Nationality German Role Mathematician Alma mater University of Breslau Notable students Emmy Noether | Doctoral students Emmy Noether Name Paul Gordan | |
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Born Paul Albert Gordan
27 April 1837
Breslau ( 1837-04-27 ) Institutions University of Erlangen-Nuremberg Academic advisors Carl Gustav Jacob Jacobi Known for Invariant theory, Gordan's lemma Died December 21, 1912, Erlangen, Germany Education University of Konigsberg, University of Wroclaw Similar People Alfred Clebsch, Emmy Noether, Carl Gustav Jacob Ja, Richard Dedekind | ||
Academic advisor Carl Gustav Jacob Jacobi | ||
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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), and a professor at the University of Erlangen-Nuremberg.
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He was born in Breslau, Germany (now Wrocław, Poland), and died in Erlangen, Germany.
He was known as "the king of invariant theory". 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.
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." 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).