a century ago it would have been difficult to find suitable 

 teachers. Just now it could be done, primarily because a number of 

 European scholars of the right type have been forced to come here, and a 

 few others have developed spontaneously within our own borders. There 

 are perhaps half a dozen of them, but they are so scattered, sometimes in 

 such unpropitious places, as to have little influence on the development of 

 industrial personnel. 



It is unfortunate that no university with strong engineering and science 

 departments has seen fit to bring this group together and establish a center 

 of training in industrial mathematics. We have estimated a demand of 

 about 10 exceptional graduates per year. If that estimate is even remotely 

 related to the facts, such a department would have a most important job 

 to do. 



Mathematics in Industry 



Subjects Used 



As Dr. H. M. Evjen, Research Physicist of the Geophysical Section 

 of the Shell Oil Company, remarks: 



"Higher mathematics, of course, means simply those branches of the science 

 which have not as yet found a wide field of application and hence have not as 

 yet, so to speak, emerged from obscurity. It is, therefore, a temporal and sub- 

 jective term." 



If this is accepted as a definition of higher mathematics^and it is a 

 valid one for the pure science as well as for its applications — it follows 



