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Hermann Grassmann is chiefly remembered for his development of a general calculus for vectors.
Grassmann taught at the Gymnasium in Stettin from 1831 until his death except for two years (1834-1836) when he taught in Berlin.
Grassmann's most important work is Die lineale Ausdehnundslehre, ein neuer Zweig der Mathematik (1844) developed the idea of an algebra in which the symbols representing geometric entities such as points, lines and planes, are manipulated using certain rules. He represented subspaces of a space by coordinates leading to point mapping of an algebraic manifold now called the Grassmannian.
Grassmann's methods were slow to be adopted but eventually they inspired the work of Élie Cartan and have since been used in studying differential forms and their application to analysis and geometry.
Grassmann wrote on many other subjects, for example electricity, colour, acoustics, linguistics and botany. At the age of 53 he became disappointed with the lack of interest in his mathematical ideas so he turned to Sanskrit studies, another of his interests. His Sanskrit dictionary is still widely used.
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Tell me about Grassmann's work on abstract linear spaces
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