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Paul Gordan - Wikipedia

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German mathematician (1837–1912)

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.[1] He was called "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] Clebsch–Gordan coefficients are named after him and Alfred Clebsch. Gordan also served as the thesis advisor for Emmy Noether.[4][5]

Gordan was born to Jewish parents in Breslau, Germany (now Wrocław, Poland), and died in Erlangen, Germany.[6]

He received his Dr. phil. at the University of Breslau with the thesis De Linea Geodetica, (On Geodesics of Spheroids) under Carl Jacobi in 1862. He moved to Erlangen in 1874 to become professor of mathematics at the University of Erlangen-Nuremberg.[4]

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][7] 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).[8][9]

He later said "I have convinced myself that even theology has its merits". He also published a simplified version of the proof.[10][11]

  1. ^ Paul Gordan Die Redaktion der Mathematische Annalen,  Mathematische Annalen (in German), March 1914, 73 (3): i–ii, doi:10.1007/BF01456698, S2CID 177804295
  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 CS1 maint: multiple names: authors list (link).
  4. ^ a b O'Connor, John J.; Robertson, Edmund F., "Paul Gordan", MacTutor History of Mathematics Archive, University of St Andrews.
  5. ^ Noether, Max by Paul Gordan, Mathematische Annalen (in German), March 1914, 75 (1): 1–41, doi:10.1007/BF01564521, S2CID 179178051
  6. ^ Bergmann, Birgit (2012). Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture. Springer. p. 60. ISBN 9783642224645.
  7. ^ Hermann Weyl, David Hilbert. 1862–1943, Obituary Notices of Fellows of the Royal Society (1944).
  8. ^ Mclarty, Colin (2008), Theology and its discontents (PDF), archived from the original (PDF) on 16 January 2009
  9. ^ McLarty, Colin (18 March 2012). "Hilbert on Theology and Its Discontents". In Doxiadis, Apostolos; Mazur, Barry (eds.). Circles Disturbed. Princeton University Press. doi:10.23943/princeton/9780691149042.003.0004. ISBN 978-0-691-14904-2.
  10. ^ 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.
  11. ^ 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.

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