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OpenAI's recent proof settling a long-standing question about the Navier-Stokes equations includes a formal proof in Lean 4, which represents a transformative breakthrough in mathematical verification. Traditionally, formalizing research mathematics required approximately 132,800 person-hours per paper, but OpenAI completed their 166-page proof verification in just 17 hours—a reduction in cost by four orders of magnitude. This dramatic efficiency gain makes formal verification practical for mathematics, security policies, smart contracts, and other mission-critical applications that were previously economically infeasible to formally verify.
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