Proceedings of the American Association for the Advancement of Science 35

Cover Proceedings of the American Association for the Advancement of Science 35
Proceedings of the American Association for the Advancement of Science 35
American Association for the Advancement of Science
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But if we should ask, in what di- rection the advance has been made, which is to characterize the development of algebra in our day, we may, I think, point to that broadening of its field and methods, which gives us multiple aU gebra.
Of the importance of this change in the conception of the oflSce of algebra, it is hardly necessary to speak : that it is really charac- teristic of our time will be most evident if we go back some two- or threescore years, to the time when the seeds were sown whi
...ch are now yielding so abundant a harvest. The failure of Mobius, Hamilton, Grassmann, Saint-Venant to make an immediate im- pression upon the course of mathematical thought in any way commensurate with the importance of their discoveries is the most conspicuous evidence that the times were not ripe for the methods which they sought to introduce. A satisfactory theory of the imaginary quantities of ordinary algebra, which is essentially a simple case of multiple algebra, with difficulty obtained recogni- 1 The Nation, Vol.

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