German mathematician who was a great formalist, and was generally regarded as the most inspiring teacher of his time (Bell 1937, p. 330). In 1842, he visited Cambridge. Upon his return, he was asked who he thought to be the greatest mathematician in England. He replied "there is none" (Boyer 1968, p. 621). When asked about his excessive devotion to his work, Jacobi responded "Certainly I have sometimes endangered my health by overwork, but what of it? Only cabbages have no nerves, no worries. And what do they get out of their perfect wellbeing?" (Bell 1937, pp. 329-330). Nevertheless, Jacobi suffered a breakdown from overwork in 1843.

Jacobi wrote the classic treatise on elliptic functions Fundamenta Nova Theoriae Functionum Ellipticarum (1829). He also studied Jacobi theta functions, which are named in his honor. Gauss had already worked out many of the properties of Elliptic Functions, but never published them. Jacobi was the first, however, to apply elliptic functions to number theory. Using this method, he proved Fermat's polygonal number theorem. In a 1835 paper, Jacobi proved that if a univariate single-valued function is doubly periodic , then the ratio of periods cannot be real, as well as the impossibility for a single-valued univariate function to have more than two distinct periods (Boyer and Merzbach 1991, p. 525).

Jacobi also reduced the general quintic equation to the form x⁵-10q²x = p. The reduction was later carried out even further by Jerrard. Jacobi also put the determinant in its modern form.

Jacobi did important work in celestial mechanics. In 1836, he found the Jacobi integral, although in a sidereal (fixed) coordinate system. Finally, he did much to develop Hamilton-Jacobi theory.

Gauss, Jerrard, Legendre, Weierstrass

Additional biographies: MacTutor (St. Andrews), Bonn