Hölder

Otto Ludwig Hölder

Born: 22 Dec 1859 in Stuttgart, Germany
Died: 29 Aug 1937 in Leipzig, Germany

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Otto Hölder worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him.

Hölder studied at the University of Berlin from 1877, attending lectures by Weierstrass, Kronecker and Kummer. He presented his dissertation to the University of Tübingen in 1882. Hölder's dissertation investigates analytic functions and summation procedures by arithmetic means.

Hölder became a lecturer at Göttingen in 1884 and while there he worked on the convergence of Fourier series. Shortly after be began working at Göttingen he discovered the inequality now named after him.

Hölder became interested in group theory through Kronecker and Klein. He proved the uniqueness of the factor groups in a composition series, the theorem now called the Jordan-Hölder theorem.

He was offered a post in Tübingen in 1889 but unfortunately he suffered a mental collapse. The faculty ar Tübingen kept their confidence in Hölder and he made a steady recovery, giving his inaugural lecture in 1890.

With the help of group theory methods he returned to a study of the irreducible case of the cubic in the Cardan-Tartaglia formula.

Hölder made many other contributions to group theory. He searched for finite simple groups, finding no new groups, and also studied groups of orders p^3, pq^2, pqr and p^4 for p, q, r primes.

From 1900 he became interested in the geometry of the projective line and later he studied philosophical questions.

References elsewhere in this archive:

Tell me about Hölder's part in the development of group theory

References:

  1. Dictionary of Scientific Biography
  2. B L van der Waerden, Nachruf auf Otto Hölder, Mathematische Annalen 116 (1939),157-165.
  3. J J Gray, Otto Hölder and Group Theory, Mathematical Intelligencer 16 (1994), 59-61.
  4. J J Nicholson, Otto Holder and the Development of Group Theory and Galois Theory (D Phil Thesis Oxford, 1993). 
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