Source: OT-Team(G), 每日经济新闻
A foreign professor at a Chinese university and Fields Medalist is speaking out against the growing use of artificial intelligence (AI) to tackle major mathematical problems, accusing AI companies of undermining mathematical research and exploiting the work of human mathematicians.
On September 11, 25 Fields Medalists jointly issued an emergency statement titled “A Severe Misalignment of AI in Mathematics,” directly challenging the way leading AI companies are using AI to tackle difficult mathematical problems.
The statement argued that treating the ability to solve mathematical problems as a benchmark for AI models is damaging to mathematical science and the mathematical community, while fundamentally diverging from mathematics’ pursuit of conceptual understanding.
The statement came shortly after OpenAI claimed that an undisclosed internal AI model had solved the existence and smoothness problem for the Navier-Stokes equations in just 88 hours.
Among the 25 signatories is Efim Zelmanov, a professor at Southern University of Science and Technology (SUSTech) in China. In an interview with reporters, Zelmanov described OpenAI’s approach as essentially “academic plunder” intended to generate publicity ahead of an IPO.
Zelmanov was awarded the Fields Medal in 1994 for his work on the restricted Burnside problem, a major problem in group theory. Together with Georgia Benkart, he also proved a coordinate theorem for Lie algebras regarded as a foundation for work on infinite-dimensional Lie theory. He was elected to the U.S. National Academy of Sciences in 2001 and became a foreign member of the Chinese Academy of Sciences in 2021.
Asked why the Fields Medalists felt compelled to speak out so quickly, Zelmanov said humanity must retain control over mathematics and warned against becoming completely dependent on AI.
“Humanity must maintain control of mathematics. Completely relying on AI is a one-way road to disaster,” he said.
He argued that AI companies have access to enormous financial resources and can deploy tens of thousands of AI agents around the clock. While these systems may appear to be capable of knowing almost everything, he said, they are built on work previously done by human mathematicians, without necessarily giving those mathematicians appropriate credit or attribution.
In his view, that raises fundamental intellectual-property concerns.
Zelmanov was particularly critical of OpenAI’s recent claim regarding the Navier-Stokes problem.
He argued that the reported progress was built on new ideas recently developed by human mathematicians. While acknowledging that he did not have conclusive evidence, he suggested that researchers working on the problem may have used OpenAI services, potentially allowing other AI agents within the company to access their research traces.
He compared the situation to two competing teams, with one team openly observing what the other is doing before deploying vastly greater resources to overtake it.
“AI agents can work day and night, while human beings need to rest,” he said.
Zelmanov offered an analogy: a group of mathematicians are like cyclists racing toward a finish line. A Spanish mathematician develops a new idea related to Girsanov’s equation, while AI systems observe human research. When the human researchers are close to the finish, AI companies can spend more than $20 million and deploy thousands of agents to work together, cross the finish line first, and then claim to have been the first to solve the problem.
He described such behavior as that of a “predator.”
“If a human scholar did this, they would become a pariah in academia and lose all their friends,” he said, arguing that, in a certain sense, it amounts to “piracy.”
According to Zelmanov, one reason is publicity.
“Because it brings exposure. It has a propaganda effect,” he said.
He also noted that many people working in AI previously studied mathematics, meaning personal motivations may also be involved. For researchers who grew up in a culture of pursuing breakthroughs, solving a famous mathematical problem can also represent a way of demonstrating progress to their former mentors.
But Zelmanov said the deeper issue is a fundamental difference in objectives between AI companies and the mathematical community.
“The goal of the mathematical community is to develop conceptual understanding and train the next generation of mathematicians,” he said. “The goal of AI companies is to create hype and publicity for an IPO.”
For mathematicians, he said, corporate publicity is not the priority. Their concern is the next generation and the continuity of mathematical research.
For hundreds of years, mathematics has developed a system in which young researchers enter graduate school, senior mathematicians propose problems of manageable difficulty, and students gradually advance by solving those problems, publishing papers and building academic careers.
The value of such problems, Zelmanov explained, is not simply whether they are interesting. Solving them often requires researchers to establish a broader theoretical foundation, thereby deepening conceptual understanding while training the next generation.
If a moderately difficult problem can instead be solved simply by pressing a button, he argued, that could fundamentally disrupt the system.
