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Christoffel was noted for his work in mathematical analysis.
Christoffel studied at the University of Berlin where he was taught by Dirichlet. He obtained his doctorate in 1856 with a dissertation on the motion of electricity in homogeneous bodies. In 1859 he became a lecturer at the University of Berlin and in 1862 he was appointed to the chair at Polytechnicum Zurich. He went to a chair at the Gewerbsakademie in Berlin.
Christoffel was professor of mathematics at the University of Strasbourg from 1872 until he was forced to retire due to ill health in 1892.
Christoffel published works on conformal mappings, Riemann's o-function, the theory of invariants, and the Christoffel reduction theorem.
Christoffel's early work was on conformal mappings of a simply connected region bounded by polygons onto a circle. In 1877 he published a paper on the propagation of plane waves in media with a surface discontinuity. This was an early contribution to the theory of shock waves.
Christoffel was interested in the theory of invariants. He wrote an important paper which contributed to the development of the tensor calculus of C. G. Ricci and Tullio Levi-Civita. The Christoffel symbols [ij,k] are fundamental in the study of tensor analysis.
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