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google-deepmind/formal-conjectures

The Formal Conjectures Authors, Moritz Firsching, Codrut Grosu, Reklle

Palomar Registrypalomar/PALOMAR-2026-08-20-000005Aug 20, 2026math.NTscore 0

Formal proof of the First Cuboid Conjecture, which states that for all positive coprime integers a, b with a ≠ b, a certain degree-8 polynomial P_{a,b}(t) over ℤ is irreducible. This conjecture was proposed by Shapirov in "Perfect cuboids and irreducible polynomials" (arXiv:1108.5348) as part of a family of three conjectures whose combined truth would imply the nonexistence of a perfect Euler brick. The proof first analyses rational factors and the symmetry F(−x) vs F(x) to reduce irreducibility of the degree-8 polynomial to irreducibility of a degree-4 factor Q_{a,b}, and the coprime branch…

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