Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups, and knot theory.

He was born at Ybbs on the Danube and studied at the University of Vienna, where he received his doctorate in 1887, and his habilitation in 1890.

In 1907 the Royal Society of London awarded him the Sylvester Medal, for his contributions to the general theory of functions.

He proposed as a generalization of eigenvalues, the concept of the spectrum of an operator, in an 1897 paper; the concept was further extended by David Hilbert and now it forms the main object of investigation in the field of spectral theory.

Wirtinger also contributed papers on complex analysis, geometry, algebra, number theory, and Lie groups.