Foreign media report that Terence Tao, a professor at UCLA and Fields Medalist, recently issued a public warning that AI is consuming open problems that truly drive the advancement of mathematics faster than the mathematical community can replenish them. According to him, the risk is not that models will produce more proofs, but that they may compress the space long explored by researchers too quickly.
High-value challenges are becoming fewer.
Terence Tao points out that math problems can be generated infinitely, but truly important ones are few. Many unsolved problems exist, yet they may not lead to new methods or significantly advance related fields. In the past, researchers relied on experience to determine which problems were worth investing months or even years of effort into.
He believes that AI is disrupting this rhythm. In the past, new tools would reduce the difficulty of certain problems while opening up new directions beyond existing capabilities. Today, the upper limits of models are unclear, making it difficult for researchers to determine which problems are still worth long-term investment and which may soon be solved directly by models.
The AI Lab has launched a problem-solving speed competition.
The report mentioned that in May this year, an OpenAI model provided a counterexample to the Erdős unit distance conjecture, addressing a mathematical problem that had existed for about 80 years. External mathematicians, including Fields Medalist Tim Gowers, subsequently verified the result.
Almost simultaneously, Anthropic researchers tested the same problem using the unreleased Claude Mythos. Company engineers said the model produced a shorter proof; some mathematicians considered its version slightly inferior to OpenAI’s overall, but it still found a viable solution.
The report also stated that Anthropic subsequently formalized the historical proof of Fermat's Last Theorem. A few days later, OpenAI solved a problem that was approximately 90 years old, just hours after a researcher publicly shared their proof. This speed is precisely what Terence Tao worries about.
It is recommended to increase the weight of the reasoning process.
Terence Tao suggests that some problems be labeled as "requiring analysis." Under this standard, the value of providing only the correct answer is diminished; researchers must also explain their reasoning and how this process offers insights into related problems.
He believes that solely pursuing the fastest extraction of answers may solve immediate problems in the short term, but at the cost of undermining the ecosystem of questions needed for future research and hindering understanding of why existing results hold true. According to the report, this suggestion has not yet been formalized into official guidelines, and the ongoing advancements by major AI labs may accelerate the mathematics community’s confrontation with debates over evaluation standards.