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Paul Gordan

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Not to be confused with Walter Gordon (physicist).

Paul Gordan
Paul Gordan
Born
Paul Albert Gordan

(1837-04-27)27 April 1837
Breslau, Province of Silesia, Kingdom of Prussia
Died21 December 1912(1912-12-21) (aged 75)
Erlangen, Kingdom of Bavaria, German Empire
NationalityGerman
Alma materUniversity of Breslau
Known forInvariant theory
Clebsch–Gordan coefficients
Gordan's lemma
Scientific career
InstitutionsUniversity of Erlangen-Nuremberg
Academic advisorsCarl Gustav Jacob Jacobi
Doctoral studentsEmmy Noether

Paul Albert Gordan (27 April 1837 – 21 December 1912) was a German mathematician known for work in Invariant theory and for the Clebsch–Gordan coefficients and Gordan's lemma. He was called "the king of invariant theory".[1][2] His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.[2] Clebsch–Gordan coefficients are named after him and Alfred Clebsch. Gordan also served as the thesis advisor for Emmy Noether.[3]

Life and Career

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He was born to Jewish parents in Breslau, Germany (now Wrocław, Poland), and died in Erlangen, Germany.[4]

He was a student of Carl Jacobi at the University of Königsberg before obtaining his PhD at the University of Breslau (1862),[5] and a professor at the University of Erlangen-Nuremberg.

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."[1][6] 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).[7][8]

He later said "I have convinced myself that even theology has its merits". He also published a simplified version of the proof.[9][10]

Publications

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  • Gordan, Paul (1885). Vorlesungen über Invariantentheorie. Vol. 1. Teubner. Retrieved 12 April 2014.
  • Gordan, Paul (1887). Dr. Paul Gordan's Vorlesungen über Invariantentheorie. Vol. 2. B. G. Teubner. Retrieved 12 April 2014.
  • Gordan, Paul (1987) [1885], Kerschensteiner, Georg (ed.), Vorlesungen über Invariantentheorie (2nd ed.), New York: Chelsea Publishing Co. or American Mathematical Society, ISBN 978-0-8284-0328-3, MR 0917266

References

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  1. ^ 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.
  2. ^ 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 {{citation}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link).
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Paul Gordan", MacTutor History of Mathematics Archive, University of St Andrews.
  4. ^ Bergmann, Birgit (2012). Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture. Springer. p. 60. ISBN 9783642224645.
  5. ^ Cite error: The named reference MacTutor was invoked but never defined (see the help page).
  6. ^ Hermann Weyl, David Hilbert. 1862–1943, Obituary Notices of Fellows of the Royal Society (1944).
  7. ^ Mclarty, Colin (2008), Theology and its discontents (PDF), archived from the original (PDF) on 16 January 2009
  8. ^ Cite error: The named reference mclarty was invoked but never defined (see the help page).
  9. ^ Gordan, P. (1899). "Neuer Beweis des Hilbertschen Satzes über homogene Funktionen". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. 1899: 240–242.
  10. ^ Klein, Felix (1979). Development of mathematics in the 19th century. Internet Archive. Brookline, Mass. : Math Sci Press. p. 311. ISBN 978-0-915692-28-6.

See also

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Sources

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