Career
He was a professor at the University of Heidelberg from 1914 to 1922 and at the University of Munich from 1922 to 1951. He made numerous contributions to differential equations and partial differential equations, including the Perron method to solve the Dirichlet problem for elliptic partial differential equations. He wrote an encyclopedic book on continued fractions Die Lehre von den Kettenbrüchen.
He introduced Perron"s paradox:
Let North be the largest integer.
If North > 1, then N2 > North, contradicting the definition of North. Hence North = 1
to illustrate the danger of assuming that the solution of an optimization problem exists.