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'Neubegründung der Mathematik,' pp. 157-177 in Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, 1. Band, 2. Heft.

Hamburg: Verlag des mathematischen Seminars, 1922. First edition. First edition, journal issue in the original printed wrappers, and a copy with excellent provenance, of the first major paper in the development of the 'Hilbert programme,' in which Hilbert put forward his proposal for a foundation for all of mathematics based on axiomatics and logic. Hilbert's programme "was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic" (Wikipedia). "According to Reid [Hilbert-Courant (1970), p. 154), Hilbert was becoming, in the early 1920s, 'increasingly alarmed by the gains that Brouwer's conception of mathematics was making among the younger mathematicians. To him, the program of the Intuitionists represented quite simply a clear and present danger to mathematics'. Hilbert interpreted intuitionism as requiring that all pure existence proofs, a large part of analysis and Cantor's theory of infinite sets would have to be given up. In particular, this would rebut some of Hilbert's own important contributions to pure mathematics. Hilbert was especially disturbed by the fact that Weyl, w

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**1922**