AI-Assisted Proof Shows Z Is Diophantine in Q With a 292-Billion-Variable Polynomial
pickover · x · 2026-11-06
Mathematician Elliot Glazer published a new manuscript proving that ℤ is Diophantine in ℚ — with heavy AI assistance.
- Constructs an integer-coefficient polynomial in 292,890,231,905 variables whose rational zero projection is exactly ℤ
- Degree below 2↑↑7; every coefficient under 2↑↑8 in absolute value
- Consequences include a refutation of Mazur's conjecture on topological closures of rational points, a universal rational Diophantine polynomial, and HTP(ℚ) being many-one equivalent to the halting set 0′
The GitHub repo includes the PDF, TeX source, constructions, proof drafts, reviews, and partial Lean formalization.
Related event: Mathematician Uses AI to Prove ℤ Is Diophantine in ℚ(3 posts)→
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