[2][3] His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.

at the University of Breslau with the thesis De Linea Geodetica, (On Geodesics of Spheroids) under Carl Jacobi in 1862.

[4] A famous quote attributed to Gordan about David Hilbert's proof of Hilbert's basis theorem, a result which vastly generalized his result on invariants, is "This is not mathematics; this is theology.

It is not clear if Gordan really said this since the earliest reference to it is 25 years after the events and after his death.

Nor is it clear whether the quote was intended as criticism, or praise, or a subtle joke.