June 17, 1921] 



SCIENCE 



543 



Applied mathematics 



Meehanios of continua (ineluding po- 

 tential theory and eleetro-magnetic 



phenomena) 4.7 



Kinematics and geometrical mechan- 

 ics 1.7 



Celestial mechanics 1.7 



Postulate theories 



8.1 

 2.5 



100.0 



It will be noticed that algebra and analysis 

 constitute about two thirds of the whole, 

 though this is not surprising in view of their 

 large variety of phases and methods. Their 

 share, however, is larger than in most coun- 

 tries, doubtless because of the prevailing ten- 

 dencies in the countries to which our mathe- 

 maticians went for training during the closing 

 decades of the last century. I can not help 

 feeling that a more even balance would be 

 desirable, because of the considerable sugges- 

 tive help of the more intuitive branches of 

 mathematics. Particularly does it seem re- 

 grettable that mathematical physics has not 

 received more attention from mathematicians. 

 It is true that some work has escaped a place 

 in the data of the present study because it 

 has not found its way into mathematical peri- 

 odicals. For instance, a former member of 

 the ordnance department has told me that he 

 has in his possession over a hundred copies, 

 mostly unpublished blue-prints, of articles on 

 ballistics. But in view of the reputed prac- 

 tical temperament of the American people, in 

 view of the racial traditions we might natur- 

 ally have inherited from Great Britain, in 

 view of its service to mathematics through its 

 great suggestiveness of interesting problems, 

 and in view of the service of mathematics, 

 through mathematical physics, to physics and 

 engineering, it does seem clear that a greater 

 cultivation of this field in this country is most 

 desirable. In fact, it might almost be con- 

 sidered as characteristic of the decade that 

 this desideratum has been repeatedly and 

 forcefully pointed out. 



One reason for the situation which exists 

 is to be found in our tendency to early and 



over specialization. Our physics departments 

 are apt to load their students with their own 

 courses, with emphasis on the experimental 

 side, often content to have their graduates 

 equipped with the calculus and a formal course 

 in differential equations; while, on the other 

 hand, little physics is usually required of 

 students concentrating in mathematics. This 

 is in part due to lack of mutual confidence, 

 and in part to the student's own haste to re- 

 ceive his degree. Instruction in mathematical 

 physics should be given by mathematical phys- 

 icists. But until we have produced a more 

 adequate supply of these, mathematician and 

 physicist must cooperate. We can at least of- 

 fer courses in those parts of mathematics 

 which are of fundamental importance to phys- 

 ics, and in which details of rigor are replaced 

 by cautions, in case of real danger, and in 

 which a sympathetic attitude toward a desire 

 to find out how nature works replaces a 

 disdain for everything aside from the mathe- 

 matical game, the instructor bearing in mind 

 that the physicist has always the appeal to ex- 

 periment with which to check his logic. On 

 the other hand, it is probable that lecture 

 courses in physics would be more frequented 

 by students of mathematics if an attempt were 

 consistently and constantly made to draw a 

 clear line between mathematical consequences 

 of previously established results and fresh ap- 

 peals to experiment or new physical hypoth- 

 eses. The more this distinction can be made, 

 and the more the physical assumptions can be 

 simplified and gathered into groups at the be- 

 ginning of course or topic, the more will the 

 course be likely to appeal to the student with 

 mathematical predisposition. 



Returning to our table for a glance at the 

 distribution of effort we find the place occu- 

 pied by algebra even higher than we should 

 expect. This is largely due to the work of 

 two men, Dickson, in the theory of numbers, 

 of groups, and in allied subjects of algebra, 

 and Miller, in the theory of groups. Other in- 

 vestigators whose work has enriched this field 

 include Blichfeldt, Carmichael, Vandiver, Bell 

 and Lehmer, in the theory of numbers ; Glenn, 

 Carmichael, Coble, Curtiss, Bennett, Metzler, 



