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".][ His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.][ Clebsch–Gordan coefficients are named after him and ]Alfred Clebsch
Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Humboldt ...
. Gordan also served as the thesis advisor for Emmy Noether
Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
.[
]
Life and Career
Gordan was born to Jewish parents in Breslau, Germany (now Wrocław
Wrocław is a city in southwestern Poland, and the capital of the Lower Silesian Voivodeship. It is the largest city and historical capital of the region of Silesia. It lies on the banks of the Oder River in the Silesian Lowlands of Central Eu ...
, Poland), and died in Erlangen
Erlangen (; , ) is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 119,810 inhabitants (as of 30 September 2024), it is the smalle ...
, Germany.[
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.][
A famous quote attributed to Gordan about ]David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time.
Hilbert discovered and developed a broad range of fundamental idea ...
's proof of Hilbert's basis theorem
In mathematics Hilbert's basis theorem asserts that every ideal (ring theory), ideal of a polynomial ring over a field (mathematics), field has a finite generating set of an ideal, generating set (a finite ''basis'' in Hilbert's terminology).
In ...
, a result which vastly generalized his result on invariants, is "This is not mathematics; this is theology
Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...
."[ 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).][
He later said "I have convinced myself that even theology has its merits". He also published a simplified version of the proof.][
]
Publications
*
*
*
References
See also
* Dickson's lemma
* Invariant of a binary form
* Symbolic method
External links
*
* Gordan's publication catalog:
{{DEFAULTSORT:Gordan, Paul
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
Academic staff of the University of Giessen
Academic staff of the University of Erlangen-Nuremberg
Mathematicians from the Kingdom of Prussia
Mathematicians from the German Empire
Presidents of the German Mathematical Society