GPT-5.4 Pro cracks a 60-year-old Erdős math problem in 80 minutes

GPT-5.4 Pro just solved Erdős Problem #1196 — a conjecture on the asymptotic behavior of primitive sets (sets where no element divides another) that had been open since the late 1960s.

The model cracked it in a single attempt after ~80 minutes of reasoning, then formatted the full proof as a LaTeX paper in another 30. The approach was novel: instead of the probabilistic methods that dominated the field since Erdős, the model used Markov chain theory anchored to the von Mangoldt function — a connection no human mathematician had made explicit before.

Terence Tao described the result as "a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdős problem." Formal verification is still underway, but expert reception has been unusually positive for an AI math result.

Why it matters: this isn't pattern-matched theorem proving — it's original analytic number theory from a model that invented its own technique to get there.