Paul du Bois-Reymond

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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

Paul du Bois-Reymond came from a Huguenot family and was a brother of the medical doctor Emil du Bois-Reymond .

From 1849 he studied medicine in Zurich and then mathematics in Königsberg and at the University of Berlin , where he received his doctorate in 1859 under Ernst Eduard Kummer ( De aequilibrio fluidorum ). He was initially a teacher in Berlin from 1861 to 1865 at the Friedrich-Werderschen Gymnasium . After his habilitation in 1865 at the University of Heidelberg , he was a lecturer and from 1868 an associate professor. In 1869 he became a full professor in Freiburg im Breisgau , in 1874 in Tübingen and in 1884 at the Technical University in Berlin .

The focus of his mathematical work was on the theory of differential equations . He became known, however, through his work on Fourier series from 1873, in which he showed the existence of a continuous function whose Fourier expansion diverges at one point. In doing so, he refuted a presumption by Dirichlet that had long been considered certain . It wasn't until about 90 years later that Lennart Carleson proved that the Fourier expansion of a continuous function converges almost everywhere . Du Bois-Reymond proved the fundamental lemma of the calculus of variations in 1879 .

Du Bois-Reymond as a private lecturer in Heidelberg

Du Bois-Reymond also dealt with fundamental questions of mathematics and was the first to give a careful proof of the mean value theorem of integral calculus . In his book General Theory of Functions , du Bois-Reymond criticizes the metaphysical presuppositions and deficiencies in justification of mathematical "Platonism" and opposes a kind of empirical standpoint.

He died of chronic kidney disease on a trip to Freiburg in April 1889 and was buried in the Old St. Matthew Cemetery in Berlin-Schöneberg (grave leveled, bronze portrait medallion, presumably modeled by Eduard Lürssen , preserved in private ownership in Berlin).

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 students 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 of Göttingen. Goettingen 1873.
  • A new theory of the convergence and divergence of series with positive terms. in: Journal for pure and applied mathematics . Berlin 76.1873, pp. 61-91. ISSN  0075-4102
  • General function theory. Tuebingen 1882.
  • Via linear partial differential equations of the 2nd order. in: Journal for pure and applied mathematics. Berlin 104.1889, pp. 241-301. ISSN  0075-4102
  • About the foundations of knowledge in the exact sciences. Tübingen 1890.

literature

Web links

Individual evidence

  1. ↑ Appointment , in the Centralblatt der Bauverwaltung , No. 43, October 25, 1884, p. 446, accessed on January 1, 2013
  2. ↑ Dubois-Reymond, Explanatory Notes on the Beginnings of the Calculus of Variations, Mathematische Annalen, Volume 15, 1879, pp. 283-314, here pp. 297, 300
  3. ^ Oskar Bolza, lectures on the calculus of variations, Teubner 1909, p. 26. According to Bolza, the oldest proof comes from Friedrich Stegmann , textbook of the calculus of variations, Kassel 1854, but there are more restrictive assumptions.
  4. ^ Mathematics Genealogy Project
personal data
SURNAME You Bois-Reymond, Paul
ALTERNATIVE NAMES Du Bois-Reymond, David Paul Gustave; Dubois-Reymond, Paul
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH December 2, 1831
PLACE OF BIRTH Berlin
DATE OF DEATH April 7, 1889
Place of death Freiburg in Breisgau