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{{Short description|German mathematician (1859–1937)}}
{{no footnotes|date=February 2013}}
{{Infobox scientist
{{Infobox scientist
| name = Otto Ludwig Hölder
| name = Ludwig Otto Hölder
| image = Hoelder Otto.jpg
| image = Hoelder Otto.jpg
⚫
| image_size = 150px
| caption = Otto Hölder
| caption = Otto Hölder
| birth_date = {{birth date|1859|12|22|df=y}}
| birth_date = {{birth date|1859|12|22|df=y}}
| birth_place = [[Stuttgart]], [[German Confederation|Germany]]
| birth_place = [[Stuttgart]], [[Kingdom of Württemberg]]
| death_date = {{death date and age|1937|08|29|1859|12|22|df=y}}
| death_date = {{death date and age|1937|08|29|1859|12|22|df=y}}
| death_place = [[Leipzig]], [[Nazi Germany|Germany]]
| death_place = [[Leipzig]], [[Nazi Germany|Germany]]
Line 14: Line 13:
| ethnicity =
| ethnicity =
| field = [[Mathematics]]
| field = [[Mathematics]]
| work_institution =
| work_institution = [[University of Göttingen]]<br>[[University of Tübingen]]<br>[[University of Leipzig]]
| alma_mater =
| alma_mater =
| education = [[University of Stuttgart]]<br>[[University of Berlin]]<br>[[University of Tübingen]]
| doctoral_advisor = [[Paul du Bois-Reymond]]
| doctoral_advisor = [[Paul du Bois-Reymond]]<ref name=mg/>
| doctoral_students = [[Emil Artin]]<br />[[David Gilbarg]]<br />[[William Threlfall]]<br />[[Hermann Vermeil]]
| doctoral_students = {{plainlist|1=
⚫
| known_for = [[Hölder's inequality]]<br />[[Hölder mean]]
*[[Emil Artin]]<ref name=mg/>
*[[William Threlfall]]<ref name=mg/>
*[[Hermann Vermeil]]<ref name=mg/>
}}
| known_for = [[Hölder condition]]<br/>[[Hölder mean]]<br/>[[Hölder summation]]<br>[[Hölder's inequality]]<br>[[Hölder's theorem]]<br>[[Composition series|Jordan–Hölder theorem]]
⚫
| children = [[Ernst Hölder]]
⚫
| spouse = Helene Hölder
| author_abbreviation_bot =
| author_abbreviation_bot =
| author_abbreviation_zoo =
| author_abbreviation_zoo =
Line 26: Line 32:
}}
}}


'''Otto Ludwig Hölder''' (December 22, 1859 – August 29, 1937) was a [[Germany|German]] [[mathematician]] born in [[Stuttgart]].
'''Ludwig Otto Hölder''' (December 22, 1859 – August 29, 1937) was a German [[mathematician]] born in [[Stuttgart]].<ref name=mactutor>{{MacTutor Biography|id=Holder}}</ref>

==Early life and education==
⚫
Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors. He 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]].<ref name=mactutor/>


⚫
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]]").<ref name=mg>{{MathGenealogy|id=18608}}</ref> Following this, he went to the [[University of Leipzig]] but was unable to [[habilitation|habilitate]] there, instead earning a second doctorate and habilitation at the [[University of Göttingen]], both in 1884.
⚫
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]].


==Academic career and later life==
⚫
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 (mathematics)|group]] of [[real number]]s, the classification of [[simple group]]s of order up to [[200 (number)|200]], the [[Automorphisms_of_the_symmetric_and_alternating_groups#The_exceptional_outer_automorphism_of_S6|anomalous outer automorphisms]] of the [[symmetric group]] ''S''<sub>6</sub> 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 [[mathematical analysis|analysis]], including the theories of [[partial differential equation]]s and [[function spaces]].
He was unable to get government approval for a faculty position in Göttingen, and instead was offered a position as extraordinary professor at Tübingen in 1889. Temporary mental incapacitation delayed his acceptance but he began working there in 1890. In 1899, he took the former chair of [[Sophus Lie]] as a full professor at the University of Leipzig. There he served as dean from 1912 to 1913, and as rector in 1918.<ref name=mactutor/>


He married Helene, the daughter of a bank director and politician, in 1899. They had two sons and two daughters. His son [[Ernst Hölder]] became another mathematician,<ref name=mactutor/> and his daughter Irmgard married mathematician [[Aurel Wintner]].<ref>{{citation
⚫
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.
| last1 = Elbert | first1 = Árpád
| last2 = Garay | first2 = Barnabás M.
| editor-last = Horváth | editor-first = János
| contribution = Differential equations: Hungary, the extended first half of the 20th century
| doi = 10.1007/978-3-540-30721-1_9
| mr = 2547513
| pages = 245–294
| publisher = Springer, Berlin
| series = Bolyai Soc. Math. Stud.
| title = A Panorama of Hungarian Mathematics in the Twentieth Century, I
| volume = 14
| year = 2006| isbn = 978-3-540-28945-6
}}; see [https://books.google.com/books?id=EWm4WzSaG3IC&pg=PA248 p. 248]</ref>


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]]''.<ref>{{citation|page=135|url=https://archive.org/details/bekenntnisderpro00natiuoft/page/135/mode/1up|title=Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat; überreicht vom Nationalsozialistischen Lehrerbund Deutschland-Sachsen|year=1933|publisher=Dresden }}</ref>
In 1933 Hölder signed the ''[[w:de:Bekenntnis der deutschen Professoren zu Adolf Hitler|Loyalty Oath of German Professors to Adolf Hitler and the National Socialist State]]''.


