ATTACKS UPON THE STUDY OF MATHEMATICS 369 



livered by Huxley before the Liverpool Pliilomathic Society^^ in which 

 he argued in favor of scientific education, as follows : 



The great peculiarity of scientific training, that in virtue of which it can 

 not be replaced by any other discipline whatsoever, is the bringing of the mind 

 directly into contact with fact, and practising the intellect in the completed form 

 of induction; that is to say, in drawing conclusions from particular facts made 

 known by immediate observation of nature. 



The other studies which enter into ordinary education do not discipline the 

 mind in this way. Mathematical training is almost purely deductive. The 

 mathematician starts with a few simple propositions, the proof of which is so 

 obvious that they are called self-evident, and the rest of his work consists of 

 subtle deductions from them. The teaching of languages, at any rate as ordi- 

 narily practised, is of the same general nature — authority and tradition furnish 

 the data, and the mental operations of the scholar are deductive. 



It will be noticed that these remarks were made at a time when 

 there was a conflict on the question of educational values between the 

 classics and mathematics, on one side, and the natural and social 

 sciences, on the other. This makes it evident that Huxley appeared in 

 this discussion in the capacity of an advocate rather than as a judge. 



Of great interest, in connection with Huxley's utterances is the 

 reply made to him by the mathematician J. J. Sylvester. To Ameri- 

 cans Sylvester's name is memorable, because at one time he was on the 

 faculty of the University of Virginia and, when the Johns Hopkins 

 University opened in 1876, Sylvester again came over from England and 

 for eight years lectured to American students on modern higher algebra. 

 He gave a powerful stimulus to the study of higher mathematics in this 

 country. Sylvester was an enthusiast. His reply to Huxley was the 

 subject of his presidential address to the mathematical and physical 

 section of the British Association, meeting at Exeter in 1869. This ad- 

 dress is of special value, because it is largely autobiographical; it tells 

 how Sylvester carried on his researches in mathematics, how he came to 

 make some of his discoveries. By his own experiences as a mathe- 

 matical investigator he tried to show that Huxley's description of 

 mathematical activity was incorrect. We can do no better than quote 

 rather freely from Sylvester's memorable address. He says: 



I set to myself the task of considering certain recent utterances of a most 

 distinguished member of this Association, one whom I no less respect for his 

 honesty and public spirit than I admire for his genius and eloquence, but from 

 whose opinions on a subject which he has not studied I feel constrained to differ. 

 Gothe has said: 



"Verstandige Leute kannst du irren sehn: 



In Sachen, namlich, die sie nicht verstehn. " 

 ' ' Understanding people you may see erring 

 In those things, to wit, which they do not understand. ..." 



He [Huxley] says "mathematical training is almost purely deductive. The 

 mathematician starts with a few simple propositions, the proof of which is so 



^ Macmillan 's Magazine, Vol. 20, London, 1869, pp. 177-184. 



