 Some of von Neumann's instant solutions to the problems that Szegő posed in calculus are sketched out on his father's stationery and are still on display at the von Neumann archive in Budapest.By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition.At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics.