  Within the next few years, however, Hilbert came to reject Russell’s logicist solution to the consistency problem for arithmetic. At the same time,  Brouwer’s  intuitionistic mathematics gained currency. In particular, Hilbert’s former student Hermann Weyl converted to intuitionism. Weyl’s paper “The new foundational crisis in mathematics”  (1921)  was answered by Hilbert in three talks in Hamburg in the Summer of 1921  (1922b).  Here, Hilbert presented his own proposal for a solution to the problem of the foundation of mathematics. This proposal incorporated Hilbert’s ideas from 1904 regarding direct consistency proofs, his conception of axiomatic systems, and also the technical developments in the axiomatization of mathematics in the work of Russell as well as the further developments carried out by him and his collaborators. What was new was the way in which Hilbert wanted to imbue his consistency project with the philosophical significance necessary to answer Brouwer and Weyl’s criticisms: the finitary point of view.