View source for G-test

{{Infobox scientist
|name              = Carl Neumann
|image             = Neumann Carl.jpg
|birth_date        = {{Birth date|1832|05|07|df=y}}
|birth_place       = [[Königsberg]], [[Province of Prussia|Prussia]]
|death_date        = {{death date and age|1925|03|27|1832|05|07|df=y}}
|death_place       = [[Leipzig]]
|residence         = 
|nationality       = [[Germany|German]]
|fields            = [[integral equation]]s
|workplaces        = [[University of Halle-Wittenberg]]<br />[[University of Basel]]<br />[[University of Tübingen]]<br />[[University of Leipzig]].
|alma_mater        = [[Königsberg University]]<br />[[University of Halle-Wittenberg|Halle]]
|doctoral_advisor  = [[Friedrich Richelot]] and [[Otto Hesse]]
|doctoral_students = [[William Edward Story]]
|known_for         = [[Dirichlet problem]]<br />[[Neumann series]]
}}
'''Carl Gottfried Neumann''' (7 May 1832 – 27 March 1925), also '''Karl Gottfried Neumann''', was a [[Germany|German]] [[mathematician]].

Neumann was born in [[Königsberg]], [[Province of Prussia|Prussia]], as the son of the mineralogist, physicist and mathematician [[Franz Ernst Neumann]] (1798-1895), who was professor of mineralogy and physics at [[Königsberg University]]. Carl Neumann studied in Königsberg and [[University of Halle-Wittenberg|Halle]] and was a professor at the universities of [[University of Halle|Halle]], [[University of Basel|Basel]], [[University of Tübingen|Tübingen]], and [[University of Leipzig|Leipzig]].

Neumann worked on the [[Dirichlet problem|Dirichlet principle]], and can be considered one of the initiators of the theory of [[integral equation]]s. The [[Neumann series]], which is analogous to the [[geometric series]]

<math> \frac{1}{1-x} = 1 + x + x^2 + \cdots </math>

but for [[Matrix (mathematics)|infinite matrices]], is named after him.

Together with [[Alfred Clebsch]] Neumann founded the mathematical research journal ''[[Mathematische Annalen]]''. He died in Leipzig.

The [[Neumann boundary condition]] for certain types of ordinary and [[partial differential equation]]s is named after him ([[#Che-05|Cheng and Cheng, 2005]]).

==Works by Carl Neumann==
* [http://gallica.bnf.fr/ark:/12148/bpt6k99577z Das Dirichlet'sche Princip in seiner Anwendung auf die Riemann'schen Flächen] (B. G. Teubner, Leipzig, 1865)
* [http://gallica.bnf.fr/ark:/12148/bpt6k99576m Vorlesungen über Riemann's Theorie der Abel'schen Integrale ] (B. G. Teubner, 1865)
* [http://gallica.bnf.fr/ark:/12148/bpt6k99615p Theorie der Bessel'schen functionen: ein analogon zur theorie der Kugelfunctionen] (B. G. Teubner, 1867)
* [http://gallica.bnf.fr/ark:/12148/bpt6k996161 Untersuchungen über das Logarithmische und Newton'sche potential] (B. G. Teubner, 1877)
* [http://resolver.library.cornell.edu/math/1924825 Allgemeine Untersuchungen über das Newton'sche Princip der Fernwirkungen, mit besonderer Rücksicht auf die elektrischen Wirkungen] (B. G. Teubner, 1896)
* [http://www.archive.org/details/uberdiemetharith00neumrich Über die Methode des arithmetischen Mittels] (S. Hirzel, Leipzig, 1887) 
* [http://www.archive.org/details/elektriskrafte00neumrich Die elektrischen Kräfte] (Teubner, 1873-1898)

==References==
* {{MacTutor Biography|id=Neumann_Carl}}
* {{MathGenealogy|id=32858}}
* <span id="Cheng-05"></span> '''Cheng, A. and D. T. Cheng''' (2005). Heritage and early history of the boundary element method, ''Engineering Analysis with Boundary Elements'', '''29''', 268–302.

{{Authority control|VIAF=14850576}}

{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Neumann, Carl Gottfried
| ALTERNATIVE NAMES = Neumann, Karl Gottfried
| SHORT DESCRIPTION = Prussian mathematician
| DATE OF BIRTH     = May 7, 1832
| PLACE OF BIRTH    = [[Königsberg]], [[Province of Prussia|Prussia]]
| DATE OF DEATH     = March 27, 1925
| PLACE OF DEATH    = [[Leipzig]]
}}
{{DEFAULTSORT:Neumann, Carl}}
[[Category:1832 births]]
[[Category:1925 deaths]]
[[Category:19th-century German mathematicians]]
[[Category:20th-century mathematicians]]
[[Category:German mathematicians]]
[[Category:People from Königsberg]]
[[Category:People from the Province of Prussia]]
[[Category:Recipients of the Pour le Mérite (civil class)]]
[[Category:University of Königsberg alumni]]
[[Category:Martin Luther University of Halle-Wittenberg alumni]]
[[Category:Martin Luther University of Halle-Wittenberg faculty]]
[[Category:University of Tübingen faculty]]
[[Category:University of Leipzig faculty]]