Paul Albert Gordan

Paul Albert Gordan (27 April 1837 – 21 December 1912) was a German mathematician, a student of Carl Jacobi at the University of Königsberg before obtaining his Ph.D. at the University of Breslau (1862),MacTutor Biography|id=Gordan.] and a professor at the University of Erlangen-Nuremberg.

He was known as "the king of invariant theory".citation|page=49|series=Invariant theory and algebraic transformation groups|title=Computational Invariant Theory|publisher=Springer-Verlag|editor1-first=Harm|editor1-last=Derkson|editor2-first=Gregor|editor2-last=Kemper|isbn=3540434763.] citation|page=85|title=Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory|editor1-first=A. N.|editor1-last=Kolmogorov|editor1-link=Andrey Kolmogorov|editor2-first=A. P.|editor2-last=Yushkevich|year=2001|publisher=Springer-Verlag|isbn=3764364424.] His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated. He and Alfred Clebsch gave their name to Clebsch-Gordan coefficients. Gordan also served as the thesis advisor for Emmy Noether.

Gordan initially rejected David Hilbert's proof of the Hilbert Basis Theorem, a result which vastly generalized his result on invariants, saying "This is not mathematics; this is theology." [Hermann Weyl, "David Hilbert. 1862-1943", Obituary Notices of Fellows of the Royal Society (1944).] The proof in question was the (non-constructive) existence of a finite basis for invariants. This proof seemed to counter the sensibilities of Gordan, whom Weyl described in his Hilbert obituary as a great "algorithmician."

He was born in Breslau, Germany (now Wrocław Poland), and died in Erlangen, Germany.

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