A General Evaluation of Christoffel

Abstract

Any attempt to rate Christoffel, or for that matter any mathematician, among his contemporary mathematicians representing all fields of mathematics is a problematic venture. It is difficult to compare a differential geometdr with a function theorist, or those working on ordinary and partial differential equations with numerical analysts. Christoffel not only contributed to all of 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. Nevertheless, it is widely recognized, at least in the German speaking countries of Europe, that Riemann was the best mathematician of the 19th century, behind Gauss and ahead of Weierstrass. 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. This second group, which may partly overlap with the former, would include such illustrious names as Möbius, von Staudt, Plücker, Heine, Du Bois-Reymond, Carl Neumann, Lipschitz, Fuchs, Schwarz, Hurwitz, and Minkowski. If one did not restrict the rating to the German speaking countries, but would further compare him with other European mathematicians of his time, the comparative evaluation would be much more difficult.