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Paul Albert Gordan (27 April 1837 – 21 December 1912) was a
Jewish-German mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, a student of
Carl Jacobi at the
University of Königsberg before obtaining his
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
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** Ph.D. (Ph.D. al ...
at the
University of Breslau
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...
(1862),
[.] and a professor at the
University of Erlangen-Nuremberg
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...
.
He was born in
Breslau, Germany (now
Wrocław
Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, r ...
, Poland), and died in
Erlangen
Erlangen (; East Franconian: ''Erlang'', Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 116,062 inha ...
, Germany.
He was known as "the king of
invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descri ...
".
[.][.] His most famous result is that the ring of
invariants of binary forms of fixed degree is finitely generated.
Clebsch–Gordan coefficients
In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In ...
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 Berlin. ...
. Gordan also served as the thesis advisor for
Emmy Noether.
A famous quote attributed to Gordan about
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...
's proof of
Hilbert's basis theorem, a result which vastly generalized his result on invariants, is "This is not
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
; this is
theology
Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing th ...
."
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is asso ...
, ''David Hilbert. 1862-1943'', Obituary Notices of Fellows of the Royal Society (1944). 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).
Publications
*
*
*
Notes
See also
*
Dickson's lemma In mathematics, Dickson's lemma states that every set of n-tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebraist L. E. Dickson, who used it to prove a re ...
*
Invariant of a binary form
*
Symbolic method
References
*, available a
DigiZeitschirften
*, available a
DigiZeitschirften
External links
*
{{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
University of Giessen faculty
University of Erlangen-Nuremberg faculty