**Elwin Christoffel** published works on conformal mappings, Riemann's o-function, the theory of invariants, and the Christoffel reduction theorem.

- Christoffel's parents both came from families who were in the cloth trade.
- Christoffel studied at the University of Berlin from 1850 where he was taught by Borchardt, Eisenstein, Joachimsthal, Steiner and Dirichlet.
- It was Dirichlet who had the greatest influence on him and Christoffel is rightly thought of as a student of Dirichlet's.
- At this point Christoffel spent three years outside the academic world.
- This is now called Christoffel's theorem.
- In 1859 Christoffel took the qualifying examination to become a university teacher and was appointed a lecturer at the University of Berlin.
- Christoffel was to have a huge influence on mathematics at the Polytechnicum, setting up an institute for mathematics and the natural sciences there.
- In 1868 Christoffel was offered a chair at the Gewerbsakademie in Berlin which is now the University of Technology of Berlin.
- This was not the first time an attempt had been made to interest Christoffel in moving to this university since a new position had been set up and the university authorities wanted an eminent mathematician to fill he post.
- Shortly after the 1868 offer to Christoffel another position was offered to him, namely to become a founding director of the new Polytechnicum at Aachen.
- This new university, now the prestigious Rheinisch- Westfälische Technische Hochschule at Aachen, must have been an attractive idea to Christoffel who was born and brought up close to Aachen.
- Christoffel, however, did not accept the Aachen position: perhaps he was already committed to the Gewerbsakademie in Berlin for he certainly left Zürich for Berlin to take up his new post on 1 April 1869.
- This move may have been a mistake for Christoffel.
- After three years at the Gewerbsakademie in Berlin, Christoffel was offered the chair of mathematics at the University of Strasbourg.
- From his appointment in 1872 Christoffel began to built up a new Institute for mathematics there much along the lines which he had followed in Zürich 10 years before.
- Christoffel was to hold this chair until he was forced to retire due to ill health in 1892.
- Christoffel supervised six doctoral students while at Strasbourg.
- Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann's o-function, the theory of invariants, orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
- Some of Christoffel's early work was on conformal mappings of a simply connected region bounded by polygons onto a circle.
- The first of these papers was written while Christoffel was at Zürich, the remaining three papers on the Christoffel-Schwarz formula were written while he was at the Gewerbsakademie in Berlin.
- Between 1865 and 1871 Christoffel published four important papers on potential theory, three of them dealing with the Dirichlet problem.
- In 1877 Christoffel published a paper on the propagation of plane waves in media with a surface discontinuity.
- Christoffel was interested in the theory of invariants.
- The Christoffel reduction theorem, so named by Klein, solves the local equivalence problem for two quadratic differential forms.
- The importance of this approach and the two concepts Christoffel introduced, at least implicitly, can only be judged when on considers the influence it has had.
- Christoffel wrote 35 papers but this does not represent the full extent of his mathematical work.
- Christoffel had developed Riemann's function theory independently, particularly in the area of ultraelliptic functions, but did not publish his research, presenting them only in his lectures, after the model of Weierstrass.
- Christoffel not only contributed to all these fields, but his interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light.
- In our opinion Christoffel's teacher Dirichlet, belongs to the next most important group of mathematicians which includes (in chronological order of birth) Jacobi, Kummer, Kronecker, Dedekind, Cantor and Klein.
- Christoffel himself should be placed in a second group following these.
- If mathematical physicists are also taken into account then Butzer and Fehér believe that Christoffel would have to be compared with Green, Hamilton, Sylvester, Helmholtz, Cayley, Kirchhoff, Maxwell, Beltrami, Lie, Boltzmann, Poincaré and Fredholm.

Born 10 November 1829, Montjoie Aachen (now Monschau), Germany. Died 15 March 1900, Strasbourg, France.

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Origin Germany, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive