Artificial intelligence (AI) has swiftly solved problems that human mathematicians could not crack for decades, prompting warnings from the mathematics community. They argue that a race among AI corporations to tackle unsolved math problems could damage the essence of mathematical research. They noted that this issue is not confined to mathematics and could threaten intellectual activity as a whole.
On the 11th (local time), 25 Fields Medalists, including Terence Tao of UCLA and Heo Jun-yi of Princeton University, raised concerns about AI's race to solve math problems in a joint statement titled "Severe goal misalignment of AI in mathematics." They emphasized that in mathematics, getting answers is not the ultimate goal; rather, the conceptual understanding, insights, and new methodologies gained in the process of solving problems matter.
The Fields Medal is awarded every four years to outstanding young mathematicians and is called the Nobel Prize of mathematics. World-class mathematicians such as Pierre Deligne, Cédric Villani, and Peter Scholze also signed the statement. They warned that global AI corporations recently using the solving of mathematical challenges as a "performance benchmark" to showcase their technology could harm mathematical research.
They said, "Solving problems is only a tool and proxy to achieve the fundamental goals of conceptual understanding and insight," adding, "There is a severe misalignment between the goals of AI corporations and those of the mathematics community. As AI changes how work is done, we must not lose sight of what the work was intended to achieve in the first place."
OpenAI's recent result sparked the controversy. OpenAI announced that it had derived a solution to the Navier–Stokes equation problem, one of the most prominent unsolved problems in mathematics, using its AI model. According to OpenAI, up to 10,000 AI agents worked simultaneously, exchanged about 2.7 million messages, and generated about 130 billion tokens, arriving at a result in 88 hours. It then had another AI model verify it in Lean, a formal proof verification system.
The Navier–Stokes problem is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. OpenAI said it would not claim the $1 million prize for this result. However, as independent verification by external mathematicians is necessary, some in academia say it is too early to accept it as a complete solution.
Professor Tao worried that the methodologies and new ideas mathematicians could gain might disappear as AI produces answers. In an interview with IBM, he noted that as AI quickly solves hard problems, human researchers could miss the intermediate discoveries and insights obtained while working through them.
This debate is not limited to OpenAI. Google DeepMind has also announced that it used AI to solve numerous unsolved math problems, signaling the start of full-fledged math competition among big tech. As AI's mathematical reasoning rapidly improves, mathematics is emerging as a new arena to showcase AI's capabilities.
What the Fields Medalists fear is not AI solving math problems per se. They say that if the "speed of getting the right answer" accelerates excessively, the research ecosystem of understanding and insight, collaboration, and verification that humans gain in the process could collapse.
In fact, AI's ability to conduct mathematical research has advanced rapidly this year. In May, OpenAI announced that it had used AI to refute a conjecture related to Erdős's 80-year-old "unit distance problem," and Google DeepMind also reported results on several unsolved Erdős problems.
In the mathematics community, there is a growing call to distinguish between using AI as a research assistant tool and allowing AI corporations to competitively dictate research goals and pace. The community has already issued the "Leiden Declaration," which calls for transparency in AI use, independent verification, and appropriate credit for research contributors.
The Fields Medalists are not saying AI use should be excluded; they said AI has the potential to strengthen and accelerate mathematical research and understanding, and the profession of mathematics should adapt accordingly. However, they emphasized that AI's impact on mathematics depends less on the technology itself and more on how it is used and governed. They framed this as a general threat to intellectual labor, not a problem unique to the mathematics community.