GPT-5.4 Pro solves Erdős Problem #1196
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| Source: HN | Original article
OpenAI’s latest flagship, GPT‑5.4 Pro, announced on Monday that it has produced a full proof of Paul Erdős’s open Problem #1196, a combinatorial question that has resisted specialist attempts for more than a decade. According to the company’s internal blog, the model spent roughly 80 minutes “thinking” before outputting a LaTeX manuscript in another 30 minutes. The proof was posted to the arXiv within hours and is already being examined by senior mathematicians, including Jared Lichtman, who has worked on the problem for seven years.
The breakthrough matters because it marks the first time a general‑purpose language model has resolved a non‑trivial, unsolved problem from the Erdős catalogue, a benchmark of pure‑math difficulty. The model’s approach—building a sub‑Markov chain and exploiting a non‑standard lemma—differs from traditional human techniques, suggesting that AI can explore unconventional proof strategies. If the result withstands peer review, it will bolster confidence that large‑scale generative models can act as autonomous research assistants, accelerating discovery in fields where intuition and creativity dominate.
OpenAI plans to subject the proof to formal verification in its upcoming “Big Potato” model, which promises tighter integration with theorem‑proving environments. The community will be watching for a formalised version in Coq or Lean, as well as for replication attempts on other open Erdős problems. Meanwhile, the rapid turnaround has sparked debate about attribution, peer‑review standards, and the future role of AI in mathematics. The next milestone will be whether GPT‑5.4 Pro’s solution survives rigorous scrutiny and becomes part of the permanent mathematical record.
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