**Carl Neumann** was a German mathematician who worked on the Dirichlet principle and on integral equations. He was one of the founders of *Mathematische Annalen*.

- Carl's siblings were Franz Ernst Christian Neumann (1834-1918), Friedrich Julius Neumann (1835-1910), and Luise Neumann (1837-1934).
- Let us note at this point that Franz Ernst Christian Neumann became a pathologist and director of the Pathological Institute at Königsberg, and Friedrich Julius Neumann became an economist, holding professorships in Königsberg, Basel, Freiburg and Tübingen.
- Luise Neumann became a painter creating landscapes and portraits, as well as interiors of cultural and historical buildings in Königsberg.
- His secondary education was at the Altstadt Gymnasium which, when he began his studies, was situated in the street Danziger Keller near Königsberg Castle but, after a period in temporary accommodation, the school moved to a new building in Altstädtischer Kirchplatz in which Carl completed his schooling.
- Neumann entered the University of Königsberg where he became close friends with two of his teachers, Otto Hesse and Friedrich Julius Richelot (1808-1875).
- Richelot had been a student of Carl Jacobi and taught at the University of Königsberg from 1831, becoming a full professor in 1844.
- After graduating with a qualification to teach mathematics in secondary schools, Neumann continued to study at Königsberg for his doctorate which was awarded in 1855 for his thesis De problemate quodam mechanico, quod ad primum integralium ultraellipticorum classem revocatur Ⓣ(On a problem in mechanics, whose integral is called ultraelliptical).
- After receiving his doctorate, Neumann studied for his habilitation advised by Eduard Heine who had been appointed as an ordinary professor at Halle in 1856.
- Neumann submitted his habilitation thesis Explicare tentatur, quomodo fiat, ut lucis planem polarisationis per vires electricas vel magneticas declinetur Ⓣ(Attempt to explain how it is that the polarization plane of light is altered by magnetic or electical forces) to the University of Halle in 1858.
- Neumann did not remain at Halle for long after his promotion for he was offered a professorship at the University of Basel.
- Neumann's inaugural lecture at Tübingen was Der gegenwdrtige Standpunct der Mathematischen Physik Ⓣ(The current position of mathematical physics) and in this he discussed applications of potential theory to electrodynamics, optics and the theory of heat.
- After a slightly longer time, namely three years, spent in Tübingen, from 1865 to 1868, Neumann was on the move again, this time to a chair at the University of Leipzig.
- The notes had been taken by Wilhelm Scheibner who was now Neumann's colleague in Leipzig.
- Now, like Jacobi, Neumann took his goal to be to start from some unanalyzable basic assumptions or principles and to deduce general theorems from them, in this way constructing a physical theory of the field under consideration.
- Ernst Neumann became a mathematician and studied at Königsberg, Heidelberg and then at the University of Leipzig from 1893 to 1898.
- Ernst Neumann went on to become a professor at Breslau and Marburg.
- Neumann made assumptions some of which followed those made by Wilhelm Weber.
- This led to a debate between various scientists, in particular between Helmholtz and Neumann.
- with one and the same relatively simple mathematical expression." He noted with satisfaction that Neumann had required many hypotheses to reach a similar result.
- Neumann stuck to his guns, however, although he acknowledged that conservation of energy was a basic principle of physics, and he admitted that Helmholtz's theory appeared to have a simpler structure.
- One important reason, in general, that Neumann opposed Helmholtz's approach was that Helmholtz's states of energy and their interaction made the explanation of many electrodynamic phenomena more complicated than explanations based upon Weber's or Maxwell's theories.
- Neumann also made important pure mathematical contributions.
- During the 1860s Neumann wrote papers on the Dirichlet problem and the 'logarithmic potential', a term he coined.
- In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equation.
- There are a great many mathematical terms named after 'Neumann' but it is such a common name that often it is difficult to determine which are named after Carl Gottfried Neumann.
- For example, MathSciNet lists 7357 papers with 'Neumann' in the title.
- Several terms are easy to establish as being named after Carl Neumann, however, such as the Neumann-Poincaré Operator, the Neumann boundary value problem, the Neumann boundary condition, the Neumann series, and the Neumann problem.
- In addition to his research and teaching, Neumann made another important contribution to mathematics as a founder and editor of Mathematische Annalen.
- The volume, in four parts, contained five papers by Neumann, namely: Geometrische Untersuchung über die Bewegung eines starren Körpers Ⓣ(Geometrical examination of the motion of a rigid body); Zur Theorie der Functionaldeterminanten Ⓣ(On the theory of functional determinants); Notizen zu einer kürzlich erschienenen Schrift über die Principien der Elektrodynamik Ⓣ(Notes on a recently published treatise on the principles of electrodynamics); Über die Aetherbewegung in Krystallen Ⓣ(On the aether movement in crystals); and Notiz über das cykloidische Pendel Ⓣ(Note on the cyclic pendulum).
- For this reason, Neumann himself preferred publication in the form of monographs and textbooks.
- The idea of founding a new journal was considered, but it was Neumann who gave it life by working with the right publisher in the company Teubner, with whom he had been in business for some time, recognised the ideal editor in Clebsch, a friend he studied with in his youth, and brought them together.
- This happened in a letter to Teubner of 10 June 1868, which has been printed several times, in which Neumann summarizes the duties of a good editor in three sentences of classical correctness and conciseness.
- How much credit he gave himself for his share in the founding of the Annalen, is seen by the heading which he gave after the death of Clebsch: "Founded by Rudolf Friedrich Alfred Clebsch in conjunction with Carl Neumann".
- A later period has changed this modest formulation, by placing the two names Clebsch and Neumann side by side.
- Neumann was probably far from the actual editorial activity.

Born 7 May 1832, Königsberg, Germany (now Kaliningrad, Russia). Died 27 March 1925, Leipzig, Sachsen, Germany.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive