THE UNITY OF SCIENCE 5 



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 

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

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

 of four contemporary writers: two of them mathematicians, 

 one a logician, one a physicist. 



The case of mathematics is the most striking because 

 most people doubtless think of mathematics as a completed, 

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

 which is or which seems to its adepts to be going through 

 the most radical and remarkable transformations of all; and 

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

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

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

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

 living English writers on pure mathematics, 2 in an article 

 published within this decade, announces to the lay public that 

 mathematics has found its true principles only within the most 

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

 ematical difficulties first clearly presented by an ancient 

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

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

 turn attacked the problems, but achieved, broadly speaking, 

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

 Dedekind, Cantor have not merely advanced these problems 

 but have completely solved them. The solutions, for those 

 acquainted with mathematics, are so clear as to leave no 

 longer the slightest doubt or difficulty. This achievement is 

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

 know of no age (except perhaps the Golden Age of Greece) 

 which has a more convincing proof to offer of the trancendent 

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

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



2 Mr. Bertrand Russell in "The International Monthly," July, 1901. 



