By 1824, Jacobi began teaching and in 1825 presented a paper concerning iterated functions to the Academy of Sciences in Berlin. The Academy did not find his results impressive and it was not published until 1961.

In 1829, Jacobi published his paper "Fundamenta nova theoria functions ellipticarum," translated to New Foundations of the Theory of Elliptic Functions, which made significant contributions to the field of elliptic functions.

Jacobi was promoted to full professor in 1832 while at the University of Konigsberg, and pursued his study of partial differential equations of the first order, which led to the publishing of "Structure and Properties of Determinants." He applied these theories to differential equations in Dynamics which again led to another publishing, Lectures in Dynamics. It was also here at the University of University of Konigsberg, that he worked on functional determinants now called Jacobian determinants.

In 1842, Jacobi became ill with diabetes and was assited with grants to move to Itay where he published many more works.

Jacobi moved to a small town called Gotha in 1848. Two years later, January of 1851, he developed influenza and smallpox and died shortly after.