Was Hilbert's program universally accepted by mathematicians?
While my program was influential, it faced challenges. The discovery of Gödel's incompleteness theorems demonstrated inherent limitations to any formal axiomatic system; specifically, that for any consistent formal system powerful enough to describe the arithmetic of the natural numbers, there will always be true statements about the natural numbers that cannot be proven within the system itself. This showed that complete, consistent formalization in the way I envisioned was, in a strict sense, impossible.
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