# 1911 Encyclopædia Britannica/Jacobi, Karl Gustav Jacob

**JACOBI, KARL GUSTAV JACOB** (1804–1851), German
mathematician, was born at Potsdam, of Jewish parentage, on
the 10th of December 1804. 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 extraordinary and in 1829 ordinary professor of
mathematics at Königsberg, and this chair he filled till 1842,
when he visited Italy for a few months to recruit his health.
On his return he removed to Berlin, where he lived as a royal
pensioner till his death, which occurred on the 18th of February
1851.

His investigations in elliptic functions, the theory of which he established upon quite a new basis, and more particularly his development of the theta-function, as given in his great treatise
*Fundamenta nova theoriae functionum ellipticarum* (Königsberg, 1829), and in later papers in *Crelle’s Journal*, constitute his grandest
analytical discoveries. Second in importance only to these are his researches in differential equations, notably the theory of the last
multiplier, which is fully treated in his *Vorlesungen über Dynamik*,
edited by R. F. A. Clebsch (Berlin, 1866). It was in analytical
development that Jacobi’s peculiar power mainly lay, and he made
many important contributions of this kind to other departments
of mathematics, as a glance at the long list of papers that were
published by him in *Crelle’s Journal* and elsewhere from 1826
onwards will sufficiently indicate. He was one of the early founders
of the theory of determinants; in particular, he invented the functional
determinant formed of the *n*^{2} differential coefficients of *n* given
functions of *n* independent variables, which now bears his name
(Jacobian), and which has played an important part in many
analytical investigations (see Algebraic Forms). Valuable also
are his papers on Abelian transcendents, and his investigations in
the theory of numbers, in which latter department he mainly supplements
the labours of K. F. Gauss. The planetary theory and other
particular dynamical problems likewise occupied his attention from
time to time. He left a vast store of manuscript, portions of which
have been published at intervals in *Crelle’s Journal*. His other
works include *Commentatio de transformatione integralis duplicis*
*indefiniti in formam simpliciorem* (1832), *Canon arithmeticus* (1839),
and *Opuscula mathematica* (1846–1857). His *Gesammelte Werke*
(1881–1891) were published by the Berlin Academy.

See Lejeune-Dirichlet, “Gedächtnisrede auf Jacobi” in the
*Abhandlungen der Berliner Akademie* (1852).