Page:A History of Mathematics (1893).djvu/339

Hermann Grassmann (1809–1877) was born at Stettin, attended a gymnasium at his native place (where his father was teacher of mathematics and physics), and studied theology in Berlin for three years. In 1834 he succeeded Steiner as teacher of mathematics in an industrial school in Berlin, but returned to Stettin in 1836 to assume the duties of teacher of mathematics, the sciences, and of religion in a school there.^[71] Up to this time his knowledge of mathematics was pretty much confined to what he had learned from his father, who had written two books on "Raumlehre" and "Grössenlehre." But now he made his acquaintance with the works of Lacroix, Lagrange, and Laplace. He noticed that Laplace's results could be reached in a shorter way by some new ideas advanced in his father's books, and he proceeded to elaborate this abridged method, and to apply it in the study of tides. He was thus led to a new geometric analysis. In 1840 he had made considerable progress in its development, but a new book of Schleiermacher drew him again to theology. In 1842 he resumed mathematical research, and becoming thoroughly convinced of the importance of his new analysis, decided to devote himself to it. It now became his ambition to secure a mathematical chair at a university, but in this he never succeeded. In 1844 appeared his great classical work, the Lineale Ausdehnungslehre, which was full of new and strange matter, and so general, abstract, and out of fashion in its mode of exposition, that it could hardly have had less influence on European mathematics during its first twenty years, had it been published in China. Gauss, Grunert, and Möbius glanced over it, praised it, but complained of the strange terminology and its "philosophische Allgemeinheit." Eight years afterwards, Bretschneider of Gotha was said to be the only man who had read it through. An article in Crelle's Journal, in which Grassmann eclipsed the geometers of that