Mathematics in Industrial Research' 



By GEORGE A. CAMPBELL 



"Sf.i.i.ino" Mathematics to the Industries 



THE necessity for mathematics in industry was recognized at 

 least three centuries ago when Bacon said: "For many parts 

 of nature can neither be invented [disco\^red] with sufficient sub- 

 tility nor demonstrated with sufficient perspicuity nor accommo- 

 dated unto use with sufficient dexterity without the aid and inter- 

 vening of mathematics." Since Bacon's time only a very small 

 part of nature has been "accommodated unto use," yet even this 

 has given us such widely useful de\ices as the heat engine, the tele- 

 graph, the telephone, the radio, the airplane and electric power 

 transmission. It is impossible to conceive that any of these devices 

 could ha\"e been developed without "the aid and intervening of 

 mathematics." Present day industry is indeed compelled, in its 

 persistent endea\'ors to meet recognized commercial needs, to make 

 use of mathematics in all of the three ways pointed out by Bacon. 

 The record of industrial research abundantly confirms his assertion 

 that sufficient subtility in discov-ery, sufficient perspicuity in demon- 

 stration, and sufficient dexterity in use can be achieved oiil\- with 

 the aid of mathematics. 



There is throughout intlustry one \itall\' important common 

 characteristic, — uncertainty'. In (nie industry the uncerlaint\" may 

 be due to the supply of raw material, the suj^pK" of labor, the supply 

 of l)raiiis or tjie sui)pl>' of capital. In another industry the uncer- 

 tainty ma\- Ik- due to the arti\it\- of competitors, to ntictiiating 

 public demand nr ici the ]),i»,i.i;c- and siiliseqiieiit inlerpretatinns of 

 statutor\' laws. Siill oilur industries are the playthings of the weather. 

 \Vhate\er the s(iur((> of iincertaint\- it is of vital importance to the 

 industry to reduce to a minimum the hazards due to each of the 

 uncertainties to which it is subjected. To a limited extent liazar(l> 

 may be transferri-d b\- means of insurance; but most uncertainties 

 cannot be dis()osed of in this manner — the\ mu>t l)e met 1>\ tlie 

 industry indi\idually. 



The practice of probal)ilities. iluTclore. has a pi. ice in e\ ei y in- 

 dustry. In fact, it occupies the lirsi place in indu>liial mathematics, 

 barring only the elenu'ntar\- arithnu'tical operatioii>. li is lemark- 

 able how subtle are the mathematical difficulties presented b\- ap- 



' Paper rcatl at the International Mathematical Congress, at Toronto, .August 

 II, 1924. 



550 



