INDCrS TRIA L MA THEM A TICS 265 



these 10 must be exceptional men, it does not seem unreasonable to ask 

 where they may be found. 



Most mathematicians now in industry were trained as physicists or 

 as electrical or mechanical engineers, and gravitated into their present 

 work because of a strong interest in mathematics. Few came from the 

 mathematical departments of universities. As scientists they are university 

 trained, but as mathematicians they are self-educated. 



Their training has not been ideal. Industrial mathematics is being 

 carried on by graduates of engineering or physics not so much because 

 of the value of that training as because of the weakness of mathematical 

 education in America. The properly trained industrial mathematician 

 should have, beyond the usual courses of college grade, a good working 

 background of algebra (matrices, tensor theory, etc.), some geometry, 

 particularly the analytic sort, and as much analysis as he can absorb 

 (function theory, theory of differential and integral equations, orthogonal 

 functions, calculus of variations, etc.). These should have been taught 

 with an attitude sympathetic to their applications, and reinforced by 

 theoretical courses in sound, heat, light and electricity, and by heavy 

 emphasis upon mechanics, elasticity, hydrodynamics, thermodynamics and 

 electromagnetic field theory. He should understand what rigor is so that 

 he will not unwittingly indulge in unsound argument, but he should also 

 gain experience in such useful but sometimes treacherous practices as the 

 use of divergent series or the modification of terms in differential equations. 

 He should have enough basic physics and chemistry of the experimental 

 sort to give him a realistic outlook on the power as well as the perils of 

 experimental technique. By the time he has acquired this training he will 

 usually also have acquired a Ph.D. degree, but the degree itself is not now, 

 and is not likely to become, the almost indispensable prerequisite to employ- 

 ment that it is in university life. 



There is nowhere in America a school where this training can be acquired. 

 No school has attempted to build a faculty of mathematics with such train- 

 ing in mind. Hence industry has had to make such shift as might be with 

 ersatz mathematicians culled from departments of physics and engineering. 

 To make matters worse, a student with strong theoretical interests who 

 enrolls in physics these days is almost certain to spend most of his time on 

 modern mathematical physics, which insists almost as little upon fidelity 

 to experience and experiment as does "pure" mathematics, from which it 

 differs more essentially in matters of language and rigor than of general 

 philosophic attitude. At the moment, therefore, engineering schools must 

 be looked upon as the most hopeful sources of industrial mathematicians. 



