M.iriiii.u.iiics ix ixDi'STNi.ii. Kr.sii.iKcn ssi 



p.iniuK iniuuviil proMcms in the theory of proI),il)ilily. I'or tliis 

 ir.iM)ii, m.uheniatirians who are entrusted with the appli(ati;)ii 

 of probability to industry must have jjreat insijjhl and acinnen. 

 I'.ven so, in a|)piyin}j prol)al)ility to any iiidustr\-, a heijinninji should 

 lie made with the simpler problems, jjoing on by gr.ulu.il steps to 

 more anil more eomplirated ones. 



Kach industr> has its own special mathematical problems, which 

 must be considered intlividually in order to determine where mathe- 

 matics should be applied. No iiulusirial problem can seem much 

 more hopeless, as a field for exact mathematics, than the subject 

 of electricity as understocnl in the time of Bacon. It was then a mere 

 collection of curious observations, such as the evanescent attraction 

 of rubbed amber. Persistent observation and careful ctirrelation 

 have, however, brought a large domain of present day electricity 

 under quantitative relations. Klectricity is now preeminently a 

 field for mathematics, and all advances in it are primarily through 

 mathematics. 



Industrial mathematics will arliie\e but liltlc unless it is under- 

 taken by persons with suitable aptitudes working under favorable 

 coniiitions, on problems which have reached the mathematical stage. 

 Industrial mathematical research involves much more than the 

 mechanical application of established mathematical formulas. It 

 involves cooperation in determining the problems to be attacked, 

 in deciding what experimental data are necessary, in obtaining these 

 data, in formulating the mathematical problem, in carrying through 

 the analytical and numerical work, in applying the results to the 

 physical actuality and in practically testing the commercial results 

 achie%ed. In this cooperation many indi\iduals may be invoKed 

 and many tentative trials may be necessary in order to determine 

 the solution which best meets all of the commercial conditions. 



The cooperation must be effective; it must produce results, and 

 these promptly. Mathematical deductions must be made intelli- 

 gible and convincing, so that they will eventuate in action even 

 when the indications of theory are apparently contrary to practical 

 experience. This is important because the most valuable theoretical 

 results are often revolutionary. 



On the part of the industrial mathematician, powers of observa- 

 tion, clear physical concepts, quick resourcefulness, creative imagi- 

 nation and constant persistency are required. These are rare human 

 (lualities. Unless industrial mathematical work is made attractive 

 to men possessing these high talents, the full measure of success 

 cannot be expected. Industrial mathematics must ofTer a career in 



