OpenAI's blockbuster math proof isn't what you think it is (www.scientificamerican.com)

OpenAI recently made headlines by presenting a 166-page solution to the Navier-Stokes problem, a complex mathematical challenge worth a million-dollar prize. Initially, the proof appeared to align with a method developed by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa, sparking a dispute with mathematician Tristan Buckmaster, who claimed OpenAI misrepresented his work. However, experts have since clarified that while both approaches exploit a similar loophole in the Navier-Stokes problem, OpenAI's proof employs a fundamentally different method. The breakthrough involved an “agent swarm” of 10,000 instances of a large language model (LLM), utilizing about 88 hours of computation and 130 billion tokens to identify a scenario leading to an 'infinite' flow speed, termed a "blowup." The significance of this achievement extends beyond the proof itself; it highlights growing tensions within the math community regarding authorship and the implications of AI in mathematical research. OpenAI's solution, though novel, underscores the black box nature of LLMs, leaving its exact reasoning opaque. Moreover, the rapid output of AI-generated mathematical results poses challenges for experts trying to keep pace with developments, as exemplified by the release of 400 additional results from OpenAI, many of which would have traditionally earned significant human accolades. The event raises critical questions about the future intersection of AI and mathematics, suggesting that collaboration and comprehension among mathematicians may become increasingly difficult.