# Paul Gordan

*https://en.wikipedia.org/wiki/Paul_Gordan*

Paul Gordan | |
---|---|

Born | Paul Albert Gordan 27 April 1837 |

Died | 21 December 1912 | (aged 75)

Nationality | German |

Alma mater | University of Breslau |

Known for |
Invariant theory Clebsch–Gordan coefficients Gordan's lemma |

Scientific career | |

Institutions | University of Erlangen-Nuremberg |

Academic advisors | Carl Gustav Jacob Jacobi |

Doctoral students | Emmy Noether |

**Paul Albert Gordan** (27 April 1837 – 21 December 1912) was a
Jewish-German^{
[1]}
mathematician, a student of
Carl Jacobi at the
University of Königsberg before obtaining his
Ph.D. at the
University of Breslau (1862),^{
[2]} and a professor at the
University of Erlangen-Nuremberg.

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

He was known as "the king of
invariant theory".^{
[3]}^{
[4]} His most famous result is that the ring of
invariants of binary forms of fixed degree is finitely generated.^{
[4]} He and
Alfred Clebsch gave their name to
Clebsch–Gordan coefficients. Gordan also served as the thesis advisor for
Emmy Noether.^{
[2]}

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."^{
[3]}^{
[5]} 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).^{
[6]}

## Publications

- Gordan, Paul (1885).
*Vorlesungen über Invariantentheorie*.**1**. Teubner. Retrieved 12 April 2014. - Gordan, Paul (1887).
*Dr. Paul Gordan's Vorlesungen über Invariantentheorie*.**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

## Notes

**^**Bergmann, Birgit (2012).*Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture*. p. 60. ISBN 9783642224645.- ^
^{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 3-540-43476-3, 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 3-7643-6442-4, OCLC 174767718CS1 maint: multiple names: authors list ( link) CS1 maint: extra text: authors list ( link). **^**Hermann Weyl,*David Hilbert. 1862-1943*, Obituary Notices of Fellows of the Royal Society (1944).**^**Mclarty, Colin (2008),*Theology and its discontents*(PDF), archived from the original (PDF) on 16 January 2009

## See also

## References

- Die Redaktion der Mathematische Annalen (1913),
"Paul Gordan",
*Mathematische Annalen*(in German),**73**(3): i–ii, doi: 10.1007/BF01456698, ISSN 0025-5831, JFM 44.0023.06, MR 1511736, S2CID 177804295, available at DigiZeitschirften. -
Noether, Max (1914),
"Paul Gordan",
*Mathematische Annalen*(in German),**75**(1): 1–41, doi: 10.1007/BF01564521, S2CID 179178051, available at DigiZeitschirften.

## External links

- 1837 births
- 1912 deaths
- 19th-century German mathematicians
- 20th-century German mathematicians
- 19th-century German Jews
- Algebraists
- Scientists from Wrocław
- People from the Province of Silesia
- University of Breslau alumni
- University of Königsberg alumni
- Humboldt University of Berlin alumni
- University of Giessen faculty
- University of Erlangen-Nuremberg faculty