About Hermann Grassmann
Hermann Günther Grassmann was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of an n-dimensional vector space V. In linguistics he helped free language history and structure from each other. In 1846, Möbius invited Grassmann to enter a competition to solve a problem first proposed by Leibniz: to devise a geometric calculus devoid of coordinates and metric properties (what Leibniz termed analysis situs). He then entered into a dispute with Grassmann about which of the two had thought of the ideas first. His son Hermann Ernst Grassmann obtained a doctorate in mathematics and became a professor of mathematics at the University of Giessen. This essay, first published in the Collected Works of 1894–1911, contains the first known appearance of what is now called linear algebra and the notion of a vector space.
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