AI Model Disproves 87-Year-Old Math Conjecture as Crypto Tracks AI Gains

An Anthropic AI model has helped disprove a mathematical conjecture that had gone unsolved for 87 years, with the result confirmed within a day because the counterexample can be checked by hand.

Levent Alpöge, a number theorist at Anthropic and a former Harvard fellow, posted the finding on X on Sunday night, crediting the company’s Claude Fable 5 model with producing the counterexample. The problem, known as the Jacobian conjecture, had been open since 1939 and appears on mathematician Stephen Smale’s list of influential unsolved problems for the century.

What The Conjecture Asked

The conjecture concerns a type of mathematical function that takes two numbers and produces two new numbers using only addition and multiplication. The question, first posed in 1939, was whether such a function can always be run in reverse: given only the output, can the original inputs always be recovered.

Mathematicians had a standard check for whether a function looked reversible on paper. The Jacobian conjecture held that any function passing that check must, in fact, always be reversible. For 87 years, nobody could prove the claim true, and nobody could find a function that broke it.

Claude Fable 5 found one. The model constructed a function that passes the standard check but cannot be reversed, because three distinct sets of inputs all produce the identical output. A function that maps multiple different inputs to one output cannot be run backward from that output, which is enough on its own to disprove the conjecture. A single counterexample was sufficient to settle a question that had stood for nearly nine decades.

AI Capability Gains Continue To Move Crypto Markets

The disproof arrives as capability gains from AI models are increasingly influencing crypto markets. Bitcoin has spent recent months trading in tandem with chipmakers and memory stocks rather than moving on catalysts specific to crypto.

The token fell sharply last week after a Chinese lab released a model that outperformed rivals on a coding benchmark, which weighed on the semiconductor sector broadly. It recovered this week as chip and memory stocks rebounded, tracking the same swing that had pulled it down days earlier.

Part of the connection between AI developments and Bitcoin’s price runs through the mining industry directly. Large Bitcoin miners have converted portions of their operations into AI data-center infrastructure in recent quarters, tying their revenue and equity value to demand for computing capacity rather than mining alone.

Some connection reflects shifts in where speculative capital is flowing. Investors who previously allocated toward crypto have increasingly directed capital toward computing infrastructure, chipmakers, and AI model developers as the pace of capability improvements has accelerated. Each demonstrated leap, including an AI system producing an original mathematical result of this difficulty, has coincided with continued capital reallocation toward direct AI exposure.

Verification Came Quickly

Unlike many advanced mathematical claims, this result did not require extended peer review before other mathematicians could confirm it. The counterexample is a concrete, explicit function rather than an abstract existence proof. Other researchers could verify by direct calculation that the three listed inputs produce the same output, settling the question within a day of the initial post.

That speed of verification distinguishes this case from many AI-assisted research claims, which often require weeks or months of scrutiny before mathematicians reach consensus on whether a proof holds. Anthropic has not released a formal paper detailing the model’s approach to the problem, and the result so far exists primarily as a social media post and the underlying counterexample itself.