Claude Improves the Estimate of the Zeros of the Riemann Zeta Function
Claude has made significant progress in estimating the zeros of the Riemann zeta function, raising the lower bound from 41.6% to 67.2%. This was achieved through new approaches and coordination of sub-agents.
Claude Improves the Estimate of the Zeros of the Riemann Zeta Function
One of the researchers, more for the sake of experimentation, asked an unpublished research version of Claude to "seriously tackle" the Riemann Hypothesis. The model did not prove the hypothesis, but it unexpectedly achieved a strong result: it increased the lower bound of the zeros of the Riemann zeta function lying on the critical line from 41.6% to 67.2%.
To understand the scale: before this, over 46 years, from 1974 to 2020, the boundary shifted only from 33.3% to 41.6%, and this was the work of dozens of mathematicians. Claude made a leap three times greater in one go.
The work took two sessions in Claude Code, approximately 31 million output tokens. Initially, the model tried over 600 ideas, but none led to a result.
Then the user wrote something like "let's try again, believe in yourself," and this, believe it or not, worked: the model coordinated about 60 sub-agents for a day and a half, running thousands of scripts and tests. Ultimately, the improved estimate came from combining ideas from recent works with results from a 2000 paper.
Peer review is not yet available, but the Lean + proof has been verified by two mathematicians from Anthropic and two external experts.
Why it matters
AnalysisThis breakthrough in research could have a significant impact on understanding the Riemann Hypothesis and its connection to number theory. The use of AI to solve complex mathematical problems opens new horizons in science.
Discuss in community
Share your questions and insights with developers
Related in Ecosystem
Practical guides, core terminology, and agent skills
Claude Becomes Smarter
Claude becomes smarter, indicating possible improvements in the model's capabilities.
Markdown Format: The Complete Guide for AI Workflows and Automation
A comprehensive hands-on guide to Markdown syntax for AI development: CommonMark standards, heading hierarchy, GFM tables, character escaping, system prompts, and CLAUDE.md guidelines.
Andrej Karpathy Built HackerTube, a YouTube-like Service, in About 2 Hours
Andrej Karpathy used Claude to filter 43 million Hacker News comments into a YouTube-like recommendation service called HackerTube in roughly two hours.
Claude + Excel for Logistics: 10 Ready-to-Use Scenarios for Rate, OTD, and Cost Audits
A practical B2B playbook on integrating Claude with Excel: ready-made system prompts, formulas, and algorithms for analyzing freight variance, OTD, suppliers, and inventory.