EISENSTEIN, FERDINAND GOTTHOLD (1823 1852), German mathematician, was born in Berlin on April 16, 1823. He was educated at Berlin university, where he became privatdozent, subsequently professor of mathematics. He was the author of a number of papers published in Crelle's Journal on the theory of numbers and elliptic functions (q.v.). In his memoir, Neue Theoreme der laoheren Arithmetik Eisenstein de veloped the theory of complex numbers (q.v.). He extended the work of Gauss in ternary quadratic forms from two to three indeterminates. He only dealt with cases of an uneven determi nant; his results were extended later by Henry Smith to cases of an even determinant. Eisenstein dealt with the theory of binary quadratic forms and discovered the first covariant used in analysis. He discussed doubly infinite products using analytical methods, this was used later by Weierstrass in representing some of his functions. In his work on the representation of numbers by sums of squares, Eisenstein showed that the general theorem was limited to eight squares; he gave the solutions for three and five squares; this work was extended later by Henry Smith.
Eisenstein was a member of the Berlin academy. He died in Berlin on Oct. 11, 1852.