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The Mathematical Sciences are at once the most perfect and the most valuable portion of human knowledge. They are valuable, not only for their own direct applications to the business of life, for the number of sciences to which they are the key, and the number of arts of which they are the foundation, but they have a value, higher and more important, if possible, in the strength which they give to the mind, and the exercise which they afford to its noblest faculties,
There is, indeed, no road to clear, forcible, and connected reasoning, but that which is opened up by the Mathematician; and whatever be a man's profession or station in the world, we are always able, from his mode of stating a proposition, or conducting an argument, to say whether he be or be not a Mathematician. In every other department of knowledge, there is some uncertainty-some hypothesis assumed, of which the foundation is unsearched or inscrutable, or something which hinges upon the undefined and undefinable properties of mind or of matter, or upon the contingency of events. Is language the medium through which one would arrive at logical precision? Then living language is mutable, and dead language is ambiguous. Is it human nature? Then who can gauge the mind, who can number its propensities, or measure its eccentricities? Is it life and manners? Then the modes vary with every
individual and with every hour. Is it medicine? Then the life of that man is short indeed who has not seen fifty nostrums and modes of treatment rise into vogue and sink into neglect, without any reason assigned, or assignable, either for their rise or their fall. Is it law? Then who shall number
the absurdities of the statute-book, to say nothing about the practice ? Chemistry is one tissue of puzzles and disputes; and in pure Physics, it is not much better. In the physical sciences there is indeed a mathematical element; and so far as this goes, they are clear, orderly, and precise; but the moment that it is left out we are in the regions of theory—the wilds of doubt and uncertainty. With the student of most of these, the ground is unstable under his feet, the path by which he advanced has closed upon him, and that by which he has still to advance has not opened : with the mathematician every step is upon sure ground; and he sees how he came and where he is to proceed. Nothing that is contingent or ideal is admitted. He hunts out every lurking sophism, rejects the smallest aberration from truth, and goes on with absolute confidence and absolute certainty.
A system of mental discipline, so valuable for the extensive and positive advantages which it affords, cannot be pressed too earnestly upon the attention of the public, or come before them in too many shapes ; and it is to be regretted, that in this age of pretended improvement, the soundness and certainty of mathematical cultivation should have given place to something far more light and Aimsy-to the mere blandishments of the Belles Lettres, or such simple preparation for a man's individual trade, as may make him a handy tool for carrying on that trade, but nothing else. In proof of this, let any look into the works of those called (not the Learned, according to the good old English phrase) but the Literati, and he will find, amid all the sparkle of their abundance of words, and all their affectation of sentiment, there is a plenteous lack of depth of thought and soundness of principle.