Dossier · Ongoing

AI proofs in mathematics

How OpenAI models have been solving decades-old mathematics and cryptography problems since July 2026 – and who verifies the proofs.

Since July 2026, reports have piled up in which OpenAI models deliver solutions to problems that had resisted the research community for decades: an alleged proof of the Cycle Double Cover Conjecture, a counterexample to a twenty-year-old assumption behind the Benjamini-Hochberg procedure, ten solved problems in mathematics and theoretical computer science from the unreleased Astra model, and two independently produced proofs on unclonable encryption.

This dossier follows the thread and the question that recurs in every single case: how reliable are the results while independent peer review is still pending? It documents the announcements themselves, the role human researchers play in the process, the verification methods – from machine-checkable Lean certificates to classical peer review – and the consequences for scientific authorship and the training of early-career researchers.

Timeline

  1. GPT-5.6 Sol Ultra proves math conjecture – experts still examining

    An AI-generated proof for a graph theory puzzle published by OpenAI sparks debate about prompt design and lack of independent verification.

  2. OpenAI: Astra model solves ten unsolved math problems

    OpenAI's upcoming model Astra provides proofs experts struggled with for years – verifiable through Lean certificates, ahead of a US model review.