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O doubt the most famous attack that has ever been made upon mathematics and its educational value was published in 1836 in the Edinburgh Review by Sir William Hamilton, professor of logic and metaphysics at Edinburgh. He must not be confounded with his contemporary, Sir William Rowan Hamilton, the inventor of quaternions. The first reading of that article by the Edinburgh philosopher makes one feel as if in an earthquake in which one's most cherished pedagogic structures are tumbling into a heap and the very foundations are being removed from under one's feet. With the strength of a superhuman giant Hamilton seems to hurl facts with unerring destructive power against the most massive educational castles of his day. The lack of utility of mathematical study, as a training of the mind, is shown by quotations from an array of authorities, gathered from all ages and nations of the civilized world, and the reader is utterly overwhelmed by this "cloud of witnesses."

Upon a second reading of Hamilton's essay one begins to see signs of weakness; an attempt to verify his quotations discloses superficiality and carelessness in the selection of representative quotations from his witnesses. I know of only one mathematician who has made an extended reply to Hamilton, though several have criticized certain parts of his essay. This extended reply is found in an article by A. T. Bledsoe in the Southern Review for July, 1877. Bledsoe, a graduate of West Point, was before the civil war professor of mathematics at Kenyon College, then at Miami University, and finally at the University of Virginia. Later he became editor of the Southern Review. His reply to Hamilton was printed in the year of his death. It was written after a most careful examination of the authorities cited by Hamilton. It is a very able article, but so far as I have been able to ascertain, it has completely escaped the attention of mathematicians. We can recommend it as interesting and even now worth reading.

A few years ago the noted German mathematician, Alfred Pringsheim, wrote a popular address on the "Utility and Alleged Inutility of Mathematics." Pringsheim, in referring to Hamilton's article,