Paul Gordan | |
|---|---|
 Paul Gordan | |
| Born | Paul Albert Gordan (1837-04-27)27 April 1837 |
| Died | 21 December 1912(1912-12-21) (aged 75) |
| Alma mater | University of Breslau |
| Known for | Invariant theory Clebsch–Gordan coefficients Gordan's lemma |
| Scientific career | |
| Institutions | University of Erlangen-Nuremberg |
| Doctoral students | Emmy Noether |
Paul Albert Gordan (27 April 1837 – 21 December 1912) was a German mathematician known for work ininvariant theory and for theClebsch–Gordan coefficients andGordan's lemma.[1] He was called "the king of invariant theory".[2][3] His most famous result is that the ring ofinvariants of binary forms of fixed degree is finitely generated.[3] Clebsch–Gordan coefficients are named after him andAlfred Clebsch. Gordan also served as the thesis advisor forEmmy Noether.[4][5]
Gordan was born to Jewish parents inBreslau, Germany (nowWrocław, Poland), and died inErlangen, Germany.[6]
He received his Dr. phil. at theUniversity of Breslau with the thesisDe Linea Geodetica, (OnGeodesics of Spheroids) in 1862.[7] He moved to Erlangen in 1874 to become professor of mathematics at theUniversity of Erlangen-Nuremberg.[4]
A famous quote attributed to Gordan aboutDavid Hilbert's proof ofHilbert's basis theorem, a result which vastly generalized his result on invariants, is "This is not mathematics; this istheology."[2][8] 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. 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).[9][10]
He later said "I have convinced myself that even theology has its merits". He also published a simplified version of the proof.[11][12]
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