A mathematician has somewhat unceremoniously announced that he has disproven an almost 90-year-old problem — with the help of Anthropic’s artificial intelligence model. The announcement sent waves through social media and the inner circles of mathematics, as the latest in a series of AI-driven mathematical achievements that shook the field and called future math into question.
What math problem did AI tackle?
The Jacobian conjecture is “false,” Harvard University mathematician and Anthropic employee Levent Alpoge said on X, thanking his “close friend Akhil for asking about it” and his “other close friend Fable” for “working during the World Cup final.” Attached was a mathematical formula, a counterexample to the decades-old problem. Despite the fact the problem “bedeviled highly accomplished mathematicians for almost 90 years,” the conjecture “proved no obstacle” for Anthropic’s “latest frontier AI model,” said Mashable.
A conjecture is an “idea that some mathematicians believe is true,” but nobody has been “able to prove or disprove,” said mathematician Melissa Lee at The Conversation. This algebraic geometry theory suggests that a “certain type of mathematical function would also work in reverse” and was “formally set out” by Ott-Heinrich Keller in 1939, said New Scientist. It was one of 18 “fiendishly difficult problems for mathematicians to tackle in the 21st century,” according to a list curated by mathematician Stephen Smale in 1998.
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The AI-generated counterexample that Alpoge shared online is the “latest in a series of AI-driven mathematical breakthroughs,” said Fortune. The technology’s “progress (or assault)” on unsolved mathematics has “compounded rapidly since mid-2025,” when models first solved “five of six problems” at the International Mathematical Olympiad.
After that, OpenAI’s model disproved an “80-year-old Erdos conjecture on combinatorial geometry” in May. In June, more than a dozen researchers from 15 universities published a declaration on AI and mathematics, urging their colleagues to “set guardrails around transparency, attribution and peer review” before AI “reshapes what mathematical knowledge even means,” Fortune added. Mathematicians, “relegated to the role of shepherd,” are left to watch AI “close these questions one-by-one, reaching places where the human mind can’t follow.” The mathematicians’ reaction is a “now familiar mixture of dread and amazement.”
What does this mean for the future of math?
The significance of the AI’s discovery varies depending on whom you ask. The counterexample did not “cause me to update my priors about what AI can and can’t do," professor and mathematician Andrew Blumberg said to Mashable. This is “exactly the kind of thing I would expect AI to be able to do.”
The counterexample to the Jacobian conjecture is still a significant achievement for AI in mathematics, Blumberg said, but there’s a difference between providing proof of a mathematical problem and showing a singular counterexample that disproves it. In other words, the counterexample “tells us essentially nothing.” Just that there are a lot of polynomials (a math equation that has numbers and letters representing variables). It’s “hard for people to check them all, but it’s not hard for machines.”
Among other “recent AI-assisted breakthroughs,” the Jacobian conjecture counterexample stands out for being “remarkably simple,” Lee said at The Conversation. The difficulty in finding the solution seems to have “lain not in an intricate construction or a lengthy proof” but rather in finding a good way of “navigating an enormous search space of possible polynomial mappings to find one with the right properties.” AI, this suggests, may “prove to be just as valuable for discovering unexpected mathematical objects as it is for constructing proofs.” What this means for the “future of mathematics and human mathematicians” remains to be seen.
For some, the recent developments with AI foreshadow a future of “increasingly capable AI models that will solve ever more complex problems,” said New Scientist. AI can “already produce master’s degrees in mathematics,” mathematician Ivan Fesenko at Westlake University in China said to the outlet. In a year, it will produce “Ph.D. degrees in mathematics.” Then the question arises, “do we really need so many mathematicians around if AI can do such things so nicely?”
