JACOBI, KARL GUSTAV JACOB (1804-1851), Ger man mathematician, was born at Potsdam, of Jewish parentage, on Dec. 10, 1804. He studied at Berlin University, where he obtained the degree of doctor of philosophy in 1825, his thesis being an analytical discussion of the theory of fractions. In 1827 he became extraordinary and in 1827 ordinary professor of mathe matics at Konigsberg, and this chair he filled until 1842. He in vestigated elliptic functions and produced in 1829 his important treatise Fundamenta nova theoriae functionum ellipticarum. He also made notable researches on differential equations, and ap plied his analysis to various dynamical problems. He intro duced the theory of the last multiplier, which is fully treated in his V orlesungen fiber Dynamik, edited by R. F. A. Clebsch (Ber lin, 1866). Jacobi advanced the theory of configurations of rotat ing liquid masses by showing that the ellipsoids which are now known as Jacobi's ellipsoids should be figures of equilibrium. He
was one of the early founders of the theory of determinants, and he invented the functional determinant formed of the differ ential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations (see ALGEBRAIC FORMS). Valuable also are his papers on Abelian transcendents, and his investigations in the theory of numbers, which supple ment the labours of Gauss. He left a vast store of manuscript, portions of which have been published at intervals in Grelle's Journal. He died in Berlin on Feb. 18, 1851.
His Gesammelte Werke were published by the Berlin Academy (1881-91). See Kiinigsberger, Karl Gustav Jacob Jacobi (1904)•