SS6 BELL SYSTEM TECHMCAL JOURNAL 



difficult to find and isolate in the form best adapted for the purpose 

 in hand. What is very greatly needed at the present time is a com- 

 pendium or unabridged dictionary of mathematical results concisely 

 and uniformly stated, and systematically classified for convenient 

 reference. What I have in mind is not a mere handbook of applied 

 mathematics, but a statement of theorems and formulas and tab- 

 ulated results expressed in the language of pure mathematics, and 

 comparable in scope and size with the "Encyklopiidie der Mathe- 

 matischen Wissenschaften." Preparation of such a compendium 

 would be a tremendous undertaking, but it would also be of the 

 greatest value. To such a collection of tools the industrial mathe- 

 matician would turn for the appropriate tool as each new problem 

 arises. 



I would have the uni\ersity training of the industrial mathematician 

 based upon such a compendium by means of judicious sampling, 

 at many points, under competent leadership. He would thus become 

 familiar with his source book as a whole and thereafter turn to it 

 instinctively and use it with confidence. At the present time, wlicn 

 the average text-book is held in low esteem and nothing has been 

 substituted which adequately fills the gap, the student of mathe- 

 matics leaves the university with a five-foot shelf of notebooks, 

 together with what he carries in his head. Neither the memory 

 nor the notebook is likely to be a reliable source of information when 

 a particular result is needed for the first time, ten years later. It 

 then becomes necessary for him to take the time to deduce the result 

 from first principles, or to hunt up lecture notes, a text-book or 

 original paper and waste much \aluable time picking up the thread 

 of the argument. The sampling to which I have referred should 

 not be that of a dilletante; it should be an inlcnsi\c grounding in 

 the fundamental concepts and iiu'thods of mathematics, and the 

 development ab initio of several well distributed bnuirhcs of m.ithc- 

 matics. 



The combination of mathematical ability with an observant mind 

 is as desirable as it is rare. The uni\ersity training should include 

 non-mathematical courses adapted for de\eloping the powers of 

 observation, or at least an appreciation of tiie necessity of coojiera- 

 ting with others who are observant. A study of the natural sciences, 

 accompanied by experimental work, should be of great value. It is 

 of course, difficult to be reasonable and not ask the impossible of the 

 university in the training of any specialist. We recognize that, at 

 best, only a beginning can be made at the university, but this be- 

 ginning should include the fundamentals and should not attempt 



