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Grassmann's “Ausdehnungslehre”


SIR ROBERT BALL asks why no one has translated the “Ausdehnungslehre” into English. The answer is as regretable as simple—it would not pay. The number of mathematicians who, after the severe courses of the universities, desire to extend their reading is very small. It is something that a respectable few seek to apply what they have already learnt. The first duty of those who direct the studies of the universities is to provide that students may leave in possession of all the best means of future investigation. That fifty years after publication the principles of the “Ausdehnungslehre” should find no place in English mathematical education is indeed astonishing. Half the time given to such a wearisome subject as Lunar Theory would place a student in possession of many of the delightful surprises of Grassmann's work, and set him thinking for himself. The “Ausdehnungslehre” has won the admiration of too many distinguished mathematicians to remain longer ignored. Clifford said of it: “I may, perhaps, be permitted to express my profound admiration of that extraordinary work, and my conviction that its principles will exercise a vast influence upon the future of mathematical science.” Useful or not, the work is “a thing of beauty,” and no mathematician of taste should pass it by. It is possible, nay, even likely, that its principles may be taught more simply; but the work should be preserved as a classic.


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GENESE, R. Grassmann's “Ausdehnungslehre”. Nature 48, 517 (1893).

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