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AI NewsAn unreleased Anthropic model made progress on one of mathâs biggest unsolved problems
An unreleased Anthropic model made progress on one of mathâs biggest unsolved problems
6:49 AM IST · August 12, 2026

For more than 150 years, the Riemann hypothesis has stood as one of the major unsolved problems in mathematics, a long-running mystery about the distribution of prime numbers. There is currentlya $1 million bountyfor a working general proof of the hypothesis, which remains unclaimed. Contemporary AI models still canât solve it either â but they can make a lot more progress than you might expect, a finding thatâs likely to reopen longstanding questions about contemporary AIâs ability to discover new scientific and mathematical ideas. On Monday, Anthropic announced that an as-yet-unreleased model had made significant progress on the Riemann hypothesis, significantly increasing the lower bound of solutions for which the hypothesis holds true. Even more impressive is how the progress was made: An Anthropic staff member without significant mathematical training prompted the model to âtake a real stabâ at proving the hypothesis, then left the model to coordinate the task across the following day and a half. All told, the model tested 650 different ideas for solving the problem, coordinating across 60 subagents and spending 31 million output tokens in total. âOut of the 60 subagents, two were responsible for developing the key mathematical ideas,â a footnote to the paper explains, â13 contributed ideas to these agents, 30 attempted (but were unable) to develop new ideas, 13 served as validators to check the correctness of the arguments, and the final two helped to write the initial paper.â The finding was confirmed by two of Anthropicâs in-house mathematicians, and formalized using the open source proof assistantLean. This is the latest in a string of mathematical breakthroughs led by large language models, or LLMs.A number of Erdos problemshave been solved by AI models over the course of this year, and the release of more powerful models has led to more impressive results. OpenAIrecently releaseda set of 10 major results proved by its internal âAstraâ model, while a separate effort from Anthropicdisproved the longstanding Jacobian conjecture. The growing body of results has caused both excitement and concern in the mathematical field. Ina public declaration signed in June, a group of prominent mathematicians raised concerns that AI could undermine critical values of the field â particularly the standard that true mathematical proofs should be âattributable to specific authors who take credit for their discovery and assume responsibility for their correctness.â But the field is still split on how mathematicians should approach the new research techniques. Ina blog post responding to the declaration, Fields Medal winner Timothy Gowers questioned whether the influence of AI might change mathematics in a more complex and positive way. âIf we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that wonât be any more problematic than the fact that stars arenât named after astronomers and most arenât named at all,â Gowers wrote.
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