M.tTHEM.iriCS IX IXnCSlKl.tl. RI.SI..IKCII 557 



to impart (It-tails of iiirrt'nl iiidiislri.il jjrarliri-. Tlu-sr di'taiU an- 

 l)fst ar(|uired in tlit- iiulustriai ciu ironiiu'iit itself. Si-lf-t raining iy 

 funiianu-ntals, on the otlu-r hand, is nuich more difficult, and is not 

 likfly to go far, unless a start has been made imdcr the faxorahle 

 ii>nditions affonled by the university. 



What I have tried to emphasize is that iiulustr%- ran realize its 

 greatest possibilities only with the aid of mathematicians, and that 

 mathematicians can tind opportunities in industry worthy of their 

 powers, however great those powers may be. To ensure the success 

 of industrial mathematics the industry must inaugurate mathematical 

 research as early as possible, mt that ample time may be afforded 

 for the gradual accumulation of information upon which mathematics 

 may be securely based, and for deriving quantitative results before 

 the necessity for commercial action arrives. The industrialist must 

 also be ready to give the mathematician's conclusions a sympathetic 

 trial even though they run contrary to established precedent. Above 

 all, industry needs mathematicians of an especially liroad type — 

 men whose interests naturally extend beyond their special field, and 

 who are flexible enough to cooperate with non-mathematicians. 

 These industrial mathematicians must inspire confidence by their 

 firm grasp of physical realities, by the relevance of their mathe- 

 matics, and by the ability to present their results clearly and con- 

 vincingly. 



