THE UNITY OF SCIENCE O 



What these revolutionary new developments in the sev- 

 eral sciences are, the specialists who are to speak of them will 

 tell you better than I can. But to illustrate the temper of 

 somt typical men of science of our time, and the nature of 

 the changes that are going on, I venture to quote the words 

 of far contemporary writers : — two of them mathematicians, 

 one i. logician, one a physicist. 



'^he case of mathematics is the most striking because 

 most )eople doubtless think of mathematics as a completed, 

 statioiary, statuesque sort of science. It is, in fact, the one 

 whichis — or which seems to its adepts to be — going through 

 the mst radical and remarkable transformations of all ; and 

 it is te mathematicians, or at least an influential school of 

 them, ^^ho are most likely to sound rhetorical, if not hyster- 

 ical, wien you get them to talking about the present move- 

 ment (f their science. Thus, one of the most brilliant of 

 living '.nglish writers on pure mathematics,- in an article 

 publishd within this decade, announces to the lay public that 

 matherr,tics has found its true principles only within the most 

 recent tnes. Speaking in the same article of certain math- 

 ematica. difficulties first clearly presented by an ancient 

 Greek, le Eleatic Zeno, this writer declares : "From Zeno's 

 time to ur own day the finest intellects of each generation in 

 turn att;ked the problems, but achieved, broadly speaking, 

 nothing. In our own time, however, three men — Weierstrass, 

 Dedekinc Cantor — have not merely advanced these problems 

 but have;ompletely solved them. The solutions, for those 

 acquainte with mathematics, are so clear as to leave no 

 longer thi slightest doubt or difficulty. This achievement is 

 probably le greatest of which our age has to boast; and I 

 know of 1 age (except perhaps the Golden Age of Greece) 

 which has more convincing proof to offer of the trancendent 

 genius of s great men." As a result of these new triumphs 

 in mathentics, Mr. Russell adds, we may anticipate a speedy 



2 Mr. Be-and Russell in "The International Monthly," July, 1901. 



