.MODERN MATHElMxVTICAL RESEARCH/ 



By Prof. G. A. Miller, 



Umversity oj Illinois. 



Mathematics has a large househokl and there are always rumors of 

 prospective additions despite her age and her supposed austerity. 

 Without aimmg to give a complete list of the names <.f the members 

 of this household we may recall here a few of the most prominent 

 ones. Among those which antedate the beginning of the Christian 

 era are surveying, spherical astronomy, general mechanics, and mathe- 

 matical optics. Among the most tln-iving younger members are 

 celestial mechanics, thermodynamics, mathematical electricity, and 

 molecular physics. 



Usually a large household serves as one of the strongest incentives 

 to activity, and mathematics has always responded heartily to this 

 incentive. As the most efficient contmued service calls for unusual 

 force and ingenuity, mathematics has had to provide for her own 

 development and proper nourishment in addition to providing as 

 liberally as possible for her household. This double object must be 

 kept prommently before our eyes if we would comprehend the present 

 mathematical activities and tendencies. 



There is another miportant uicentive to mathematical activity 

 which should be mentioned in this connection. Mathematics has 

 been very hospitable to a large number of other sciences and as a 

 consequence some of these sciences have become such frequent 

 visitors that it is often difficidt to distinguish them from the regular 

 members of the household. Among these visitors are economics, 

 dynamical geology, dynamical meteorology, and the statistical parts 

 of various biological sciences. Visitors usually expect the best that 

 can be provided for them, and the efforts to please them frequently 

 lead to a more careful study of available resources than those which 

 arc put forth in providing for the regular household. 



We have thus far spoken only of what might be called the material- 

 istic incentives for mathematical development. While these have 

 always been very significant, it is doubtful whether they have been 

 the most powerful. Symmetry, harmony, and elegance of form have 



• Read before the Illinois Chapter of the Society of the Sigma Xi, April, 1912, aud reprinted by jjermission 



from Sck'uco, .Tunc 7, 191"-?. 



187 



