Carl Neumann

Carl Gottfried Neumann (also Karl; 7 May 1832 – 27 March 1925) was a German mathematical physicist and professor at several German universities. His work focused on applications of potential theory to physics and mathematics. He contributed to the mathematical formalization of electrodynamics and analytical mechanics. Neumann boundary conditions and the Neumann series are named after him.

Biography Carl Gottfried Neumann was born in Königsberg, Prussia, as one of the four children of the mineralogist, physicist and mathematician Franz Ernst Neumann (1798–1895), who was professor of mineralogy and physics at the University of Königsberg. His mother Luise Florentine Hagen (born 1800) was the sister-in-law of mathematician Friedrich Wilhelm Bessel.

Neumann's wife died in 1876 and Neumann retired from the Leipzig University in 1911. . (This is not quite correct as Maxwell theory is not Galilei invariant: Both Hertz and Neumann did not give up absolute time.) He also argued that for Newtonian mechanics to make sense there should exist an immovable object in the universe called the Body Alpha, relative to which all speeds can be measured. The problem of reference frames was solved in 1905 by Albert Einstein's special relativity.

In 1865, he wrote Vorlesungen über Riemanns Theorie der Abelschen Integrale on abelian integrals. This book popularized Bernhard Riemann’s work on multivalued functions among mathematicians.

Several objects developed later in mathematics are named after his Neumann problem including the Neumann–Neumann methods and the Neumann–Poincaré operator by Henri Poincaré.

Selected works

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)