OpenAI recently announced that its AI model had solved the Navier-Stokes problem, one of the world's toughest math problems. The company's tone was celebratory, emphasizing its goal of empowering scientists to advance research and technology that benefits humanity. However, mathematicians have expressed mixed feelings about the achievement, citing difficulties in understanding the solution.
The Navier-Stokes problem concerns a set of equations used to describe fluid flow, widely used in physics and engineering. Despite its importance, researchers do not fully understand why the equations work. A solution could yield a new toolkit for understanding complex fluid solutions, leading to better models of turbulence and lift in aircraft. Mathematicians had been working towards an answer for years, sensing they were close to a breakthrough.
OpenAI's solution was reportedly found using 10,000 AI agents working for 88 hours, generating around 130 billion output tokens. The company's pricing suggests the solution cost between $6-$10 million to compute. However, the announcement sparked controversy, with mathematician Tristan Buckmaster claiming OpenAI approached him with an offer to put him on their paper if he dropped his collaborator, Levent Alpöge.
Mathematicians who reviewed OpenAI's 166-page proof described it as difficult to read and virtually unreadable. The paper lacks clear explanations of important parts, routine sections, and connections to other areas of research. Buckmaster and others have expressed frustration that the rushed results seem muddled, forcing him to publish his own preliminary results, also heavily influenced by AI.
While OpenAI's proof is taking weeks to untangle, few mathematicians believe it's incorrect. The company also produced a piece of computer code called a Lean formalization, which checks if proofs are correct. If the code can be compiled, the proof is considered complete. This verification process has provided some confidence in the solution.
In response to criticism, OpenAI announced the establishment of an independent mathematics advisory group to help with the review and dissemination of new results. However, the group will not advise on the pace of OpenAI's internal progress on mathematics. Mathematicians had signed a statement decried "misaligned goals" between AI companies and the mathematics community.
The intersection of AI and mathematics is rapidly evolving, with large language models appearing capable of producing real results that could lead to new discoveries. However, the collaboration between humans and AI remains a topic of debate, with some calling for more effective partnerships to unlock the full potential of AI in mathematics.
Key points
- OpenAI's AI model solves Navier-Stokes problem, but understanding lags
- Mathematicians struggle to grasp solution due to dense, 166-page manuscript
- Controversy surrounds OpenAI's announcement, with concerns over rushed results and collaboration with human mathematicians
