Kurt Gödel publishes in 1931, in Vienna, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems"), where he proves his two incompleteness theorems: no consistent formal system powerful enough to describe arithmetic can be both complete, and no such system can prove its own consistency from within itself. The result, first presented incidentally at a conference in Königsberg in September 1930, destroys at its root Hilbert's program, which sought to ground all of mathematics on a set of axioms that was both consistent and complete. John von Neumann, present at that conference, independently arrived at the corollary of the second theorem almost immediately after hearing Gödel, although Gödel already had it independently. Gödel's theorems would lay the conceptual groundwork on which, more than three decades later, Paul Cohen would prove the independence of the continuum hypothesis from the axioms of set theory.