==Mathematical contributions==
== See also ==
[[Holder's inequality]], named for Hölder, was actually [[mathematical proof|proven]] earlier by [[Leonard James Rogers]]. It is named for a paper in which Hölder, citing Rogers, reproves it;<ref>{{citation
* [[Hölder mean]]
| last = Maligranda | first = Lech
* [[Hölder summation]]
| doi = 10.7153/mia-01-05
| issue = 1
| journal = Mathematical Inequalities & Applications
| mr = 1492911
| pages = 69–83
| title = Why Hölder's inequality should be called Rogers' inequality
| volume = 1
| year = 1998| doi-access = free
}}</ref> in turn, the same paper includes a proof of what is now called [[Jensen's inequality]], with some side conditions that were later removed by Jensen.<ref>{{citation
| last1 = Guessab | first1 = A.
| last2 = Schmeisser | first2 = G.
| doi = 10.1007/s00013-013-0522-3
| issue = 6
| journal = [[Archiv der Mathematik]]
| mr = 3069109
| quote = under the additional assumption that <math>\varphi''</math> exists, this inequality was already obtained by Hölder in 1889
| pages = 561–570
| title = Necessary and sufficient conditions for the validity of Jensen's inequality
| volume = 100
| year = 2013| s2cid = 56372266
}}</ref>
⚫
Hölder is also noted for many other [[theorem]]s including 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 (mathematics)|group]] of [[real number]]s, the classification of [[simple group]]s of [[order of a group|order]] up to 200, the [[Automorphisms of the symmetric and alternating groups#The exceptional outer automorphism of S6|anomalous outer automorphisms]] of the [[symmetric group]] ''S''<sub>6</sub>, 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 [[mathematical analysis|analysis]], including the theories of [[partial differential equation]]s and [[function space]]s.


== References ==
== References ==
{{reflist}}
* {{MacTutor Biography|id=Holder}}
* {{MathGenealogy|id=18608}}


{{Authority control}}
{{Authority control}}
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[[Category:1859 births]]
[[Category:1859 births]]
[[Category:1937 deaths]]
[[Category:1937 deaths]]
[[Category:Scientists from Stuttgart]]
[[Category:Humboldt University of Berlin alumni]]
[[Category:University of Tübingen alumni]]
[[Category:Academic staff of Leipzig University]]
[[Category:University of Stuttgart alumni]]
[[Category:Academic staff of the University of Tübingen]]
[[Category:Academic staff of the University of Göttingen]]

Latest revision as of 21:48, 27 July 2024

Ludwig Otto Hölder
Otto Hölder
Born(1859-12-22)22 December 1859
Stuttgart, Kingdom of Württemberg
Died29 August 1937(1937-08-29) (aged 77)
Leipzig, Germany
NationalityGerman
EducationUniversity of Stuttgart
University of Berlin
University of Tübingen
Known forHölder condition
Hölder mean
Hölder summation
Hölder's inequality
Hölder's theorem
Jordan–Hölder theorem
SpouseHelene Hölder
ChildrenErnst Hölder
Scientific career
FieldsMathematics
InstitutionsUniversity of Göttingen
University of Tübingen
University of Leipzig
Doctoral advisorPaul du Bois-Reymond[1]
Doctoral students

Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart.[2]

Early life and education

[edit]

Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors. He 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.[2]

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").[1] Following this, he went to the University of Leipzig but was unable to habilitate there, instead earning a second doctorate and habilitation at the University of Göttingen, both in 1884.

Academic career and later life

[edit]

He was unable to get government approval for a faculty position in Göttingen, and instead was offered a position as extraordinary professor at Tübingen in 1889. Temporary mental incapacitation delayed his acceptance but he began working there in 1890. In 1899, he took the former chair of Sophus Lie as a full professor at the University of Leipzig. There he served as dean from 1912 to 1913, and as rector in 1918.[2]

He married Helene, the daughter of a bank director and politician, in 1899. They had two sons and two daughters. His son Ernst Hölder became another mathematician,[2] and his daughter Irmgard married mathematician Aurel Wintner.[3]

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.[4]

Mathematical contributions

[edit]

Holder's inequality, named for Hölder, was actually proven earlier by Leonard James Rogers. It is named for a paper in which Hölder, citing Rogers, reproves it;[5] in turn, the same paper includes a proof of what is now called Jensen's inequality, with some side conditions that were later removed by Jensen.[6] Hölder is also noted for many other theorems including 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 S6, 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.

References

[edit]
  1. ^ a b c d e Otto Hölder at the Mathematics Genealogy Project
  2. ^ a b c d O'Connor, John J.; Robertson, Edmund F., "Otto Hölder", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ Elbert, Árpád; Garay, Barnabás M. (2006), "Differential equations: Hungary, the extended first half of the 20th century", in Horváth, János (ed.), A Panorama of Hungarian Mathematics in the Twentieth Century, I, Bolyai Soc. Math. Stud., vol. 14, Springer, Berlin, pp. 245–294, doi:10.1007/978-3-540-30721-1_9, ISBN 978-3-540-28945-6, MR 2547513; see p. 248
  4. ^ Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat; überreicht vom Nationalsozialistischen Lehrerbund Deutschland-Sachsen, Dresden, 1933, p. 135
  5. ^ Maligranda, Lech (1998), "Why Hölder's inequality should be called Rogers' inequality", Mathematical Inequalities & Applications, 1 (1): 69–83, doi:10.7153/mia-01-05, MR 1492911
  6. ^ Guessab, A.; Schmeisser, G. (2013), "Necessary and sufficient conditions for the validity of Jensen's inequality", Archiv der Mathematik, 100 (6): 561–570, doi:10.1007/s00013-013-0522-3, MR 3069109, S2CID 56372266, under the additional assumption that exists, this inequality was already obtained by Hölder in 1889
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