840 



SCIENCE 



[N. S. Vol. XLIV. No. 1146 



calculus. Newton and Leibnitz made inde- 

 pendent discoveries in this field. Newton 

 chose a rather clumsy notation, Leibnitz 

 our present notation. The English mathe- 

 maticians used the Newtonian notation and 

 were hampered to such an extent that they 

 fell far behind the continental mathemati- 

 cians in the development of the calculus. 

 The graph is an example of an almost uni- 

 versal scientific symbol for representing 

 tabulated data. Some one has said that we 

 capitalize our knowledge in an equation. 

 The natural scientist finds a well-developed 

 symbolism in mathematics and proceeds to 

 make use of it without taking the trouble 

 <of creating one of his own. 



I have spoken of the service of mathe- 

 matics to the natural sciences. There is 

 a return service. The natural sciences fur- 

 nish a rich field for mathematical research. 

 One of the problems that has called forth 

 the efforts of many mathematicians in the 

 recent past has been the three body prob- 

 lem. There are many others of lesser note 

 and many more still untouched. In a num- 

 ber of the Bulletin of the American Mathe- 

 matical Society for 1914, there appeared a 

 letter from a Mr. Paaswell, an engineer, 

 enumerating a number of engineering prob- 

 lems which he thinks the mathematician 

 should attack. Physics and mathematics 

 have acted and reacted upon each other to 

 the enrichment of both. "Witness the work 

 of J. C. Maxwell. 



The natural sciences and developments 

 based upon them not only furnish a rich 

 field for mathematical research, but a field 

 which promises to quickly make mathe- 

 matics of service to the world. The scien- 

 tist in any field feels justified in his labors 

 if he discovers new facts, whether or not 

 they are immediately applicable to the 

 problems of daily life. He hopes they will 

 be serviceable some day. The investigator 

 in pure mathematics may work for the 



pleasure he gets from his mental creations, 

 but in most men there is the deeper purpose 

 of serving the world. The natural sciences 

 furnish a field for the choice of postulates, 

 the development of the consequences of 

 which gives prospect of practical worth in 

 the immediate future. 



The mathematician is always confronted 

 by the question of the consistency of his 

 postulates. If these are chosen from some 

 natural science, he can often find some phys- 

 ical system in which his postulates are veri- 

 fied. This exhibition of an example in 

 which the postulates are verified and which 

 from the fact of its physical existence offers 

 no contradictory conclusions, is the best 

 proof of consistency. 



In our colleges and technical schools the 

 time the engineering student or student of 

 pure science gives to mathematics is re- 

 duced to a minimum in order to make room 

 for more technical subjects, and in our 

 graduate schools the mathematical student 

 is given little opportunity to study any- 

 thing but pure mathematics. The result 

 is that one group of students knows too 

 little mathematics to develop properly their 

 field of study and the other group knows 

 too little of the natural sciences and their 

 application to apply to them their knowl- 

 edge of mathematics. 



How can we remedy this? I do not 

 know. Not every engineering student or 

 student of pure science should be required 

 to become proficient in mathematics, nor 

 every mathematician be required to become 

 an engineer. This would be a great waste 

 of time and effort without commensurate 

 returns. The sooner, however, some plan 

 is worked out whereby the pure science or 

 engineering student of marked mathemat- 

 ical ability is given a chance to develop that 

 ability, or the mathematical student with 

 a tendency to applied mathematics is given 

 opportunity in that direction, the sooner 



