ChatGPT-5.2 Independently Proves Mathematical Conjecture, Pioneering ‘Vibe Proving’

The Data Analytics Lab at Vrije Universiteit Brussel (VUB) studied Conjecture No. 20, proposed by Ran and Teng in 2024, concerning the region containing the non-real spectrum of four-cyclic row-stochastic nonnegative matrices. The work shows that OpenAI’s ChatGPT-5.2 (Thinking) can contribute original proofs at the research level, though its results still require rigorous human verification.

The paper was uploaded to arXiv on February 21, 2026, under identifier 2602.18918. The team analyzed seven ChatGPT conversations and four proof drafts using a generate, review and repair process. The model constructed the main argument, while human researchers corrected gaps involving quadrants, inequalities and endpoints. The result was a verifiable proof, and the team named the method “vibe proving.”