Paul du Bois-Reymond

Paul du Bois-Reymond (1831 to 1889) was a German mathematician, born in Berlin, who died in Freiburg, and the brother of Emil du Bois-Reymond. His 1859 doctoral thesis, De Aequilibrio Fluidorum, treated the mechanical equilibrium of fluids, and he went on to work on the theory of functions and mathematical physics, with interests in Sturm-Liouville theory, integral equations, variational calculus and Fourier series. In 1873 he constructed a continuous function whose Fourier series does not converge, and in a paper of 1875 he used for the first time the method of diagonalization later associated with Cantor. He also developed a theory of infinitesimals and is associated with the fundamental lemma of the calculus of variations. His Théorie générale des fonctions appeared in French translation in 1887.