Paul Du Bois-Reymond

David Paul Gustave Du Bois -Reymond ( born December 2, 1831 in Berlin, † April 7, 1889 in Freiburg im Breisgau ) was a German mathematician.

Life and work

He came from a Huguenot family, and was a brother of the physician Heinrich Emil du Bois- Reymond.

Paul du Bois- Reymond in 1849 studied medicine in Zurich and then mathematics at Königsberg and at the Humboldt University of Berlin, where he received his doctorate in 1859 at Ernst Eduard Kummer ( De aequilibrio fluidorum ). He was initially 1861-1865 high school teacher in Berlin ( Friedrich- Werder cal school). After his habilitation in 1865 in Heidelberg, he was a lecturer at the University of Heidelberg ( from 1868 associate professor ), in 1869 a full professor in Freiburg im Breisgau, 1874 in Tübingen and in 1884 at the Technical University in Berlin.

The focus of his mathematical work was in the theory of differential equations. The best known, however, is his work on Fourier series from the year 1873. In this he showed the existence of a continuous function whose Fourier development diverges at a point. He thus refuted a long time as certain applicable conjecture of Dirichlet. It was not until about 90 years later, Lennart Carleson proved that the Fourier development of a continuous function converges almost everywhere.

Du Bois -Reymond also dealt with fundamental questions of mathematics and gave the first a careful proof of the mean value theorem of integral calculus. In his book General Function theory you criticized Bois- Reymond, the metaphysical assumptions and inadequate reasoning of the mathematical " Platonism " and sets the contrary a kind of empirical standpoint.

He was buried in the Old St. Matthew Cemetery in Berlin- Schöneberg ( leveled grave, portrait medallion in bronze, probably modeled by Eduard Lürssen, received in Berlin privately owned).

In 1874 he became a member of the Bavarian Academy of Sciences in Munich, in 1883 he was elected a member of the Leopoldina.

His doctoral include Carl Cranz, Otto Hölder and Rudolf Mehmke.

Works

• About the Fourier series. in: News of the Royal Society of Sciences and the Georg August University in Göttingen. Göttingen 1873.
• A new theory of convergence and divergence of series of positive terms. In: Journal of Pure and Applied Mathematics. Berlin 76.1873, p.61 - 91st ISSN 0075-4102
• General Function Theory. Tübingen 1882.
• About linear partial differential equations of 2nd order. In: Journal of Pure and Applied Mathematics. Berlin 104.1889, p.241 - 301. ISSN 0075-4102
• On the foundations of knowledge in the exact sciences. Tübingen 1890.