Hilbert's Program is a foundational project in mathematical logic initiated by David Hilbert in the early 20th century, aimed at providing a secure foundation for all of mathematics through formalization and proof of consistency. The program sought to establish that all mathematical truths could be derived from a finite set of axioms using formal proofs, thereby ensuring the reliability of mathematics as a whole. However, it faced significant challenges due to Gödel's Incompleteness Theorems, which showed inherent limitations in proving consistency within the framework of arithmetic.
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