An Unreleased Claude Model Made Real Progress on a 167-Year-Old Math Problem

Anthropic said Monday that an unreleased research version of Claude made significant progress on a problem tied to the Riemann hypothesis, one of mathematics’ most famous unsolved questions.

This problem dates back to 1859 and carries a $1 million Clay Mathematics Institute bounty that remains unclaimed. The intelligence model didn’t solve the hypothesis itself.

But while attempting to solve it, it improved a longstanding lower bound on the proportion of zeros of the Riemann zeta function known to satisfy the hypothesis from 41.6% to 67.2%. Two Anthropic mathematicians reviewed and validated the result before the company published it. 

An Assignment Nobody Expected to Succeed

Anthropic’s research post described the result’s origin awkwardly: a staff member gave Claude what the company called “an unreasonable challenge” by asking it to take a real shot at the Riemann hypothesis.

The person already knew the language model was unlikely to solve a problem that has challenged mathematicians for more than 150 years.

Claude didn’t succeed at that original ask, but Anthropic said it made unexpected progress on a related problem along the way. 

The staffer, Jarred Sumner, who is not a mathematician, mainly encouraged Claude after the initial prompt with messages like “keep going” and “believe in yourself.” 

Anthropic said this appeared to help Claude overcome its initial doubts about making meaningful progress.

A Process Built on Trial, Error, and Self-Checking

The company says the model tested 650 approaches before finding one that worked, coordinating 60 subagents that ran 2,400 shell commands and wrote hundreds of Python scripts to check the numerical validity of the emerging proof.

Anthropic’s breakdown shows that only two subagents out of 60 developed the key mathematical ideas, while 13 served purely as validators checking the other agents’ reasoning and 30 tried approaches that failed.

That ratio, two successful contributors out of 60, may look inefficient, but it mirrors human mathematical collaboration: most approaches to hard problems fail, while parallel attempts increase the chance that one succeeds.

That pattern is also emerging in other AI-driven math breakthroughs, including an unreleased OpenAI reasoning model that itself solved the 80-year-old Erdős unit distance problem.

Part of a Pattern That’s Splitting the Math Community

TechCrunch placed Monday’s announcement within a growing list of AI-assisted math results this year. 

OpenAI recently published 10 major results from its internal Astra model, while a separate Anthropic effort disproved the long-standing Jacobian conjecture using a similar approach. That record is fueling debate among mathematicians. 

TechCrunch pointed to the Leiden Declaration, signed by prominent mathematicians in June, which warned that AI-generated results could weaken mathematics’ tradition of assigning proofs to authors who take responsibility for their correctness.

Fields Medal winner Timothy Gowers challenged that view, comparing an authorless future in mathematics to stars, which are not named after the astronomers who discover them and often have no names at all.

The debate is not about whether Claude’s proof is correct, as two independent experts confirmed it. 

It is about what happens to mathematics as AI begins solving hard problems through unsupervised experimentation instead of the decades of human study the field has traditionally required.

Source: Learning more about Claude’s mathematical capabilities