Unpublished Anthropic model makes significant progress on one of the biggest unsolved mathematical problems

Anthropic announced last Sunday that a model it has not yet deployed has been able to achieve a significant progress on the Riemann hypothesis one of the oldest and most important unsolved mathematical problems in history.

The Artificial Intelligence (AI) laboratory, in a publication made on its website, has shared the details of the progress obtained by the research AI model on the fraction of zeros of the Riemann zeta function.

The Riemann hypothesis, formulated by German mathematician Bernhard Riemann in 1859, maintains that there is a hidden, infinitely precise pattern behind the distribution of prime numbers.

In fact, it is considered the most important unsolved problem in pure mathematics, and being one of the seven Millennium Problems of the Clay Institute, it has a prize of one million dollars for whoever manages to prove the hypothesis.

The model did not prove the Riemann hypothesis, although it did manage to increase the known lower bound of zeros that satisfy the hypothesis, going from 41.6 to 67.2%, which means an unprecedented increase of 25.6 points percentages.

A member of the Anthropic team, with no specialized mathematical training, asked Claude to solve one of the most famous problems in mathematics, a task that brought him to Anthropic’s AI 36 hours of continuous autonomous work.

During the day and a half, Claude tried 650 different ideas without successconsumed around 31 million tokens and deployed a network of around 60 specialized sub-agents, among which, as can be read in the footnotes, two were in charge of generating mathematical ideas, 13 of conceptual support, 30 to explore new avenues and 13 dedicated entirely to the verification of arguments.

Claude’s discovery was confirmed internally by two mathematicians from the AI ​​laboratory and formalized in Lean, an open source proof assistant that computationally verifies the validity of theorems.

This milestone, achieved by a model that Anthropic has not yet published, comes shortly after the same AI laboratory found mathematical flaws in cryptographic algorithms with Claude Mythos Preview, or OpenAI published a series of problems solved by its internal ‘Astra’ model.