ATTACKS UPON THE STUDY OF MATHEMATICS 361 



writes down the names of a dozen authorities cited by Hamilton, and 

 then says : " I am ashamed to confess that before reading Hamilton's 

 article I did not know a single one of these great authorities even by 

 name ; an extenuating circumstance is the fact that some of these names 

 I could not find even in the scientific directories." However, Hamilton 

 does quote from several noted mathematicians — D'Alembert, Descartes, 

 Pascal, Dugald Stewart — men whose opinions are worthy of serious 

 consideration and study. 



Let us now take up Hamilton's essay. It takes the form of a review 

 of William Whewell's " Thoughts on the Study of Mathematics as a 

 Part of a Liberal Education," published in 1835. Whewell was at that 

 time fellow and tutor in Trinity College, Cambridge. Later he became 

 head master of Trinity. At that time the University of Cambridge 

 was laying unusual stress upon mathematics; mathematical skill was 

 the chief requirement in the tripos examinations. Hamilton looked 

 upon the Cambridge plan with disfavor and seized upon Whewell's 

 small pamphlet as a pretext to enter upon a demonstration of the inutil- 

 ity of mathematical study as an exercise of the mind. 



In every dispute it is necessary to state the issue clearly and then to 



adhere to it steadily. The issue is thus stated by Hamilton :^ 



Before entering on details, it is proper here, once for all, to premise, — in 

 the first place, that the question does not regard the value of mathematical 

 science, considered in itself, but the utility of mathematical study, as an exercise 

 of the mind; and in the second, that the expediency is not disputed of leaving 

 mathematics, as a coordinate, to find its level among the other branches of 

 academical instruction. It is only contended that they ought not to be made the 

 principal, far less the exclusive object of encouragement. We speak not of 

 professional, but of liberal education. 



This statement of the issue is quite clear. Moreover, the position 

 taken here is quite fair. Few educators of the present time would take 

 marked exception to it. Mathematics was to occupy a coordinate posi- 

 tion in the curriculum with other studies. But Sir William soon for- 

 gets his position. He does not adhere to the point of dispute, as laid 

 down by himself, but proceeds to prove that mathematics is " not an 

 improving study." He says:^ 



If we consult reason, experience and the common testimony of ancient and 

 modern times, none of our intellectual studies tend to cultivate a smaller number 

 of the faculties, in a more partial manner, than mathematics. 



He proceeds to adduce testimony to the effect that* 



"the cultivation afforded by the mathematics is, in the highest degree, one-sided 

 and contracted, ' ' that mathematics ' ' freeze and parch the mind, ' ' ° that this 



^ Edi7iburgh Eeview, Yo\. 62, 18S6, Tp. All. . 



^Loc. cit., p. 419. :'^/ y^ 



* Loc. cit., p. 421. 

 ^ Loc. cit., p. 421. 

 'Loc. cit., p. 421. 



VOL. LXXX.— 25. 



