The New International Encyclopædia/Jacobi, Karl Gustav Jakob

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JACOBI, Karl Gustav Jakob (1804-51). A German mathematician, the brother of Moritz Hermann Jacobi, the physicist. He was born in Potsdam, studied in Berlin, and began his teaching there as privat-docent in 1824, but soon after went as professor of mathematics to Königsberg. He became a member of the Prussian Academy of Sciences in 1836, and in 1842 took up his permanent residence in Berlin, lecturing at the university. Jacobi's great work was in the theory of elliptic functions, of which he and Abel (q.v.) were the founders. He also contributed to the theory of numbers, to analytical mechanics, and to the study of determinants. A very important determinant bears the name Jacobian. (See Determinants.) He also founded the theory of Abelian functions. The following important works appeared in his lifetime: Fundamenta Nova Theoriæ Functionum Ellipticarum (1829); Canon Arithmeticus (1839); De Formatione et Proprietatibus Determinantium (1841; ed. by Stäckel, 1896); Mathematische Werke (3 vols,, partly posthumous, 1846-71). His Vorlesungen über Dynamik was published posthumously (1866; 2d ed, 1884). His Gesammelte Werke (1881-91; 7 vols, and suppl.) were published by the Berlin Academy. His essay, “Uber die vierfach periodischen Functionen zweier Variabeln,” etc., was translated from the Latin and edited by Weber (1895). For sketch of his life, consult: Lejeune-Dirichlet, “Gedächtnisrede auf Jacobi,” in the Abhandlungen der Berliner Akademie (1852; printed in Jacobi's Gesammelte Werke, vol. i.).