Hermann Grassmann

Hermann Grassmann (1809 to 1877) was a German polymath, known in his own day as a linguist and now also as a mathematician, who was also a physicist, general scholar and publisher. He studied theology at the University of Berlin from 1827 and had no university training in mathematics, yet from his base as a teacher in Stettin he worked out the ideas of his 1844 book on the theory of linear extension, which preceded and exceeded what is now called a vector space. He introduced the Grassmannian, the space that parameterizes all k-dimensional linear subspaces of an n-dimensional vector space. His mathematics was little noted until he was in his sixties, and an unfavourable report by Ernst Kummer ended his chance of a university post. In linguistics he helped free language history and structure from each other.