[1] In 1815 he paused his education at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was wounded in the Battle of Ligny.

Subsequently, he enrolled at Berlin University in 1818 as a student of theology, but soon turned to scientific subjects.

[2] Devoting himself next to optics, he produced memoirs which earned him a high place among early searchers of a true dynamical theory of light.

In 1832, by the aid of a particular hypothesis as to the constitution of the ether, he reached by a rigorous dynamical calculation results agreeing with those obtained by Augustin Louis Cauchy, and succeeded in deducing laws of double refraction closely resembling those of Augustin-Jean Fresnel.

This assumption substantially reduced the number of independent constants and greatly simplified the elastic equations.

In 1900, Voigt attributed this principle to Neumann's 1832 paper even though, at most, all that was present in that work was an implicit assumption that the symmetry of the phenomenon was equal to that of the crystal.

Bernhard Minnigerode (1837–1896), another student of Neumann, first expressed this relation in written form in 1887 in the journal Neues Jahrb.

[3] In 1845, Neumann introduced the magnetic vector potential to discuss Ampère's circuital law.