Machine-Checkable Proofs and AI Advancements
The mathematicians published machine-checkable proofs of a significant mathematical result. OpenAI announced its achievement on a call with reporters, claiming an internal model proved that 3D Navier-Stokes can develop a singularity in finite time.
OpenAI’s Claim:
- They assert that their model, reportedly more capable than GPT-6 Astra, achieved this using approximately 10,000 agents over 88 hours, at a cost estimated in the millions of dollars.
- The result was described during a press call, but the proof itself remained unpublished.
Related Developments:
- Tristan Buckmaster and Levent Alpoge from NYU and Anthropic, respectively, published preprints on closely associated problems, including the incompressible porous medium equation and the 3D incompressible Euler equations.
- These preprints included Lean formalisations, allowing the proofs to be machine-checked rather than solely relied upon.
Dispute and Verification:
- Buckmaster expressed skepticism about OpenAI’s claim, questioning the origin of their research direction and potential involvement of private Codex material.
- OpenAI denies these allegations, stating that neither their researchers nor agents accessed user data, and the internal model solved the problem through distinct means.
- The absence of a published proof and the lack of direct access to the methodology raise questions, emphasizing the importance of machine-checkable proofs in mathematics.
Implications:
- This incident highlights the significance of verification in AI-driven research, especially when models are involved.
- The ability to machine-check proofs is crucial, as demonstrated by DeepMind’s experience with Lean formalisations.
- OpenAI’s announcement, while exciting, underscores the need for transparent and verifiable evidence in the AI community.