An AI Took a Stab at the Riemann Hypothesis
For over 150 years, the Riemann hypothesis has haunted mathematicians. It’s a deceptively simple question about the distribution of prime numbers, and it carries a $1 million bounty for anyone who cracks a general proof. That prize remains unclaimed. But now, an unreleased Anthropic model has made a dent.
On Monday, Anthropic announced that one of its internal models significantly increased the lower bound of solutions for which the hypothesis holds true. That’s not a full proof — nowhere close. But it’s real progress on a problem that has resisted the world’s best minds for generations.
What’s more striking is how it happened. A staffer with minimal mathematical training simply prompted the model to “take a real stab” at the problem, then walked away for a day and a half.
How the Model Worked: 60 Sub-Agents, 650 Ideas, 31 Million Tokens
The scale of the effort is hard to wrap your head around. Over roughly 36 hours, the model tested 650 different approaches, coordinating across 60 sub-agents and burning through 31 million tokens in the process.
According to a footnote in the accompanying paper, the labor split was surprisingly organic:
- 2 sub-agents developed the key mathematical ideas
- 13 contributed supporting ideas to those two
- 30 tried but failed to generate new approaches
- 13 acted as validators, checking the correctness of arguments
- 2 helped write the initial paper
It’s almost like watching a research lab assemble itself. And the results weren’t just hand-waved — Anthropic’s in-house mathematicians confirmed the findings, and the proof was formalized using the open-source proof assistant Lean.
The Growing Wave of AI Mathematical Breakthroughs
This isn’t an isolated event. Over the past year, large language models have been quietly racking up wins in pure mathematics. Several Erdős problems have fallen to AI, and OpenAI recently published ten major results from its internal “Astra” model. Anthropic itself previously disproved the long-standing Jacobian conjecture.
The pattern is clear: as models get more powerful, their mathematical output gets more impressive. But that’s precisely what’s making some mathematicians nervous.
Why Some Mathematicians Are Worried
In June, a group of prominent mathematicians signed a public declaration expressing concern that AI could erode the field’s core values. Their worry centers on attribution — the standard that proofs should be “attributable to specific authors who take credit for their discovery and assume responsibility for their correctness.”
If a model generates a proof, who’s responsible for it? The prompt-writer? The company that built the model? No one at all? Those aren’t just philosophical questions; they have real implications for how mathematics is taught, published, and credited.
Not Everyone Sees It as a Threat
But the mathematical community is far from united. Fields Medal winner Timothy Gowers pushed back on the declaration in a blog post, suggesting the shift might not be as catastrophic as some fear.
“If we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that won’t be any more problematic than the fact that stars aren’t named after astronomers and most aren’t named at all,” Gowers wrote.
It’s a compelling analogy. We don’t know who first noticed that the sun rises in the east, and we don’t lose sleep over it. Maybe mathematical discovery will eventually feel the same way.
What This Means for the Future of Discovery
This Anthropic result raises a bigger question: if an untrained staffer can prompt a model into meaningful progress on one of math’s hardest problems, what happens when actual experts start using these tools deliberately?
The answer might be that AI doesn’t replace mathematicians — it accelerates them. Instead of spending months chasing dead ends, researchers could use models to explore hundreds of avenues in a single weekend. The AI sub-agents mathematics approach used here is essentially a brute-force search of idea space, and it worked.
That doesn’t mean the Riemann hypothesis falls tomorrow. The $1 million bounty is still safe. But the fact that a machine can now make a meaningful dent in a 150-year-old problem — largely on its own — should give us all pause. The next breakthrough might not come from a human at all.
