OpenAI Is Close to Solving the Hodge Conjecture, Math May Be the Next Testing Ground for Large Models

According to The Information, OpenAI is close to solving the Hodge Conjecture, one of the Millennium Prize Problems. The controversial Navier-Stokes existence and smoothness problem is also part of this set of seven major math problems. A source says OpenAI staff expect the Hodge Conjecture may be solved soon.

The Hodge Conjecture studies whether certain geometric features in shapes defined by polynomial equations can always be described by simpler algebraic structures. Even if a solution is found, OpenAI may not announce it right away. The company is considering how to release the news with the math community to avoid another PR crisis.

Some OpenAI researchers believe that after software engineering, math is the most natural next testing ground for large models. Both rely on step-by-step logical reasoning, and results can be automatically verified. Some researchers predict that the automation process seen in software engineering could unfold in math within the next 6 to 9 months. Solving hard math problems also helps automate machine learning research itself, an important step toward "AI developing AI."