# Carl Neumann

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

Carl Neumann
Born7 May 1832
Died27 March 1925 (aged 92)
NationalityGerman
Alma materKönigsberg University
Halle
Known forDirichlet problem
Neumann series
Scientific career
Fieldsintegral equations
InstitutionsUniversity of Halle-Wittenberg
University of Basel
University of Tübingen
University of Leipzig.
ThesisDe problemate quodam mechanico, quod ad primam classem integralium ultraellipticorum revocatur[1]
Doctoral advisorFriedrich Richelot and Otto Hesse
Doctoral studentsWilliam Edward Story
Emil Weyr

## Biography

Neumann was born in Königsberg, 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 Halle and was a professor at the universities of Halle, Basel, Tübingen, and Leipzig.

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 and Rudolf Clausius 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.[2] Maxwell makes reference to the electrodynamic theory developed by Weber and Neumann in the Introduction to A Dynamical Theory of the Electromagnetic Field (1864).

Neumann worked on the Dirichlet principle, and can be considered one of the initiators of the theory of integral equations. The Neumann series, which is analogous to the geometric series

${\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+\cdots }$

but for 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 equations is named after him (Cheng and Cheng, 2005).

## Notes

1. Christa Jungnickel, Russell McCormmach, Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein (1990) Vol. 1. p. 181.

## References

• O'Connor, John J.; Robertson, Edmund F., "Carl Neumann", MacTutor History of Mathematics archive, University of St Andrews.
• Carl Neumann at the Mathematics Genealogy Project
• Cheng, A. and D. T. Cheng (2005). Heritage and early history of the boundary element method, Engineering Analysis with Boundary Elements, 29, 268–302.
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