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ATTACKS UPON THE STUDY OF MATHEMATICS

livered by Huxley before the Liverpool Philomathic Society[1] 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 ordinarily 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 Americans 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 address 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 mathematical 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. Göthe has said:

"Verständige 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

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