Page:Popular Science Monthly Volume 80.djvu/365

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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 inutility 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:[1]

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 position in the curriculum with other studies. But Sir William soon forgets 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:[2]

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[3]

"the cultivation afforded by the mathematics is, in the highest degree, one-sided and contracted," that mathematics "freeze and parch the mind,"[4] that this
  1. Edinburgh Review, Vol. 62, 1836, p. 411.
  2. Loc. sit., p. 419
  3. Loc. sit., p. 421
  4. Loc. sit., p. 421