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

Paul Gordan

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 the Hilbert 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).

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

Publications

Gordan, Paul (1987) [1887], Kerschensteiner, Georg, ed., Vorlesungen über Invariantentheorie (2nd ed.), New York: Chelsea Publishing Co., ISBN 978-0-8284-0328-3, MR917266

Notes

^ a b O'Connor, John J.; Robertson, Edmund F., "Paul Gordan", MacTutor History of Mathematics archive, University of St Andrews..

^ 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 3540434763, OCLC 49493513.

^ 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 3764364424, OCLC 174767718.

^ Hermann Weyl, David Hilbert. 1862-1943, Obituary Notices of Fellows of the Royal Society (1944).

References

Die Redaktion der Mathematische Annalen (1913), "Paul Gordan" (in German), Mathematische Annalen 73 (3): i–ii, doi:10.1007/BF01456698, ISSN 0025-5831, JFM 44.0023.06, MR1511736, available at DigiZeitschirften.

Noether, Max (1914), "Paul Gordan" (in German), Mathematische Annalen 75 (1): 1–41, doi:10.1007/BF01564521, available at DigiZeitschirften.

External links

O'Connor, John J.; Robertson, Edmund F., "Paul Gordan", MacTutor History of Mathematics archive, University of St Andrews.

Paul Gordan at the Mathematics Genealogy Project

Mclarty, Colin (2008), Theology and its discontents on the myth surrounding Gordan's comment about mathematics and theology

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