Fields Medalist June Huh questions AI’s ability to formulate mathematics’ next big questions

The mathematics community has been shaken since OpenAI announced on Sept. 8 that one of its AI models had found a solution to the Navier-Stokes equations — one of seven notoriously difficult mathematical problems with a $1 million prize for each solution.

Twenty-five Fields Medal winners issued a joint statement on Sept. 11 that criticized the growing race to use AI to solve mathematical problems and said the competition was “detrimental to the science of mathematics.” 

June Huh, a professor of mathematics at Princeton University who became the first person of Korean descent to win the Fields Medal in 2022, also cosigned the statement. 

“It is still difficult to say that AI can independently venture beyond the existing boundaries of mathematics,” Huh said. "The reason solving a major unsolved problem matters is not the answer itself, but that solving it allows us to ask the next question."

The JoongAng Ilbo conducted an email interview with Huh on Sept. 16 to discuss his thoughts on the impact AI could have on mathematics and, more broadly, human creativity. Below are excerpts from the interview, edited for length and clarity.

Q. How far has AI's mathematical ability come?

A. AI is already better than any individual at quickly learning and connecting known definitions, theorems and methods. But it remains unclear whether current models can open up "new territory." Suppose an AI were trained only on mathematics available up to 1900. Could it independently produce advances comparable to what humanity achieved over the following century?

Doesn't OpenAI's solution to a major unsolved problem count as opening up “new territory?”

We need to distinguish between a “new result” and a “new direction of thought.” This latest AI result came from a specific line of inquiry that human researchers had already opened up, and it is understood that a very large number of agents and enormous computing resources were devoted to solving the problem. This alone is not enough to say that AI can independently venture beyond the existing boundaries of mathematics.

What would change if AI solves major unsolved problems and gives us the answers?

In the science fiction novel “The Hitchhiker's Guide to the Galaxy” (1979), a hyperintelligent species builds a supercomputer to find the answer to the “ultimate question of life, the universe, and everything.” After 7.5 million years of calculation, the computer comes back with “42” as the ultimate answer.

What makes that scene funny is not that the answer is wrong. It shows how void it can be to have an answer when you don't even know what the question is.

Why is that void?

If what we know is a circle, then the larger the circle becomes, the longer its boundary with what we don't know becomes. Major unsolved problems are like lighthouses on that boundary. They show us places our thinking has yet to illuminate.

Solving a major problem is about more than determining whether a proposition is true or false. It reveals something we could not see before and makes it possible for us to ask the next question. Whether the answer comes from AI or a person, a good answer leads to a better question.

But the problem is not the answer itself. It is the environment surrounding it. Hundreds of AI-written papers are already being produced every day. If we reach a point where everyone writes papers but no one reads them, we could end up producing more knowledge while understanding less.

Answers themselves do not destroy creativity. But the way we obtain those answers, and the speed at which we obtain them, could dry up the soil in which creativity grows.

Do you think pure academic research itself will decline in the AI era?

Mathematics and physics will not disappear, but the way pure academic research is conducted and the system that helps sustain it as a profession could change significantly.

If AI takes over repetitive exploration and allows people to spend more time on concepts, questions and explanations, pure academic research could become richer than it is today.

On the other hand, if we lose the experience of asking questions, enduring failure and pursuing research over long periods, intellectual curiosity and research skills could weaken across generations.

The belief that AI can do anything if you throw enough tokens at it is intellectual surrender — and a dangerous gamble with one of humanity’s greatest assets: curiosity.

OpenAI's solution has also sparked a copyright debate. What do you make of that?

We don’t know enough yet to say whether unpublished research or prompts were actually used. But many researchers believe Tristan Buckmaster, Levent Alpöge and other scholars [who have raised the issue] or those who came before them would have gotten there eventually. 

Rather than focusing only on who announced the findings first, we need to fully document where the ideas began and how they developed.

Do you use AI in your own research?

I actively use OpenAI's Astra and Anthropic's Claude Fable in all of my research. They are useful for quickly going through unfamiliar terminology and previous findings and for identifying possible connections between facts. I also ask several models the same question and compare how their answers differ.

Could the race between countries for rapid AI advances become an obstacle to pure academic research?

If visible metrics become the only goal, pure academic research will become a testing ground for showcasing AI performance. If we continue to create an environment that values answers over questions, our capacity for research could deteriorate across generations.

What advice would you give young mathematicians about using AI?

I tell researchers to actively use AI and experience for themselves what it does well and where it gets stuck. I think it will become increasingly important to develop an eye for distinguishing between problems AI models can solve quickly and those they still cannot.

BY SUNG JI-WON [[email protected]]