 Following the publication of Russell’s paradox, Hilbert presented an address to the Third International Congress of Mathematicians in 1904, where, for the first time, he sketched his plan to provide a rigorous foundation for mathematics via syntactic consistency proofs. But he did not return to the subject in earnest until 1917, when he began a series of lectures on the foundations of mathematics with the assistance of Paul Bernays. Although Hilbert was impressed by the work of Russell and Whitehead in their Principia Mathematica, he became convinced that the logicist attempt to reduce mathematics to logic could not succeed, due in particular to the non-logical character of their axiom of reducibility. At the same time, he judged the intuitionistic rejection of the law of the excluded middle as unacceptable to mathematics. Therefore, in order to counter concerns raised by the discovery of the logical and set-theoretic paradoxes, a new approach was needed to justify modern mathematical methods.