MATHEMATICS AND THE SCIENCES — LASLEY 197 



an effort to understand its function in the domain of scientific think- 

 ing. This relation seems to be much like that of the guide to the 

 mountain climber. Hardly could a guide be better fitted for his 

 task. Bound to the traveler by a philosophical bond they rise or fall 

 together. The assistance is by no means all on one side. Many are 

 the instances in which the problems of the scientist have enriched the 

 theories of the mathematician. Many are the instances in which the 

 theories of the mathematician have aided in the solution of the prob- 

 lems of the scientist. The equations of the mathematician are re- 

 garded by many as the only language which nature speaks. Helm- 

 holtz expressed this thought in the words, "the final aim of all na- 

 tural science is to resolve itself into mathematics." Jeans has this 

 in mind in his statement, "all the pictures which science draws of 

 nature, and which alone seem capable of according with observational 

 fact, are mathematical pictures * * * the Universe seems to 

 have been designed by a pure mathematician." Even Galileo back 

 in the beginning of what we are pleased to call modern science said, 

 "Nature's great book is written in mathematical language." Wliite- 

 head maintains that the aim of scientific thought is, "to see what is 

 general in what is particular and what is permanent in what is 

 transitory." In this vision science utilizes the general abstraction 

 of mathematics and adopts its theory of invariants. The concept of 

 progressive change is basic in the study of natural phenomena. This 

 same idea is the mud sill of the calculus. "With the calculus as a 

 key," continues Whitehead, "mathematics can be successfully applied 

 to the explanation of the course of nature." Wlien classical physics 

 suffered the impact of the Michelson-Morley experiment it was forced 

 by its own findings to reexamine its foundations. "In this emer- 

 gency," to quote Dantzig, "it was entirely due to the flexible mental 

 apparatus with which the mathematician supplied them, that the 

 physical sciences have at all survived this drastic revision." Kich- 

 ards asserts that "when we reach the core of physical reality, the 

 truth is presented in mathematical equations." Weyl claims that in 

 the long ago the Pythagoreans held that the world was not "a chaos, 

 but a cosmos harmoniously ordered by invariable mathematical laws." 

 Jeans expresses it in the words, "Nature seems to know the rules of 

 mathematics as the mathematicians have formulated them in their 

 studies without drawing on experience of the outer world." 



We come now to the end of tonight's account of this amazing jour- 

 ney of the scientist. In saying farewell to our scientific traveler we 

 hear that insistent injunction from the mouth of his guide, so aptly 

 put by Dantzig, "Read your instruments and obey mathematics; for 

 this is the whole duty of the scientist." 



