Carl Gottfried Neumann (May 7, 1832 - March 27, 1925) was a German mathematician.

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.

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

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.