For decades, solving the world’s hardest mathematical problems has been considered a uniquely human pursuit, requiring imagination, persistence and the ability to explore ideas beyond established methods. Artificial intelligence, meanwhile, has largely been viewed as a tool for computation and analysis. A Harvard mathematician’s collaboration with an experimental AI model has gained widespread interest after the system helped identify a possible solution to an 87-year-old mathematical mystery. Although the result awaits formal verification, researchers are examining whether AI could become a valuable partner in advanced mathematical research.
An AI model may have cracked an 87-year-old math problem
As reported by arXiv, the problem at the centre of the discussion is the Jacobian conjecture, first proposed in 1939 by the German mathematician Eduard Ott-Heinrich Keller. Despite its simple appearance, it has resisted decades of serious mathematical effort and remains one of the best-known unsolved questions in algebra.At its heart, the conjecture concerns certain polynomial transformations. In simple terms, it asks whether a particular kind of mathematical mapping can always be reversed using another polynomial mapping. The statement is easy enough to write down, yet proving or disproving it has defeated specialists for generations.Sometimes, proving a mathematical statement false does not require an elaborate argument. A single valid counterexample is enough. If even one example breaks the rule, the conjecture no longer holds.In an X post, mathematician Levent Alpöge, “hello there the jacobian conjecture is false…”
Levent Alpöge: A Harvard mathematician worked with Anthropic’s AI model Fable
Levent Alpöge, a 33-year-old mathematician at Harvard University, recently decided to approach the question with assistance from Anthropic’s experimental AI model known as Fable.Working over the course of a single Sunday, Alpöge searched specifically for a counterexample rather than a complete proof. According to posts shared online, the collaboration produced a candidate example that appears to contradict the long-standing conjecture.The proposed counterexample itself is remarkably compact, consisting of only 216 characters. Its size has surprised many observers because the difficulty of the problem lies not in writing a long expression but in finding one that genuinely satisfies every mathematical requirement.
AI and Mathematicians verify key calculations before official review
The finding has not yet passed through formal peer review, which remains an essential part of mathematical research. Independent verification is still needed before the result could be accepted as definitive.Even so, early reactions have attracted attention. Several mathematicians have reportedly examined the calculations independently and reached the same conclusion regarding the arithmetic involved. Others reproduced parts of the work using established mathematical software, including SymPy, while formal proof tools such as Lean were also used to test aspects of the argument.Additional AI systems were drawn into the verification process as well. Different large language models were asked to inspect the proposed counterexample, creating an unusual situation where one AI-assisted mathematical result was being checked with the help of other AI systems alongside traditional methods.
A different role for artificial intelligence
Large language models are gradually finding a place inside mathematical research, although not in the way many people first imagined. They are rarely expected to replace mathematical reasoning. Instead, researchers are beginning to use them as collaborators that can suggest approaches, generate examples worth investigating or identify gaps in an argument that deserve closer attention.That changes the rhythm of research rather than the standards by which results are judged. Every important claim still requires rigorous verification, but some of the exploratory work that once consumed weeks can now be carried out much more quickly.Formal verification has become another area where AI is beginning to make a practical contribution. Systems capable of translating mathematical arguments into languages understood by proof assistants allow complex reasoning to be checked mechanically, reducing the chance that hidden logical mistakes remain unnoticed.
The final verdict awaits as AI’s role in mathematics continues to grow
Whether Alpöge’s proposed counterexample ultimately survives detailed scrutiny remains uncertain. Mathematical history contains many examples of celebrated claims that were later corrected or withdrawn after closer examination.Even if further review identifies problems, the episode has highlighted something that many researchers have been noticing over the past few years. AI systems are becoming increasingly useful during the creative stages of mathematical work, helping researchers explore possibilities that would previously have taken far longer to test.
