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Place of Mathematics in University Education.
CHARLTON T. LEWIS,
PROFESSOR OF PURE MATHEMATICS IN TROY UNIVERSITY,
DELIVERED BEFORE THE TRUSTEES AT THEIR ANNUAL MEETING,
JULY 20TH, 1859.
PUBLISHED BY THE TRUSTEES.
STROY, N. Y.:
“Mathematics from the first have been triumphant over the husk; Philosophy is still militant for the kernel.” Such is the judgment of Sir William Hamilton, one of the highest authorities, certainly, in any question which authority can decide; and among all thinkers our age has seen, one of the noblest inheritors of a yet unfulfilled
He urges as a leading and fatal objection to the use of Mathematics in education, that they deal only with the husks of truth. He would accordingly proscribe them, where mental culture is the aim. He further objects to this study certain special evil effects upon the mind. It is so true, so absolute and unquestionable in every step and every result, that it loses all the force of truth. It is so reliable in its methods, that it compels belief, and trains the mind to skepticism! So rigid and exacting in its proofs that it makes men credulous and superstitious ! If all these sad and opposite results do indeed proceed “from the study of Mathematics, we can wonder no longer that one tree is the tree of the knowledge of both good and evil. We must agree with one of the church fathers who referred this science to a very low, bad source indeed, and join the superstitious Banquo in saying,
" 'tis strange,
And oftentimes to win us to our harm
But who can believe it? To all who love this science, to all whose eye is not evil through prejudice, Truth as revealed by Mathematics is Truth in her native beauty, with her disguises stript away; and thus seen, led out from the veils of form and matter bebind which half her light is quenched, into the clear air of exact knowledge, she is the purest and sweetest “ daughter of the voice of God;”—while, the more absolute the Truth, the surer is the signet of the Divine.
If then we free Sir William's aphorism, as we may, from the sneer about “husk and kernel," it means simply that “Mathematics have always been triumphant; Philosophy is still militant.” Now this occurs in a piece of special pleading against Mathematics. He wishes to drive them out from the course of mental training utterly, reserving only those elementary branches which every educated man needs in daily life; and to substitute a course of metaphysical study. We are justified then in accepting these words as being, in the author's view, what they really are in themselves, an epitome of the history of these two sciences. But what a confession does the special advocate of metaphysics make, in his very plea! He would reject from education a triumphant branch, and would substitute for it a militant branch. He would supplant an established science by that which is only struggling to become a science, He would put away a method which has broken down a thousand barriers, each of which threatened to become the horizon of huinan knowledge forever, in favor of one which has never yet made one step of real progress, because its starting point changes with every mind that attempts it; and whose chief contribution to science, an enemy might say, has been the multiplication of the known species of monomania!
Glance hastily at the history of the two. You see that Mathematics have been always steadily progressive; met. aphysics have been fixedly stationary. The former