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Alfred Clebsch

German mathematician (1833-1872)

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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. He subsequently taught in Berlin and Karlsruhe. His collaboration with Paul Gordan in Giessen led to the introduction of Clebsch-Gordan coefficients for spherical harmonics, which are now widely used in quantum mechanics.

Together with Carl Neumann at Göttingen, he founded the mathematical research journal Mathematische Annalen 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.

His wife was Dorothe Charlote Mathilde Heinel (1838-1866), Alfred and Dorothe Clebsch had four sons: Ernst Friedrich Alfred Clebsch (1859-1945); Arthur Friedrich Alfred Clebsch (1860-1931); Eduard Friedrich Alfred Clebsch (1861-1895), who became a medical doctor in Ems; and Alfred Friedrich Clebsch (1864-).

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Related topics

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 was called the Clebsch graph by Seidel because of its relation to the configuration of 16 lines on the quartic surface discovered in 1868 by the German mathematician Alfred Clebsch.

Clebsch representation

In physics and mathematics, the Clebsch representation of an arbitrary three-dimensional vector field v {\displaystyle {\boldsymbol {v}}({\boldsymbol {x}})} is: v = ∇ φ + ψ ∇ χ , {\displaystyle {\boldsymbol {v}}={\boldsymbol {\nabla }}\varphi +\psi \,{\boldsymbol {\nabla }}\chi ,} where the scalar fields φ ( x ) {\displaystyle \varphi ({\boldsymbol {x}})} , ψ ( x ) {\displaystyle ,\psi ({\boldsymbol {x}})} and χ ( x ) {\displaystyle \chi ({\boldsymbol {x}})} are known as Clebsch potentials or Monge potentials, named after Alfred Clebsch (1833-1872) and Gaspard Monge (1746-1818), and ∇ {\displaystyle {\boldsymbol {\nabla }}} is the gradient operator.

Clebsch surface

In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch and Klein (1873), all of whose 27 exceptional lines can be defined over the real numbers. The term Klein's icosahedral surface can refer to either this surface or its blowup at the 10 Eckardt points.