Can machines prove everything? Turing, Gödel and the practical limits of AI mathematics
jamestagg · x · 2026-09-12
The author poses a philosophical question: with the Turing test passed, can OpenAI and others keep finding proofs until nothing remains?
- Gödel and Turing set theoretical limits, but is there a practical limit stopping a machine from proving everything a human could?
- He uses a cosmological analogy: imagine the universe starts with some information and fixed computational rules; galaxies form, life evolves, and eventually a mathematician proves a theorem — the proof follows from the same starting information, like pressing play on a DVD.
- Theorems by Kolmogorov and Matiyasevich tell us something about the size of information needed to explain mathematics, framing the boundary of machine provability.
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