Karl Gustav Jakob Jacobi
1804-1851

Born in Potdam, Germany. Received his doctorate in Berlin, 1825. On the faculty in Königberg, 1826 on. Professor, 1831. Imaginative, intense, had various conflicts with other mathematicians.

Introduced the Jacobian determinant in the theory of differential mappings. Studied ordinary and partial differential equations and their connections, introduced the "last multiplier", important in the integration of dynamical equations using constants of the motion. Developed Hamilton-Jacobi theory in general form in 1837, investigated the separation of variables in the HJ equations, demonstrated integrability for many problems, some not solvable in Lagrangian form. Investigated the calculus of variations in the large, geodesics, focii, and the conditions for minima. Formulated Jacobi's version of the principle of least action. Showed in 1837 that contact (canonical) transformations preserve the form of Hamilton's equations, discovered the Jacobi identity.