For over 150 years, the Riemann hypothesis has stood as one of mathematics' most elusive puzzles, a mystery centered on the distribution of prime numbers. A $1 million bounty for a complete proof remains unclaimed, and contemporary AI models still cannot crack it. Yet a recent experiment from Anthropic reveals these models can push much further than expected, reigniting a contentious debate about whether machines can truly drive scientific discovery. Main Developments Anthropic announced Monday that an unreleased model made significant progress on the Riemann hypothesis, substantially raising the lower bound of solutions for which the hypothesis holds true. The achievement stands out not just for the result, but for how it was reached: an Anthropic staff member with no significant mathematical training prompted the model to attempt a real proof, then stepped back. Over the following day and a half, the model autonomously coordinated a massive effort. It tested 650 distinct ideas for solving the problem, coordinating across 60 subagents and spending 31 million output tokens in total. Of those subagents, two developed the key mathematical ideas, 13 contributed supporting ideas, 30 attempted but failed to generate new approaches, 13 served as validators, and two helped write the initial paper. Read also: Joby's $500M Bet: Why Defense Is Key to Flying Taxis Anthropic's in-house mathematicians confirmed the findings, and the proof was formalized using the open-source proof assistant Lean. This verification process ensures the result meets rigorous standards, even though the reasoning path was largely machine-generated. The company has not yet specified when the model will be publicly released. Background This achievement is part of a recent wave of AI-driven mathematical breakthroughs. Over the past year, large language models have solved a number of Erdős problems, with more powerful systems yielding increasingly impressive results. OpenAI recently published 10 major results proved by its internal Astra model, while Anthropic separately disproved the longstanding Jacobian conjecture. The accelerating pace has sparked both excitement and concern within the mathematical community. In June, a group of prominent mathematicians signed a public declaration warning that AI could undermine core values of the field, particularly the expectation that proofs be attributable to specific authors who take responsibility for their correctness. The debate remains unresolved. Why It Matters The stakes extend far beyond one hypothesis. If AI can meaningfully contribute to solving problems that have stumped humans for centuries, it challenges fundamental assumptions about creativity, authorship, and the nature of mathematical proof. The field is split on how to respond, with some fearing a loss of accountability and others seeing opportunity. Fields Medal winner Timothy Gowers offered a contrarian perspective in a blog post responding to the declaration. He questioned whether AI's influence might change mathematics in a complex, positive way, suggesting that a world where theorems are no longer tied to individual mathematicians might be no more problematic than the fact that stars aren't named after astronomers. What's Next The immediate question is whether Anthropic will release the model and the full paper, which could invite broader scrutiny from the mathematical community. Independent verification of the Riemann hypothesis progress will be crucial, as will attempts to apply similar autonomous approaches to other open problems. The field's ongoing debate over AI's role will likely intensify as results accumulate. For now, the $1 million bounty for a full Riemann hypothesis proof remains unclaimed. But the demonstration that a non-expert can direct an AI to make substantial progress suggests that the next breakthrough may come from an unexpected direction. How mathematicians reconcile these tools with their professional norms will shape the discipline's future.