36o TEE POPULAR SCIENCE MONTHLY 



A EEVIEW OF THEEE FAMOUS ATTACKS UPON THE 



STUDY OF MATHEMATICS AS A TEAINING 



OF THE MIND 



By Peofessok FLORIAN CAJORI 

 colorado college 



"XnrO doubt the most famous attack that has ever been made upon 

 -L 1 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 con- 

 temporary, Sir William Eowan 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 na- 

 tions 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 ex- 

 tended 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 Univer- 

 sity 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 Prings- 

 heim, wrote a popular address on the " Utility and Alleged Inutility 

 of Mathematics."^ Pringsheim, in referring to Hamilton's article, 



* ' ' Ueber den Wert und angeblichen TJnwert der Mathematik, ' ' Von Alfred 

 Pringsheim, Muenchen, 1894. 



