LLMs solving original math proofs
A Brussels study shows commercial LLMs like ChatGPT‑5.2 are now solving original math proofs and outperforming their coding/text abilities on pure logical tasks — a notable reasoning milestone (x.com). For teams building verification or symbolic reasoning tools, this opens new integration opportunities for proof‑assistance workflows (x.com).
An arXiv preprint titled "Early Evidence of Vibe‑Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT‑5.2 (Thinking)" was posted Feb. 24, 2026 by researchers at the Vrije Universiteit Brussel's Data Analytics Lab (authors: Brecht Verbeken, Brando Vagenende, Marie‑Anne Guerry, Andres Algaba, Vincent Ginis). (arxiv.org) The paper reports a resolved instance of "Conjecture 20" from Ran and Teng (2024), specifically giving necessary-and-sufficient region conditions and explicit boundary‑attainment constructions for the exact nonreal spectral region of a 4‑cycle row‑stochastic nonnegative matrix family. (arxiv.org) The authors document seven shareable ChatGPT‑5.2 (Thinking) threads and four versioned proof drafts that together produced the final argument, characterizing their workflow as an iterative "generate → referee → repair" pipeline. (arxiv.org) The team coins the workflow term "vibe‑proving" (by analogy with "vibe‑coding") and emphasizes the model used was a consumer subscription instance of ChatGPT‑5.2 (Thinking) rather than a bespoke research model. (vub.be) Authors report that the LLM was most effective at high‑level proof search while human experts were required for final verification and closure, a point underscored in the lab's March 16, 2026 press release and accompanying coverage. (vub.be) (phys.org) Beyond the theorem itself, the paper frames a process‑level contribution: the auditable, shareable ChatGPT threads and versioned drafts expose where LLM assistance reduces search cost and where symbolic verification bottlenecks remain for future human‑in‑the‑loop theorem‑proving systems. (arxiv.org)
