Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician.

His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in 1907–1909.

[1] He conjectured the Koebe quarter theorem on the radii of disks in the images of injective functions, in 1907.

His conjecture became a theorem when it was proven by Ludwig Bieberbach in 1916, and the function

providing a tight example for this theorem became known as the Koebe function.