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, structure, space, models, and change.
History
On ...
who made important contributions to
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
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 descri ...
. He attended the
University of Königsberg
The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Prussi ...
and was habilitated at
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
. He subsequently taught in Berlin and
Karlsruhe
Karlsruhe ( , , ; South Franconian: ''Kallsruh'') is the third-largest city of the German state (''Land'') of Baden-Württemberg after its capital of Stuttgart and Mannheim, and the 22nd-largest city in the nation, with 308,436 inhabitants. ...
. His collaboration with
Paul Gordan
__NOTOC__
Paul Albert Gordan (27 April 1837 – 21 December 1912) was a Jewish-German mathematician, a student of Carl Jacobi at the University of Königsberg before obtaining his PhD at the University of Breslau (1862),. and a professor a ...
in
Giessen
Giessen, spelled Gießen in German (), is a town in the German state (''Bundesland'') of Hesse, capital of both the district of Giessen and the administrative region of Giessen. The population is approximately 90,000, with roughly 37,000 univers ...
led to the introduction of
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 ...
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.
Since the spherical harmonics form a ...
, which are now widely used in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
.
Together with
Carl Neumann
Carl Gottfried Neumann (also Karl; 7 May 1832 – 27 March 1925) was a German mathematician.
Biography
Neumann was born in Königsberg, Prussia, as the son of the mineralogist, physicist and mathematician Franz Ernst Neumann (1798–1895), who w ...
at
Göttingen
Göttingen (, , ; nds, Chöttingen) 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. At the end of 2019, 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
Saint-Venant ( vls, Papingem) is a commune in the Pas-de-Calais department (administrative division) in the Hauts-de-France region of France.
Geography
Saint-Venant is situated some northwest of Béthune and west of Lille, at the junction o ...
translated Clebsch's work on
elasticity
Elasticity often refers to:
*Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress
Elasticity may also refer to:
Information technology
* Elasticity (data store), the flexibility of the data model and the cl ...
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 mathematical field of graph theory, the Clebsch graph is either of two 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 the dimension-5 halved cube graph; it wa ...
*
Clebsch representation In physics and mathematics, the Clebsch representation of an arbitrary three-dimensional vector field \boldsymbol(\boldsymbol) is:
\boldsymbol = \boldsymbol \varphi + \psi\, \boldsymbol \chi,
where the scalar fields \varphi(\boldsymbol), \psi(\bol ...
*
Clebsch surface
In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by and , all of whose 27 exceptional lines
can be defined over the real numbers. The term Klein's icosahedral sur ...
*
Eigenvalues and eigenvectors
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
*
Helmholtz equation
In mathematics, the eigenvalue problem for the Laplace operator is known as the Helmholtz equation. It corresponds to the linear partial differential equation
\nabla^2 f = -k^2 f,
where is the Laplace operator (or "Laplacian"), is the eigenv ...
*
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 hyperboloid ...
*
Pentagram map
In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a ne ...
*
Quaternary cubic
References
External links
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{{DEFAULTSORT:Clebsch, Alfred
1832 births
1872 deaths
19th-century German mathematicians
Algebraic geometers
Scientists from Königsberg
People from the Province of Prussia
University of Königsberg alumni
Humboldt University of Berlin faculty
Karlsruhe Institute of Technology faculty
University of Giessen faculty
University of Göttingen faculty