David Hilbert

David Hilbert publishes 'Grundlagen der Geometrie', axiomatizing geometry and emphasizing formal axiomatic method

Hilbert presents his 23 problems at International Congress, including consistency of arithmetic (Problem 2)

Hilbert proposes his program to prove consistency of mathematics using finitary methods

Hilbert and Ackermann publish 'Grundzüge der theoretischen Logik', first modern textbook on mathematical logic

Gödel announces his incompleteness theorems at Königsberg conference, shocking the mathematical community