Gordan studied in his native Breslau, at Königsberg, and at Berlin before becoming professor of mathematics at the University of Erlangen. For most of his mathematical career his research was concentrated on a single field, the study of indeterminates. The central problem in the field, which Gordan eventually solved, was to prove the existence of a finite basis for binary forms of any given degree. His result was subsequently refined and extended by many workers including Gordan himself. Gordan's proof was long and complicated and the result was re-proved in 1888 by David Hilbert using newer and far simpler methods. In collaboration with Rudolf Clebsch, Gordan also wrote a book on Abelian functions that included the central theorem now known as the Clebsch–Gordan theorem. This work was influential in giving a new direction to algebraic geometry.