Carl Gottfried Neumann (also Karl; 7 May 1832 – 27 March 1925) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Biography

Neumann was born in

Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was name ...

Prussia Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an ...

, as the son of the mineralogist, physicist and mathematician

Franz Ernst Neumann Franz Ernst Neumann (11 September 1798 – 23 May 1895) was a German mineralogist, physicist and mathematician. Biography Neumann was born in Joachimsthal, Margraviate of Brandenburg, near Berlin. In 1815 he interrupted his studies at Berlin to ...

(1798–1895), who was professor of mineralogy and physics at Königsberg University. Carl Neumann studied in Königsberg and Halle and was a professor at the universities of Halle,

Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS ...

Tübingen Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in three ...

, and

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...

. While in Königsberg, he studied physics with his father, and later as a working mathematician, dealt almost exclusively with problems arising from physics. Stimulated by Bernhard Riemann's work on electrodynamics, Neumann developed a theory founded on the finite propagation of electrodynamic actions, which interested

Wilhelm Eduard Weber Wilhelm Eduard Weber (; ; 24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph. Biography of Wilhelm Early years Weber was born in Schlossstrasse i ...

and

Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...

into striking up a correspondence with him. Weber described Neumann's professorship at Leipzig as for "higher mechanics, which essentially encompasses mathematical physics," and his lectures did so.

Christa Jungnickel Christa Jungnickel (11 April 1935 – 12 August 1990) was a German-American historian of science. Life Jungnickel was originally from Germany, one of three daughters of a German soldier who was lost in Russia during World War II. As a teenager, ...

, Russell McCormmach, '' Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein'' (1990) Vol. 1. p. 181. Maxwell makes reference to the electrodynamic theory developed by Weber and Neumann in the Introduction to

A Dynamical Theory of the Electromagnetic Field "A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...

(1864). Neumann worked on the

Dirichlet principle In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation. Formal statement Dirichlet's principle states that, if the functio ...

, and can be considered one of the initiators of the theory of

integral equation In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ...

s. The

Neumann series A Neumann series is a mathematical series of the form : \sum_^\infty T^k where T is an operator and T^k := T^\circ its k times repeated application. This generalizes the geometric series. The series is named after the mathematician Carl Neumann ...

, which is analogous to the

geometric series In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series :\frac \,+\, \frac \,+\, \frac \,+\, \frac \,+\, \cdots is geometric, because each suc ...

\frac = 1 + x + x^2 + \cdots

but for infinite matrices or for

bounded operator In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X \to Y between topological vector spaces (TVSs) X and Y that maps bounded subsets of X to bounded subsets of Y. If X and Y are normed vector ...

s, is named after him. Together with Alfred Clebsch, Neumann founded the mathematical research journal '' Mathematische Annalen''. He died in Leipzig. The

Neumann boundary condition In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative appli ...

for certain types of ordinary and partial differential equations is named after him ( Cheng and Cheng, 2005).

Works by Carl Neumann

Neumann, Carl – Hydrodynamische Untersuchungen, 1883 – BEIC 12393955

* * * *
Das Dirichlet'sche Princip in seiner Anwendung auf die Riemann'schen Flächen
(B. G. Teubner, Leipzig, 1865)
Vorlesungen über Riemann's Theorie der Abel'schen Integrale
(B. G. Teubner, 1865) *
Theorie der Bessel'schen functionen: ein analogon zur theorie der Kugelfunctionen
(B. G. Teubner, 1867)
Untersuchungen über das Logarithmische und Newton'sche potential
(B. G. Teubner, 1877) *
Über die Methode des arithmetischen Mittels
(S. Hirzel, Leipzig, 1887)
Allgemeine Untersuchungen über das Newton'sche Princip der Fernwirkungen, mit besonderer Rücksicht auf die elektrischen Wirkungen
(B. G. Teubner, 1896)
Die elektrischen Kräfte
(Teubner, 1873–1898)

Notes

References

* * * Cheng, A. and D. T. Cheng (2005). Heritage and early history of the boundary element method, ''Engineering Analysis with Boundary Elements'', 29, 268–302. {{DEFAULTSORT:Neumann, Carl 1832 births 1925 deaths 19th-century German mathematicians 20th-century German mathematicians Scientists from Königsberg People from the Province of Prussia Recipients of the Pour le Mérite (civil class) University of Königsberg alumni Martin Luther University of Halle-Wittenberg alumni Martin Luther University of Halle-Wittenberg faculty University of Tübingen faculty Leipzig University faculty Recipients of the Thorvaldsen Medal Burials at the Garrison Cemetery, Copenhagen

Biography

See also

Works by Carl Neumann

Notes

References