While the rest of the globe was glued to the World Cup on Sunday night, Levent Alpöge took a quiet break from the chaos to drop a bombshell on X. He had used Anthropic’s Fable 5 to disprove the Jacobian conjecture.
That is not a small deal. The Jacobian conjecture has haunted algebraic geometers for nearly nine decades. It made it onto Stephen Smale’s famous list of open problems back in 1998. It bedeviled some of the sharpest minds in history.
And a frontier AI model just waved it away.
Fable 5 is Anthropic’s latest heavy hitter. It is also the public-facing sibling of “Claude Mythos Preview.” Anthropic claims that version was too dangerous for the public because of its advanced cybersecurity capabilities. But here, it was used to dismantle a foundational piece of mathematics.
Alpöge is a fellow at Harvard’s Society of Fellows. His LinkedIn shows an affiliation with Anthropic. Naturally, we asked Anthropic what was going on. We are waiting to see if they have more to say.
So what does this actually mean? Is this a giant leap for artificial intelligence? Or just a smart calculator finding a needle in a haystack?
It’s not what you think it is
Andrew Blumberg, a professor with joint appointments in math and computer science at Columbia, had a blunt reaction.
“This did not cause me to update my prios about what AI can and can’t do,” Blumberg told Mashable.
Blumberg sits on the board of the First Proof project. This initiative specifically tests if large language models can handle research-level math. So, his take carries weight. He isn’t an outsider looking in. He knows the terrain.
Blumberg argued that finding a counterexample is exactly what you would expect a capable AI to do. If there is a concise counterexample that humans missed because manually checking thousands of polynomials is a pain, then of course the machine finds it. It is not hard for a computer to check them all. It is hard for humans.
This distinction matters.
There is a huge difference between providing a single counterexample that breaks a conjecture and offering a full, constructive proof that advances the field.
Blumberg used a sharp metaphor to explain why this feels underwhelming.
“Suppose that Moses came down from the Mountain with tablets, and on the table was written, ‘Cancer can be cure. Would you care?”
You don’t just want the answer. You want to learn something from the answer.
The Jacobian conjecture was considered important by Smale not because of the conjecture itself, but because solving it would reveal deeper structures of nature. A single counterexample tells us very little about those structures. It just says, “Nope, doesn’t hold.”
Blumberg put it plainly. The result “tells us essentially nothing.” It’s just a demonstration that machines can check things faster than we can.
Context matters in AI math breakthroughs
The Jacobian conjecture is not the only major math problem to fall to AI recently.
OpenAI announced in May that an internal model had disproved the Erdős unit distance conjecture. This is a central problem in discrete geometry.
But Blumberg argues that the Erdős result was actually more productive. Why? Because OpenAI didn’t just spit out a counterexample. They provided a full disproof.
“The disproof there already has led to interesting because experts in the area unpacked the logic,” Blumberg said. “They used it to do other things.”
With the Jacobian counterexample, the story might end there. Blumberg admits he is not an expert in algebraic geometry. He cannot say if there is some unique structural quirk in Alpöge’s counterexample that will spark new research. But on the surface? It lacks the “interesting” quality that drives scientific progress forward.
It proves AI can do the grunt work. It does not necessarily prove it can do the heavy lifting of mathematical insight.
Why this still feels significant
Even if Blumberg is right that the mathematical insight is thin, the sheer velocity of this discovery is worth noting.
Alpöge is connected to Anthropic. Fable 5 is a powerful tool. The problem is 90 years old. The convergence of these facts happened on a Sunday evening while most of us were cheering for soccer teams.
It highlights a shift in how mathematical research might evolve. We are moving into an era where AI does not just assist with calculations but can actively hunt for contradictions in long-standing theories.
The Jacobian conjecture may not change how we view the structure of the universe. But it does change how we view our reliance on computational power to test our deepest assumptions.
Ziff Davis, the parent company of Mashable, filed a lawsuit against OpenAI in April 2025. The suit alleges copyright infringement regarding AI training data. This legal backdrop adds another layer of complexity to the relationship between these tech giants and the mathematical communities they are increasingly intersecting with.
We will keep watching. And we will keep asking: Does finding the answer matter more than understanding why the answer is true?
