# Otto Hölder

**Otto Ludwig Hölder** (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart.

Otto Ludwig Hölder | |
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Otto Hölder | |

Born | |

Died | 29 August 1937 77) | (aged

Nationality | German |

Known for | Hölder's inequality Hölder mean |

Scientific career | |

Fields | Mathematics |

Doctoral advisor | Paul du Bois-Reymond |

Doctoral students | Emil Artin David Gilbarg William Threlfall Hermann Vermeil |

Hölder first studied at the *Polytechnikum* (which today is the University of Stuttgart) and then in 1877 went to Berlin where he was a student of Leopold Kronecker, Karl Weierstraß, and Ernst Kummer.

He is noted for many theorems including: Hölder's inequality, the Jordan–Hölder theorem, the theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers, the classification of simple groups of order up to 200, the anomalous outer automorphisms of the symmetric group *S*_{6}, and Hölder's theorem, which implies that the Gamma function satisfies no algebraic differential equation. Another idea related to his name is the Hölder condition (or Hölder continuity) which is used in many areas of analysis, including the theories of partial differential equations and function spaces.

In 1877, he entered the University of Berlin and took his doctorate from the University of Tübingen in 1882. The title of his doctoral thesis was "Beiträge zur Potentialtheorie" ("Contributions to potential theory"). He worked at the University of Leipzig from 1899 until his retirement.

In 1933 Hölder signed the *Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State*.