Jacobi He received his early education from an uncle, and, by the end of his first year at the Gymnasium (1816-17), he was ready to enter the University of Berlin. Because the university did not accept students under the age of 16, he had to wait until 1821; however, at the end of the 1823-24 academic year, he was qualified to teach mathematics, Greek, and Latin.
With the presentation of his doctoral dissertation and his conversion to Christianity, a position was opened for him at the University of Berlin in 1825. The following year, Jacobi became a professor of mathematics at the University of Königsberg. In 1844, for health reasons, he moved to Berlin, where he gave occasional lectures at the university. During the revolutionary uprisings of 1848, a reckless speech cost Jacobi his stipend, although the University of Berlin eventually gave him a position. In 1851, Jacobi succumbed to the flu and smallpox.
His work De Formatione et Proprietatibus Determinantium (1841; “Regarding the structure and properties of determinants”) made pioneering contributions to the theory of determinants. He invented the functional determinant (formed from the differential n2 coefficients of n determined functions with n independent variables) that bears his name and played an important role in many analytical investigations.
Jacobi carried out important research on first-order partial differential equations and applied them to differential equations of dynamics. His Vorlesungenüber Dynamik (1866; “Lectures on Dynamics”) relates his work with differential equations and dynamics. The Hamilton-Jacobi equation now plays an important role in the presentation of quantum mechanics.