Carl Jacobi – Biography of Carl Jacobi

Carl Gustav Jacob Jacobi, who was born on December 10, 1804, in Potsdam, Prussia (now Germany), was a German mathematician who, together with Niels Henrik Abel of Norway, founded the theory of elliptic functions.

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.

Jacobi he became known in his early days, through his work on elliptical functions, which won the admiration of the Frenchman Adrien-Marie Legendre, one of the leading mathematicians of his time. Unaware of the similar efforts of the Norwegian mathematician Niels Henrik Abel, Jacobi formulated a theory of elliptic functions based on four theta functions. The quotients of theta functions produce the three elliptical Jacobian functions. His results on elliptical functions were published in Fundamenta Nova Theoriae Functionum Ellipticarum (1829; “New foundations of the theory of elliptic functions”). In 1832 he showed that, just as elliptic functions can be obtained by inverting elliptic integrals, hyperelipic functions can also be obtained by inverting hyperexpathic integrals. This success led him to the formation of the theory of abelian functions, which are complex functions of several variables.

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.