Christoffel, Elwin Bruno (1829–1900)

German mathematician. He made a fundamental contribution to the differential geometry of surfaces, carried out some of the first investigations that later resulted in the theory of shock waves, and introduced what are now known as the Christoffel symbols into the theory of invariants.

Christoffel was born in Montjoie (now Monschau), near Aachen, and studied at Berlin. His first professorship was at the Polytechnicum in Zürich, Switzerland, 1862–69; the second at Berlin; and from 1872 he was at the University of Strasbourg.

In Allgemeine Theorie der geodätischen Dreiecke (1868), he presented a trigonometry of triangles formed by geodesics on an arbitrary surface. Christoffel's paper ‘Über die Transformation der homogen Differentialausdrücke zweiten Grades’ (1869) introduced the symbols that later became known as Christoffel symbols of the first and second order. The series of other symbols of more than three indices, including the four-index symbols already introduced by Bernhard Riemann, is now known as the Riemann–Christoffel symbols.

Christoffel formulated a theorem that also bears his name, concerning the reduction of a quadrilateral form. In 1877, Christoffel published a paper on the propagation of plane waves in media with a surface discontinuity, and thus made an early contribution to shock-wave theory. In Vollständige Theorie der Riemannschen θ-Function (published posthumously), Christoffel gave an independent interpretation of Riemann's work on surface geometry.