AI in Math: 25 Fields Medalists Warn, One Responds

Reporter: Zhou You, China Newsweek

Editor: Du Wei

Operations Editor: Wang Lin

On September 11 local time, 25 Fields Medalists, including Terence Tao and Yu Deng, jointly issued a statement titled "Serious Misalignment of Artificial Intelligence in Mathematics," pushing the "battle" between AI companies like OpenAI and Anthropic and the mathematics community to a climax. The statement said that AI companies' practice of using solving mathematical problems as a benchmark for model capabilities has caused damage to mathematical science itself and the mathematics community, and has significantly diverged from the fundamental goal of the mathematics community to pursue conceptual understanding.

This divergence has become increasingly evident recently. On September 8, OpenAI claimed that its undisclosed internal AI model solved the existence and smoothness problem of the Navier-Stokes equations (N-S equations) in 88 hours. The N-S equations are core equations describing fluid motion and are widely used in weather forecasting, aircraft design, and other fields. The Clay Mathematics Institute (CMI) in the United States listed the existence and smoothness problem as one of the seven Millennium Prize Problems in 2000, with a $1 million prize.

However, New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpoge had previously made key progress on related issues and publicly released their results on September 7. Buckmaster subsequently criticized OpenAI, believing that it increased its investment only after hearing about their progress. He revealed that he had used his unpublished drafts and derivations in OpenAI's code tools and suspected that OpenAI's model had accessed them without permission. OpenAI denied this claim but admitted that it could not completely rule out the indirect role of user data in model training. Currently, OpenAI has no intention of claiming the CMI prize. The mathematics community has not yet given formal recognition to OpenAI's proof.

OpenAI's approach quickly sparked a heated debate about academic priority, data ethics, and the boundaries of AI scientific research. Since May this year, multiple mathematical problems have been solved by AI, and OpenAI recently revealed that it has turned its attention to another Millennium Prize Problem, the Hodge conjecture.

AI continues to dim the beacons of human mathematics. Stanislav Smirnov, a professor at the University of Geneva in Switzerland, is a 2010 Fields Medalist and one of the 25 signatories of the statement. On September 12, he gave an exclusive interview to China Newsweek.

Stanislav Smirnov Photo/Video screenshot

"Like Laborers Complaining About Being Replaced by Excavators"

China Newsweek: The statement went from drafting to publication in just a few days. What was the main reason for such urgency?

Smirnov: Most colleagues did not anticipate that this matter would progress so quickly, nor did they anticipate that it would cause such controversy. Given the rapid development of AI, we need to act quickly now to establish rules for the future.

China Newsweek: The statement uses the term "serious misalignment." What is the fundamental divergence between the mathematical goals of AI companies and the mathematical goals upheld by the mathematics community itself?

Smirnov: First, we must answer the question: What is the purpose of society supporting mathematical research? Mathematics, like music and art, is an important part of human culture and the foundation of many other disciplines and technologies. For many mathematicians, the cultural and artistic value of mathematics is most important.

Many social applications spawned by mathematics, from mobile phones and airplanes to machine learning itself, were originally created in pursuit of the beauty of science. So far, AI companies have used mathematics as an indicator to measure the capabilities of large models, which is understandable. These models have become so powerful that it is difficult to find suitable evaluation benchmarks. But current evaluation methods often produce lengthy proofs of famous conjectures, while the ideas that may emerge during the exploration of these conjectures may be more important.

Two friends once told me that mathematicians complaining about AI proofs are like manual laborers complaining about being replaced by machines. I think this analogy should be placed in the context of archaeological excavation. Excavators are indeed faster, but they may damage precious artifacts. These artifacts would be well preserved if excavated by a group of workers who work much more slowly.

China Newsweek: OpenAI's statement about the N-S equations has sparked much controversy. Buckmaster claims that OpenAI only mobilized its model to "race ahead" after learning that his team had made progress. How do you view such incidents?

Smirnov: We have seen that some large models appropriate others' ideas without attribution, or use unpublished ideas. If a human mathematician did this, it would be considered a serious violation of academic ethics. Some people think that AI plagiarizing humans is acceptable, but I do not agree with this view.

But the more important issue now is that different groups and individuals hold vastly different views on this. We do need to formulate new rules to resolve such conflicts. We should realize that further development of AI may lead to major changes in how it operates, so our understanding of AI also needs to be constantly revised. From a positive perspective, we can seek dialogue and balance among all stakeholders, but this requires effort.

China Newsweek: The statement does not advocate eliminating AI and acknowledges that AI has the potential to assist and accelerate mathematical research. What is your ideal AI tool for mathematical research?

Smirnov: AI is very good at understanding known information, conducting experiments, and testing whether existing methods can solve current problems. But they are not good at judging the effectiveness of new methods or proposing truly novel ideas. However, their level is improving rapidly, and I estimate that in the next few years we will have to adjust traditional research methods. But I am confident that we can find many uses for artificial intelligence that benefit not only science and society but also the development of AI companies themselves.

Equal Access Has Not Yet Arrived

China Newsweek: Among recent AI-driven mathematical breakthroughs, which specific progress surprised you the most? Why is it so worrying?

Smirnov: So far, I have not seen anything that particularly surprised me. Some problems that truly interest me still seem beyond the capabilities of AI. What worries me most is that focusing too much on obtaining proofs rather than understanding research goals may harm both science itself and its potential applications.

China Newsweek: If students can obtain proofs directly from AI, can they still receive sufficient mathematical training? Is the process of struggling with difficulties and eventually finding answers on their own still important?

Smirnov: Even for experienced researchers, AI can cause great harm. A scholar friend of mine admitted that after using AI to generate course exercises and answers for a year, he found that his ability to solve problems at the student level had deteriorated significantly. I find that most students are aware of this risk and will try to solve problems themselves, using AI only as a hint.

China Newsweek: If AI can produce mathematical conclusions on a large scale, what is the significance of human mathematicians' work? Will the speed at which humans digest these conclusions become a new bottleneck for mathematical progress?

Smirnov: The way AI currently researches and solves problems is more formalistic. Perhaps the final results can be understood, but by whom? One possibility is that we are witnessing the birth of a new kind of scientific work, namely mining ideas from AI-generated texts. Can AI itself really generate new ideas? At present, the answer seems to be no, but I cannot say for sure.

China Newsweek: When using AI to generate mathematical proofs, is it more difficult to properly cite previous research? In the long run, will this lead to a break in the continuity of human knowledge?

Smirnov: In principle, yes, especially when humans cannot understand AI proofs. But if we find ways to avoid this situation and find a good way of human-machine collaboration, AI may instead become a very useful tool.

I have tried to apply AI to my own research problems, but the most advanced models still seem not very practical, perhaps because they lack some key understanding. However, AI is an excellent tool for retrieving known information in a field or proofreading articles.

China Newsweek: Some people may think that the recent series of events is an inevitable result of AI knowledge equal access. What do you think?

Smirnov: I have not seen much equal access yet. Most progress has been achieved using models that are not publicly available. In fact, if AI companies could share resources with mathematicians instead of trying to do everything themselves, the situation might be much better. I believe this will happen soon. AI companies and mathematicians will eventually reach some consensus, and equal access will follow.