Jacobi, Carl Gustav Jacob (1804–1851)

German mathematician and mathematical physicist, much of whose work was on the theory of elliptical functions, mathematical analysis, number theory, geometry, and mechanics.

Jacobi was born in Potsdam. A child prodigy, he went to Berlin University in 1821 and graduated in the same year. In 1826 he joined the staff at Königsberg (now Kaliningrad) University, becoming professor in 1832.

Jacobi invented a functional determinant – now called the Jacobian determinant – which has been of considerable use in later analytical investigations, and was even supportive in the development of quantum mechanics. He advanced the theory of the configurations of rotating liquid masses by showing that the ellipsoids now known as Jacobi's ellipsoids are figures of equilibrium.

Jacobi was always trying to link together different mathematical disciplines. For instance, he introduced elliptic functions into number theory and into the theory of integration, which in turn connected with the theory of differential equations and his own principle of the last multiplier.

His book Fundamenta nova theoriae functionum ellipticarum of 1829 introduced his own concept of hyperelliptic functions.