Carl Jacobi, German Mathematician
Carl Gustav Jacob Jacobi (December 10, 1804 - February 18, 1851) was a German mathematician and the first Jewish mathematician to be appointed professor at a German university. He studied at Berlin University, where he obtained the degree of Doctor of Philosophy in 1825, his thesis being an analytical discussion of the theory of fractions. In 1827 he became a professor and in 1829, a tenured professor of mathematics at Konigsberg University, and held the chair until 1842. One of his greatest accomplishments was his theory of elliptic functions and their relation to the elliptic theta function. Theta functions are of great importance in mathematical physics. He discovered many of the fundamental properties of theta functions, including the functional equation and the Jacobi triple product formula, as well as many other results on q-series and hypergeometric series. He also made fundamental contributions in the study of differential equations and to rational mechanics, notably the Hamilton-Jacobi theory. He was the first to apply elliptic functions to number theory. He introduced the Jacobi symbol; contributions to higher reciprocity laws, investigations of continued fractions, and the invention of Jacobi sums. He was one of the early founders of the theory of determinants and invented the Jacobian determinant. He suffered a breakdown from overwork in 1843. He moved to Berlin, where he lived as a royal pensioner until his death in 1851 at the age of 46. He was a brother of the German engineer and physicist Moritz Hermann von Jacobi.
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