No algorithm solves Hilbert's Tenth Problem over Q: OpenAI release's slept-on math result, explained
aran_nayebi · x · 2026-10-08
Researcher Aran Nayebi highlights an underrated result from OpenAI's recent release: no algorithm can solve Hilbert's Tenth Problem over Q. Unlike the 80-year human approach (Julia Robinson, Poonen) of first defining the integers inside Q, the proof sidesteps that entirely — using sequences of finite rational tests plus elliptic-curve/size constraints to transfer undecidability from Z to Q.
Related event: OpenAI Model Proves Hilbert's Tenth Problem Undecidable over the Rationals(5 posts)→
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