Industrial Research 



269 



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 experimental evidence. 

 For the typical engineer these statements may be re- 

 versed. Confronted by a carefully thought-out theory 

 which predicts a certain result, and a carefully per- 

 formed experiment which fails to produce it, the typical 

 mathematician asks first, "What is wrong with the ex- 

 periment?" 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 physicist would resort to the laboratory. 

 For the same reason the mathematician in his "pure" 

 form delights in building logical structures, such as 

 topology or abstract algebra, wliich have no apparent 

 connection with the world of physical reality and which 

 would not interest the typical engineer; while conversely 

 the engineer or physicist in his "piu-e" form takes great 

 interest in such useful information as a table of hard- 

 ness data which may, so far as he is aware, be totally 

 imrelated to any theory, and which the typical mathe- 

 matician would find quite boring. 



A second characteristic of the typical mathematician 

 is his highly critical attitude toward the details of a 

 demonstration. For almost any other class of men an 

 argimient may be good enough, even though some minor 

 question remains open. For the mathematician an ar- 

 gument is either perfect in every detail, in form as well 

 as in substance, or else it is wrong. There are no inter- 

 mediate classes. He calls this "rigorous thinking," and 

 says it is necessary if his conclusions are to be of per- 

 manent value. The typical engineer calls it "hair split- 

 ting," and says that if he indulged in it he would never 

 get anything done. 



The mathematician also tends to idealize any situa- 

 tion with which he is confronted. His gases are "ideal," 

 his conductors "perfect," his surfaces "smooth." He 

 admires this process and calls it "getting down to essen- 

 tials"; the engineer or physicist is likely to dub it some- 

 what contemptuously "ignoring the facts." 



A foiu-th and closely related characteristic is the 

 desire for generality. Confronted with the problem of 

 solving the simple equation a; ^— 1 = 0, he solves x"— 1 =0 

 instead. Or asked about the torsional vibration of a 

 galvanometer suspension, he studies a fiber loaded with 

 any number of mirrors at arbitrary points along its 

 length. He calls this "conserving his energy"; he is 

 solving a whole class of problems at once instead of 

 dealing with tliem piecemeal. The engineer calls it 

 "wasting liis time"; of what use is a galvanometer 

 with more than one mirror? 



In the vast army of scientific workers who cannot be 

 tagged so easily with the badge of some one profession, 

 those may properly be called "mathematicians" whose 

 work is dominated by these foxir characteristics of 

 greater confidence in logical than experimental proof, 

 severe criticism of details, idealization, and generaliza- 

 tion. The boundaries of the profession are perhaps not 

 made sharper by this definition, but it has the merit of 

 being based upon type of mind, wliich is an attribute 

 of the man himself, and not upon such superficial and 

 frequently accidental matters as the courses he took in 

 college or the sort of job he holds. 



It is, moreover, a more fundamental distinction than 

 can be drawn between, say, physicist, chemist, and 

 astronomer. That is why the mathematician holds 

 toward industry a different relationship than other 

 scientists, a relationship which must be clearly under- 

 stood by management if his services are to be success- 

 fully exploited. 



The Place of the Mathematician 

 in Industrial Research 



The typical mathematician described above is not 

 the sort of man to carry on an industrial project. He 

 is a dreamer, not much interested in things or the 

 dollars they can be sold for. He is a perfectionist, 

 imwiUing to compromise; idealizes to the point of 

 impracticality ; is so concerned with the broad horizon 

 that he cannot keep his eye on the ball. These traits 

 are not weaknesses; they are, on the contrary, of the 

 highest importance in the job of finding a system of 

 thought which wiU harmonize the complex phenomena 

 of the physical world, that is, in reducing nature to a 

 science. The job of industry, however, is not the 

 advancement of natural science, but the development, 

 production, and sale of marketable goods. The 

 physicist, the chemist, and especially the engineer, 

 with their interest in facts, things, and money are 

 obviously better adapted to contribute directly to 

 these ends. To the extent that the mathematician 

 takes on project responsibility, he is forced to compro- 

 mise; he must specialize instead of generalize; he must 

 deal with concrete detail instead of abstract principles. 

 Some mathematicians cannot do these things at all; 

 some by diligence and self-restraint can do them very 

 well. To the extent, however, that they succeed along 

 these lines they are functioning not as mathematicians 

 but as engineers. As mathematicians their place in 

 industry is not to supply the infinite attention to 

 practical detail by wliich good products, convenient 

 services, and efficient processes are devised ; their func- 

 tion is to give counsel and assistance to those who do 

 supply these things, to appraise their everyday prob- 

 lems in the light of scientific thought, and conversely to 



