According to a report published in TechCrunch by AI Editor Russell Brandom on August 11, 2026, an unreleased artificial intelligence model developed by Anthropic has succeeded in making significant progress toward solving the Riemann hypothesis—one of the most central and long-standing unsolved problems in mathematics. This achievement, which has been verified by the company's in-house mathematicians and formally structured, is expected to reopen long-standing questions regarding the capability of modern AI systems to autonomously discover and develop groundbreaking scientific and mathematical concepts.
The Riemann Hypothesis and the New Scientific Achievement
For more than 150 years, the Riemann hypothesis has stood as one of the central unsolved problems in the field of mathematics. It remains an ongoing mystery directly concerning the distribution of prime numbers. The scientific and research significance of this hypothesis is so profound that a $1 million bounty is currently offered for a working general proof of the hypothesis—a reward that remains unclaimed to this day.
Although contemporary AI models are still unable to solve the Riemann hypothesis in its entirety, the new research findings demonstrate that these models can achieve far more progress than initially expected. On Monday, Anthropic officially announced that an as-yet-unreleased model of its own had made significant progress on the Riemann hypothesis, successfully increasing the lower bound of solutions for which the hypothesis holds true.
How the Breakthrough Was Achieved: The Action of 60 Sub-Agents
A particularly impressive and surprising aspect of this scientific milestone lies in how this research progress was actually achieved by the system. According to the official report, an Anthropic staff member—who does not possess advanced mathematical training or a broad academic background in mathematics—prompted the model to "take a real stab" at proving the complex hypothesis. Following this simple initial prompt, the staff member left the model to autonomously run, manage, and coordinate the complex task over a period of a day and a half.
During this day and a half of autonomous activity, the model tested no fewer than 650 different ideas to solve the mathematical problem. The model's workflow was executed by coordinating and managing 60 different sub-agents, with the total cost of running the project amounting to 31 million.
A footnote in the research paper precisely outlines the complex division of labor and the internal structure of the various sub-agents that participated in this task:
- Out of the 60 sub-agents, two were directly responsible for developing the key mathematical ideas that led to the scientific breakthrough.
- 13 additional sub-agents contributed ideas and passed them to these leading agents for further development.
- 30 sub-agents attempted to develop new ideas of their own but were unable to do so during the run.
- 13 sub-agents served as validators whose role was to carefully inspect and verify the correctness and accuracy of the arguments and proofs presented.
- The final two sub-agents assisted in writing the initial draft of the scientific paper describing the findings.
Verification of Findings and Formal Grounding
The scientific results and progress achieved by Anthropic's model did not remain merely hypothetical. The research findings were verified and confirmed by two in-house mathematicians employed at Anthropic itself. Furthermore, to ensure logical and scientific accuracy and provide a solid foundation, the findings underwent a formalization process using Lean—an open-source proof assistant designed for proving mathematical theorems and claims.
This achievement joins a series of significant mathematical breakthroughs recently led by Large Language Models (LLMs). Over the course of this year, a number of Erdos problems have been successfully solved by AI models, with the release of more powerful and advanced models leading to even more impressive and complex results.
For instance, OpenAI recently released a set of ten major results successfully proved by its internal development model known as "Astra." In parallel, a separate research effort led by Anthropic successfully disproved the long-standing Jacobian conjecture—another mathematical problem that had occupied researchers for a long period and remained unsolved until now.
Concern and Excitement in the International Mathematics Community
The rapid accumulation of mathematical and research results achieved through AI systems is generating significant interest, but also deep concerns and anxiety within the scientific and mathematical community. In an official public declaration signed in June by a group of prominent mathematicians, serious concerns were raised that the growing use of AI could undermine and damage critical and fundamental values that have guided the field for generations.
The primary concern outlined in the public statement directly relates to the accepted standard that true mathematical proofs should be "attributable to specific authors who take credit for their discovery and assume responsibility for their correctness" regarding the scientific validity of the arguments they present.
Despite these concerns, the mathematical community remains divided on how mathematicians and researchers should approach these new research techniques and integrate them into their scientific work. In a blog post responding to the June declaration, Fields Medal winner Timothy Gowers questioned these concerns and wondered whether the influence of AI might actually change mathematics in a more complex and positive way.
Gowers wrote the following in his post: "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' words reflect an alternative perspective that views technological shifts as an opportunity to reshape scientific research, moving beyond the focus on individual credit and traditional frameworks of attribution and citation in the field.