“We may get an answer that is correct, but it absolutely cannot provide any conceptual understanding, nor can it leave anything inspiring for the next generation of mathematicians,” he said.
Zelmanov acknowledged that AI is extremely powerful and continues to improve rapidly. Human mathematicians themselves use AI, he said, and “we cannot put the genie back in the bottle.”
But he opposes what he called a “hostile takeover” of mathematics, warning that it could damage the broader research ecosystem.
Asked whether an AI-generated proof would still be missing something even if it were mathematically correct, Zelmanov drew a distinction between knowing that a result is true and understanding why it is true.
“All mathematical knowledge and correct solutions can usually be traced back to several great underlying ideas,” he said.
Conceptual understanding, in his view, means identifying those ideas—and that is what ultimately drives mathematics forward.
“If a proof is merely ‘correct,’ then what?” he said. “The essence of mathematics is understanding.”
Without that understanding, he questioned what it would actually mean to win a competition between humans and machines.
Zelmanov also warned that AI could eventually threaten the career prospects of young mathematicians if the current trajectory continues.
“We need to train human mathematicians who have conceptual understanding and truly understand what is happening in mathematics, so they can continue developing the field,” he said.
Zelmanov was equally skeptical of calls from prominent technology executives—including Anthropic CEO Dario Amodei, SpaceX CEO Elon Musk and OpenAI CEO Sam Altman—for a slowdown in frontier AI development.
“I honestly don’t understand what they mean by ‘slowing down,’” he said.
He suggested that such calls could represent another form of publicity, particularly as some members of the public have become concerned about the massive data centers required to support AI.
“They may feel that this is what some people want to hear,” he said.
Looking at the history of technology, Zelmanov argued that technological development has continually moved forward and said he did not believe companies would genuinely slow down.
In his view, such statements are largely gestures rather than actions with substantial consequences.
As AI develops, will mathematicians increasingly become responsible for checking or validating AI-generated results?
Zelmanov said he has not seen that shift happen yet and sees no reason to expect it soon.
As he has emphasized throughout the debate, he said, what AI currently does is fundamentally built upon the work of human mathematicians.
“Without mathematics, there is no AI,” he said.
Mathematicians, he added, continue to do what they have always done: search for new ideas and conduct their own research.
“We should not overestimate AI or exaggerate its role,” he said. “So far, it has only solved some moderately difficult problems.”
For students studying mathematics in the AI era, Zelmanov believes the fundamentals remain essential.
“They still need to study fundamental mathematics,” he said, because modern advances are built upon centuries of mathematical knowledge and core ideas developed by humans.
He pointed to modern cryptography and coding theory as an example.
Today, billions of people exchange encrypted information constantly when using email, credit cards and other digital services. Yet the mathematical foundations behind such technologies can be traced back to the work of 19th-century French mathematical prodigy Évariste Galois.
For around 150 years, Galois’ theories were widely regarded outside mathematics as having little practical use. Eventually, however, highly educated researchers transformed those mathematical ideas into foundations for modern technology.
Looking ahead a decade, Zelmanov was asked whether it would represent a major breakthrough if AI solved problems that had challenged mathematicians for decades, even if humans could not fully understand the resulting proofs.
He said that, so far, even the most sophisticated solutions produced by AI remain rooted in human work. He therefore does not expect such a scenario to arise in the short term.
But if AI one day claimed to have solved a problem while human mathematicians disagreed, Zelmanov said he would still place his trust in humans.
“I am committed to a human-centered position—I care about human beings, not AI agents,” he said.
Asked what he would least want AI to take away from mathematicians, he identified what he called the “divine sparkle” of creativity.
Mathematicians, he said, bring a broad perspective to problems, consider potential real-world applications and appreciate the beauty of mathematics.
When Galois developed his groundbreaking theories, he could not have known that they would become important to technology 150 years later. What drove him was his pursuit of mathematical beauty.
“For mathematicians, mathematics is also an art,” Zelmanov said. “I don’t think AI can surpass us on the artistic side.”
He added one final qualification: “Never say never.”
If AI were eventually to surpass humans even in that realm, he said, the implications would extend far beyond mathematics and pose a serious challenge for humanity as a whole.