AI-assisted proof shows ℤ is Diophantine in ℚ via a 292M-variable polynomial
littmath · x · 2026-11-06
Mathematician Elliot Glazer announced, with help from AI models (Astra and Claude), a proof that ℤ is Diophantine in ℚ: an integer-coefficient polynomial in 292,890,231,905 variables whose rational zero projection is exactly ℤ, of degree < 2↑↑7 with coefficients bounded by 2↑↑8. Consequences include a refutation of Mazur's conjecture on topological closure of rational points, a universal rational Diophantine polynomial, and HTP(ℚ) being many-one equivalent to the halting set 0′ — a major step on Hilbert's tenth problem over ℚ and a landmark for AI-assisted mathematics.
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