Anthropic Achieves Mathematical Research Breakthrough with AI Agents

Anthropic announced research results that unconditionally raised the proportion of non-trivial zeros of the Riemann zeta function lying on the critical line from 41.6% to 67.25%.

The author field of this paper lists CLAUDE instead of a human, representing the outcome of approximately 60 Claude sub-agents reviewing each other to construct the proof. This result holds high academic value because it was derived without assuming the Riemann Hypothesis.

Key features are as follows:

• AI-based research: Although it started from an experimental request rather than a mathematical research plan, the AI agents collaborated to surpass existing records in the mathematical community.
• Formal verification: The main theorems in the paper were formally verified using Lean 4, and the related repository has been made public.
• New methodology: To overcome the limitations of the existing 'mollifier' methodology, linear algebra tools such as Sylvester's law of inertia and the rank-trace inequality were used to bypass the sign problem of the zeros.

While this research does not prove the Riemann Hypothesis itself, it is an important case demonstrating that AI can directly participate in high-level mathematical reasoning and proof processes to achieve actual academic progress.