69() THE century's gkeat men in science. 



convince himself of it by looking over almost any modern treatise — 

 say, Salmon on Higher Plane Curves. That voUime, for example, 

 would be found replete with theorems hardly any of which hold good 

 for any curves that could really exist. Realizable curves have hardly 

 l)cen studied at all, for the reason that they do not yield a beautiful 

 theory, such as is Jiow exacted. Modern mathematics is highly artistic. 

 A simple theme is chosen, some conception pretty and charming in itself. 

 Then it is shown that by simply holding this idea up to one's eye and 

 looking through it a whole forest that before seemed a thick and 

 tangled jungle of brushes and }>riers is seen to be in reality an orderly 

 garden. The word generalization really can not be fully understood 

 without studying modern mathematics; nor can the beaut}" of general- 

 ization l>e in any other way so well appi'cciated. There is here no 

 need of throwing out •'extreme cases." Far from that, it is precisely 

 in tlic cxti-eme cases that the power and l)eauty of the magic e3'eglass 

 is most ap))arent and most marvellous. Let me take l)ack the word 

 '* magic." though, for the reasonableness of it is just its crowning 

 charm. 1 must not t)e led away from my ])oint. to expatiate upon 

 the repos(>fulness of the new mathematics, upon how it relieves us of 

 that tiresome imj). man. and from the most importunate and unsatis- 

 factory of the race, one's self. Suffice it to say that it is so reasonable, 

 so simple, so easy to read, when the right \iew has once been attained, 

 that the student may easily forgc^t what ai-duous labors were expended 

 in coustiuctiug th«' lirst convenient pathway to that lofty summit, 

 that mastery over intricacies, far ))evond that of the eighteenth-century 

 master. "It nuist not be sup})ose(l." said C. (i. .1. Jacol)i, one of the 

 simplifying pioneers, '"that it is to a gift of nature that I owe such 

 mathematical power as I possess. No; it has come by hard work, 

 hard work. Not mere industry, but brain-splitting thinking — hard 

 work; hard work that has often endangered m}' health.'' Such reflec- 

 tions enable us to perceive that if modern mathematics is great, so also 

 were the men who made it great. 



The science next in abstractness after mathematics is logic. The con- 

 tributions of the eighteenth century to this subject were enormous. 

 In pure logic the doctrine of chances, which has been the logical 

 guide of the exact sciences and is now illuminating the pathwa}^ of the 

 theory of evolution, and is destined to still higher uses, received at 

 the hands of Jacob Bernouilli and of Laplace developments of the tirst 

 importance. In the theory of cognition Berkeley and Kant laid solid 

 foundations; their personal greatness is incontestable. This is hardly 

 true of Hume. In the nineteenth century Boole created a method of 

 miraculous fruitfulness, which aided in the development of the logic 

 of relatives, and threw great light on the doctrine of probability, and 

 thereby upon the theory and rules of inductive reasoning. De Morgan 

 added an entirely new kind of syllogism, and brought the logic of 



