In the early 1920s, in talks in Hamburg in 1921 and in lectures at Göttingen, David Hilbert set out his Beweistheorie, proof theory. Its aim was to make the proofs of mathematics themselves the object of investigation, and to show that no contradiction could ever be derived within the system.
On 8 September 1930 Hilbert spoke at a congress of German scientists and physicians in Königsberg. In mathematics, he said, there is no Ignorabimus, no “we shall not know.” He ended with the words Wir müssen wissen. Wir werden wissen. We must know. We will know. The words are on his gravestone in Göttingen. On the day before, at a conference in the same city, Kurt Gödel had announced the result that dealt Hilbert’s program a severe blow.