AI model originates new proof of Odlyzko-Poonen conjecture, fully formalized in Lean
fedzbar · x · 2026-09-30
- Constantin Kogler published his first paper in which an AI model entirely came up with a new proof, which he then spent time understanding and rewriting.
- The result proves the Odlyzko-Poonen conjecture unconditionally: a monic polynomial with constant coefficient 1 and remaining coefficients drawn uniformly from {0,1} is irreducible over the rationals with probability tending to one as degree grows.
- The model found a niche but known trick (dubbed the "twin factorization trick") yielding a rather simple solution to a longstanding question.
- The proof is fully formalized in Lean; the 11-page paper is on arXiv (2609.26771).
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