Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a 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, mathematical structure, structure, space, Mathematica ...
who made important contributions to
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and
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 descr ...
. He attended the
University of Königsberg
The University of Königsberg () was the university of Königsberg in Duchy of Prussia, which was a fief of Poland. It was founded in 1544 as the world's second Protestant Reformation, Protestant academy (after the University of Marburg) by Duke A ...
and was habilitated at
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
. He subsequently taught in Berlin and
Karlsruhe
Karlsruhe ( ; ; ; South Franconian German, South Franconian: ''Kallsruh'') is the List of cities in Baden-Württemberg by population, third-largest city of the States of Germany, German state of Baden-Württemberg, after its capital Stuttgart a ...
. His collaboration with
Paul Gordan
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 ...
in
Giessen
Giessen, spelled in German (), is a town in the Germany, German States of Germany, state () of Hesse, capital of both the Giessen (district), district of Giessen and the Giessen (region), administrative region of Giessen. The population is appro ...
led to the introduction of
Clebsch–Gordan coefficients for
spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics co ...
, which are now widely used in
quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
.
Together with
Carl Neumann
Carl Gottfried Neumann (also Karl; 7 May 1832 – 27 March 1925) was a German Mathematical physics, mathematical physicist and professor at several German universities. His work focused on applications of potential theory to physics and mathemati ...
at
Göttingen
Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...
, he founded the mathematical research journal ''
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
'' in 1868.
In 1883,
Saint-Venant translated Clebsch's work on
elasticity into French and published it as ''Théorie de l'élasticité des Corps Solides''.
Books by A. Clebsch
Vorlesungen über Geometrie(Teubner, Leipzig, 1876-1891) edited by Ferdinand Lindemann.
Théorie der binären algebraischen Formen(Teubner, 1872)
Theorie der Abelschen Functionenwith P. Gordan (B. G. Teubner, 1866)
Theorie der Elasticität fester Körper(B. G. Teubner, 1862)
See also
*
Clebsch graph
In the mathematics, mathematical field of graph theory, the Clebsch graph is either of two complement (graph theory), complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. The 80-edge graph is ...
*
Clebsch representation
*
Clebsch surface
*
Eigenvalues and eigenvectors
In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...
*
Helmholtz equation
In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation:
\nabla^2 f = -k^2 f,
where is the Laplace operator, is the eigenvalue, and is the (eigen)fun ...
*
Hyperboloid model
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of ''n''-dimensional hyperbolic geometry in which points are represented by points on the forward sheet ''S''+ of a two-sheeted hyperboloi ...
*
Pentagram map
*
Quaternary cubic
References
External links
*
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{{DEFAULTSORT:Clebsch, Alfred
1833 births
1872 deaths
19th-century German mathematicians
Algebraic geometers
Scientists from Königsberg
People from the Province of Prussia
University of Königsberg alumni
Academic staff of the Humboldt University of Berlin
Academic staff of the Karlsruhe Institute of Technology
Academic staff of the University of Giessen
Academic staff of the University of Göttingen
Mathematicians from the Kingdom of Prussia