In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc.

He used this time to advance his knowledge, showing interest in all subjects, including Latin, Greek, philology, history and mathematics.

[4][5] In 1821 Jacobi went to study at Berlin University, where he initially divided his attention between his passions for philology and mathematics.

[3] During the Revolution of 1848 Jacobi was politically involved and unsuccessfully presented his parliamentary candidature on behalf of a Liberal club.

This led, after the suppression of the revolution, to his royal grant being cut off – but his fame and reputation were such that it was soon resumed, thanks to the personal intervention of Alexander von Humboldt.

His grave is preserved at a cemetery in the Kreuzberg section of Berlin, the Friedhof I der Dreifaltigkeits-Kirchengemeinde (61 Baruther Street).

This was developed in his great treatise Fundamenta nova theoriae functionum ellipticarum (1829), and in later papers in Crelle's Journal.

Theta functions are of great importance in mathematical physics because of their role in the inverse problem for periodic and quasi-periodic flows.

The equations of motion are integrable in terms of Jacobi's elliptic functions in the well-known cases of the pendulum, the Euler top, the symmetric Lagrange top in a gravitational field, and the Kepler problem (planetary motion in a central gravitational field).

He also made fundamental contributions in the study of differential equations and to classical mechanics, notably the Hamilton–Jacobi theory.

It was in algebraic development that Jacobi's particular power mainly lay, and he made important contributions of this kind in many areas of mathematics, as shown by his long list of papers in Crelle's Journal and elsewhere from 1826 onwards.

His other works include Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem (1832), Canon arithmeticus (1839), and Opuscula mathematica (1846–1857).