377 The new results follow the company’s announcement from last month, according to which it succeeded in cracking the Navia-Stokes equation. This equation is one of the “millennium problems”, a series of mathematical puzzles that were considered so complex that a million dollar reward was offered to whoever could solve each one. While the achievement illustrated what the most advanced artificial intelligence models are capable of, it also raised questions about whether OpenAI’s systems were demonstrating creative thinking, or whether they were simply completing the final stages of mathematical proofs after drawing ideas from the work of human mathematicians. Similar to the Navia-Stokes solution, the new solutions were also obtained using an advanced model that has not yet been released to the public.
A few weeks ago, OpenAI announced that it is cooperating with an advisory committee of mathematicians, operating from the Institute for Advanced Research in Princeton and independent of technology companies, with the aim of formulating ways of presenting the results to the scientific community. The committee proposed, among other things, to reveal the instructions given to the artificial intelligence agents and their thought process. The company partially responded, and provided for 10 of the solutions summaries detailing how the model arrived at the result, when the average calculation time was about three hours per solution. Many of the proofs were verified using Lean, a programming language for logic testing.
However, the tension between the tech giant and academia remains. The advisory committee made it clear that it does not support the practice of technology companies testing their commercial models on advanced mathematical problems. On the other hand, Dan Roberts, head of the research team at OpenAI, claimed that the examination is necessary to create better tools, and the proofs are simply a byproduct of this process. Tristan Beckmaster, a mathematician at New York University who worked on the mathematical problem solved by OpenAI, was sharply critical, warning that human researchers using the models may be inadvertently providing them with the information that allows the AI to coupon them. “I don’t think they did their due diligence,” Beckmaster said of the massive release of the results.
Mathematicians are now grappling with whether the accelerated pace of problem solving is helping or hurting the field, especially as human understanding of the solutions lags behind. As Kai Sheikh, a student at the University of Toronto, put it: “Humans have two competing natures: a tendency to compete and an ability to appreciate beauty. It seems that this is a case where the former is trying to suffocate the latter.”