# The New International Encyclopædia/Jacobi, Karl Gustav Jakob

**JACOBI**, Karl Gustav Jakob (1804-51). A
German mathematician, the brother of Moritz
Hermann Jacobi, the physicist. He was born
in Potsdam, studied in Berlin, and began his
teaching there as privat-docent in 1824, but soon
after went as professor of mathematics to Königsberg.
He became a member of the Prussian
Academy of Sciences in 1836, and in 1842
took up his permanent residence in Berlin,
lecturing at the university. Jacobi's great work
was in the theory of elliptic functions, of which
he and Abel (q.v.) were the founders. He also
contributed to the theory of numbers, to analytical
mechanics, and to the study of determinants.
A very important determinant bears the name
Jacobian. (See Determinants.) He also
founded the theory of Abelian functions. The
following important works appeared in his lifetime:
*Fundamenta Nova Theoriæ Functionum*
*Ellipticarum* (1829); *Canon Arithmeticus*
(1839); *De Formatione et Proprietatibus*
*Determinantium* (1841; ed. by Stäckel, 1896);
*Mathematische Werke* (3 vols,, partly posthumous,
1846-71). His *Vorlesungen über Dynamik* was
published posthumously (1866; 2d ed, 1884).
His *Gesammelte Werke* (1881-91; 7 vols, and
suppl.) were published by the Berlin Academy.
His essay, “Uber die vierfach periodischen
Functionen zweier Variabeln,” etc., was translated
from the Latin and edited by Weber (1895). For
sketch of his life, consult: Lejeune-Dirichlet,
“Gedächtnisrede auf Jacobi,” in the
*Abhandlungen der Berliner Akademie* (1852; printed in
Jacobi's *Gesammelte Werke*, vol. i.).