Tao Zhexuan warns: AI is solving mathematical problems faster than new problems emerge

Tao Zhexuan warns: AI competition is exhausting "good problems" in mathematics

Tao Zhexuan, a professor at the University of California, Los Angeles, widely regarded as the most outstanding pure mathematician alive today, has sounded an alarm about the current accelerating artificial intelligence competition in mathematics. The 2006 Fields Medal winner issued a warning yesterday on Mathstodon, a math-focused platform, pointing out that artificial intelligence is draining the reserve of high-quality open problems in the field-the unsolved mysteries that really move mathematics forward. He emphasized that the key lies not in the proof or the paper, but in asking "good questions."

Scarce quality problems and ecosystem crises

Anyone can invent an infinite number of new mathematical problems; technically, the 10th billionth number of pi is an open problem that has not yet been calculated. However, the vast majority of these are meaningless because most problems do not provide new insights into the wider field of mathematics. As Tao Zhexuan wrote, what really matters is knowing which issues are worth investing in.

"In short, indiscriminate uses powerful problem extraction tools to achieve short-term goals of solving immediate problems, but at the expense of sacrificing the ecosystem needed for the next wave of progress or hindering understanding of the progress that has been made." Tao Zhexuan wrote.

With the release of inference models and the latest generation of cutting-edge AI systems, major laboratories have begun to invest huge computing resources into mathematical and scientific problems. Companies such as Anthropic and OpenAI have applied their models to problems that have plagued human mathematicians for decades. The research results cover fields such as quantum physics, applied mathematics and medicine. However, mathematics is different: Really difficult problems are relatively scarce, and researchers often need to select carefully and spend months or even years solving specific problems.

In the past, identifying these problems relied on the "difficulty landscape" within the discipline-that is, which problems are trivial, which require real effort, and which are hopeless to solve under current tools. New methods will always smooth out some difficult landscapes, but they will also open up new frontiers beyond their limits. Tao Zhexuan believes that artificial intelligence has broken this model because no one can tell exactly where the boundary of a certain model's capabilities lies.

Real case: How AI changes the pace of mathematical research

Tao Zhexuan is not describing a hypothetical scenario. In May, an OpenAI model overturned the 80-year-old Erdýs unit-distance conjecture, an old question about how many pairs of points on a plane can be exactly one unit apart. External mathematicians, including Fields Medal winner Tim Gowers, verified this result.

Within the same week, Anthropic researcher Lvent Alpöge typed the same question into the company's unreleased top-level model, Claude Mythos. To ensure offline operation and inability to replicate OpenAI's announced solutions, Anthropic engineer Sholto Douglas called the results "a cute and simple proof" that is shorter than OpenAI's version. Mathematician Daniel Litt believes it is slightly inferior to OpenAI's version, although Mythos also found OpenAI's own solution.

Just this week, Anthropic formalized a century-old proof of Fermat's Last Theorem; days later, OpenAI cracked a 90-year-old problem, just hours after a researcher published his own proof and subsequently co-authored a paper with Anthropic researchers.

Reversals and potential solutions to open science

It is this kind of competition that worries Tao Zhexuan. "We are now seeing that even just rumors that someone is working on a certain issue can trigger a lot of AI-driven efforts to 'smooth out' the original research project before it reaches its full potential." He wrote.

Tao Zhexuan believes that this approach ultimately reverses the century-old tradition of open science. His proposed remedy is to label certain questions as "analysis-required," which means that the correct original answer is of limited value unless the answer is accompanied by an inference process that reveals the nature of the adjacent question. He likened this to food banks that stopped accepting any donations that were simply "edible".

Either implement this measure or ban the use of AI in mathematics. Tao Zhexuan said that the latter is not technically feasible. Currently, the proposal has not yet been translated into any policy, and based on the current behavior of large AI laboratories, even the former may not be technically feasible now.