Foreign media reports that Professor UCLA, the Fields Medalist, recently warned publicly that AI is consuming those open problems that truly drive the advancement of the discipline at a faster pace than the mathematics community can generate new problems. According to him, the risk does not lie in models producing more proofs, but rather in their potential to too quickly compress the space for researchers to explore over the long term.
High-value problems are becoming less common.
Tao Zhe-xuan pointed out that mathematical problems can be generated infinitely, but not many of them are truly important. Many unsolved problems, although they exist, may not lead to new methods and it is also difficult for them to drive progress in related fields. In the past, researchers relied on experience to determine which problems were worth investing months or even years of time on.
He believes that AI is disrupting this rhythm. In the past, new tools would reduce the difficulty of some problems, but they also opened up new directions beyond the boundaries of current capabilities. Nowadays, the upper limits of models are not clear, making it difficult for researchers to determine which problems are still worth investing in over the long term and which might be quickly solved directly by the models.
AI The laboratory has launched a problem-solving competition.
It was reported that in May this year, the model of OpenAI provided a counterexample to the conjecture about unit distances in Erdős, touching on a mathematical problem that has existed for about 80 years. External mathematicians, including Fields Medalist Tim Gowers, subsequently conducted verifications.
Almost at the same time, Anthropic researchers also used the yet-to-be-published Claude Mythos to test the same problem. Company engineers stated that the proof provided by this model was shorter; however, some mathematicians believed that its version was slightly inferior to OpenAI, but it still found a viable solution.
The report also stated that Anthropic subsequently completed the formalization of the historical proof of Fermat's Last Theorem. A few days later, OpenAI solved a problem that had been unsolved for about 90 years, and this was just a few hours after another researcher had made their proof public. Such speed is precisely what Tao Zhe-xuan is concerned about.
It is recommended to increase the weight of the reasoning process.
Tao Zhe-xuan proposed that some problems could be marked as "requiring analysis." Under this standard, the value of providing a correct answer alone would be diminished, and researchers would need to explain both their reasoning process and the insights that process can offer for related problems.
He believes that focusing solely on extracting answers as quickly as possible can indeed solve immediate problems in the short term, but the cost is a weakening of the problem ecosystem necessary for future research, and it is also not conducive to understanding why the existing findings hold true. According to reports, this suggestion has not yet been formalized into a rule. However, the continuous advancement of large AI laboratories may lead to an earlier confrontation over evaluation standards in the mathematical community.
