# Paul Gordan

Paul Gordan
Paul Gordan
Born Paul Albert Gordan
27 April 1837
Breslau
Died 21 December 1912 (aged 75)
Erlangen
Nationality German
Institutions University of Erlangen-Nuremberg
Alma mater University of Breslau
Doctoral students Emmy Noether
Known for Invariant theory

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),[1] and a professor at the University of Erlangen-Nuremberg.

He was known as "the king of invariant theory".[2][3] His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.[3] He and Alfred Clebsch gave their name to Clebsch–Gordan coefficients. Gordan also served as the thesis advisor for Emmy Noether.[1]

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."[2][4] The proof in question was the (non-constructive) existence of a finite basis for invariants. 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, and nor is it clear whether the quote was intended as criticism, or praise, or a subtle joke. Gordan himself encouraged Hilbert and used Hilbert's results and methods, and the widespread story that he opposed Hilbert's work on invariant theory is a myth (though he did correctly point out in a referee's report that some of the reasoning in Hilbert's paper was incomplete).[5]

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

## Notes

1. ^ a b
2. ^ a b Harm Derksen, Gregor Kemper. (2002), Derkson, Harm; Kemper, Gregor, eds., Computational Invariant Theory, Invariant theory and algebraic transformation groups, Springer-Verlag, p. 49, ISBN 3-540-43476-3, OCLC 49493513.
3. ^ a b edited by A. N. Kolmogorov, A. P. Yushkevich ; translated from the Russian by A. Shenitzer, H. Grant and O. B. Sheinin. (2001), Kolmogorov, A. N.; Yushkevich, A. P., eds., Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, Springer-Verlag, p. 85, ISBN 3-7643-6442-4, OCLC 174767718.
4. ^ Hermann Weyl, David Hilbert. 1862-1943, Obituary Notices of Fellows of the Royal Society (1944).
5. ^ Mclarty, Colin (2008), Theology and its discontents (PDF)