Anthropic says an experimental version of its Claude AI system improved a longstanding mathematical bound related to the Riemann hypothesis, raising it from 41.6% to 67.2%. Claude produced the result while unsuccessfully attempting to solve the Riemann hypothesis, drawing on decades of previous mathematical research and extensive computational testing. Anthropic mathematicians reviewed the work, outside experts examined the paper, and Claude produced a formally verifiable version of the proof using Lean. The result does not prove the Riemann hypothesis, but Claude made progress on a related question involving the zeros of the Riemann zeta function. In a blog post, Anthropic said two mathematicians on its staff studied and validated Claude’s paper, and the company also asked number theorists Brian Conrey and Dan Goldston to examine the work. The finding emerged unexpectedly, and it didn’t seem to be the result from expert prompt engineering. Staff member Jarred Sumner initially asked Claude to “take a real stab” at proving the Riemann hypothesis. The model failed at that larger task but identified a way to combine earlier mathematical results to improve the known lower bound. Anthropic said it does not expect Claude’s method to lead directly to a proof of the Riemann hypothesis. The significance may lie in how the result was produced: Claude searched through possible approaches, coordinated dozens of AI subagents, performed numerical tests, examined previous research and subjected its own work to repeated attempts at falsification. Bernhard Riemann proposed the hypothesis in 1859.