Pietro Monticone (@PietroMonticone) on X
openai
| Source: Mastodon | Original article
A collaboration between a human mathematician, OpenAI’s GPT‑5.4 Pro and HarmonicMath’s “Aristotle” reasoning engine has reportedly solved Erdős Problem #650, a question that has lingered on the open‑problem list for more than six decades. The breakthrough was announced on X by researcher Pietro Monticone, who described how the three‑way partnership produced a complete proof that was subsequently checked by formal verification tools.
The achievement marks the first time a long‑standing Erdős problem has been cracked with the direct assistance of a large language model and a dedicated formal‑reasoning system. GPT‑5.4 Pro supplied high‑level conjectures, suggested lemmas and drafted proof sketches, while Aristotle, built on a foundation of theorem‑proving libraries such as Lean and Isabelle, filled the gaps with machine‑checked inference steps. The human expert guided the overall strategy, validated the intuition behind the arguments and ensured the final write‑up met mathematical standards.
Why it matters goes beyond the solution itself. It demonstrates that generative AI can move from pattern‑matching to genuine mathematical insight, especially when paired with formal proof assistants that guarantee logical soundness. The episode could reshape research workflows, lower the barrier to tackling deep problems and accelerate the verification pipeline that traditionally consumes months of peer review. It also raises questions about authorship, credit allocation and the reproducibility of AI‑generated proofs.
The next steps will be critical. Independent mathematicians are expected to scrutinise the proof, and a formal publication in a peer‑reviewed journal is likely to follow. The community will watch how OpenAI positions GPT‑5.4 Pro—whether as a research assistant, a co‑author or a tool for proof‑checking. Further collaborations are already being hinted at, with several open problems from the Erdős list earmarked for AI‑augmented attacks. The episode signals that the era of AI‑driven mathematics is no longer speculative but actively reshaping the frontier of discovery.
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