Summary of Key Points
This news highlights breakthroughs in the field of scientific research using AI: Anthropic’s Claude model, through multi-agent collaboration, has increased the lower bound for the proportion of zeros in the Riemann Hypothesis that lie on the critical line from 41.6% (a milestone achieved by humans over several decades) to 67.2%. Companies like OpenAI have also made significant advancements in mathematics, with top scientists (including Fields Medal and Nobel laureates) joining AI firms, marking the transition of “AI-driven scientific discovery” (AI4S) from a concept to reality. The way scientific research is conducted is being fundamentally transformed by AI.
1. Claude’s “Unexpected Breakthrough” on the Riemann Hypothesis: From a Morning Run Inspiration to 67.2%
The Riemann Hypothesis remains an unsolved problem in mathematics, with a $1 million reward at stake for 167 years. It focuses on the distribution of prime numbers and the locations of zeros; mathematicians cannot prove that all zeros lie on the critical line but can only determine the lower bound for their proportion. It took humans decades to raise this lower bound to 41.6%.
An Anthropic employee had the idea of using Claude to attempt to prove the hypothesis during a morning run. Although Claude did not succeed on its own, it utilized 60 “small intelligent agents” (AI assistants working together) to run code for over a day and a half, write hundreds of Python scripts, and execute 2,400 commands. Two agents eventually found a crucial approach, raising the lower bound to 67.2%. While officials emphasize that this method may not ultimately prove the hypothesis, the process is significant as it demonstrates that AI can organize teams to solve problems that have stumped humans for decades.
2. AI in Mathematics Becoming the “New Norm”: Not Just the Riemann Hypothesis
Claude’s achievement is not an isolated case:
- In May, OpenAI used AI to prove the Erdős unit distance conjecture; a Fields Medal laureate called it “the most interesting mathematical result generated by AI.”
- In August, OpenAI launched a free program providing the top ChatGPT model to 100,000 scientists and announced achievements in areas such as high-dimensional geometry and coding theory.
- AI’s capabilities have progressed rapidly: from solving high school-level math problems in 2024 to making major mathematical breakthroughs every month by 2026.
3. Top Scientists “Voting with Their Feet”: From Critics to Core Members of AI Companies
AI firms are no longer just competing for engineers but also for the most talented scientists:
- Jacob, the new Fields Medalist and a mathematician at the University of Toronto, previously criticized the risks of AI but was convinced by OpenAI’s examples and joined to work on AI security and validation.
- John, the Nobel laureate behind AlphaFold (an AI that solves protein structures), left Google DeepMind to join Anthropic, bringing his expertise in structural biology.
The reason is clear: AI can now perform scientific research, and what limits its potential are no longer just coding skills but scientists with a deep understanding of cutting-edge knowledge—those who know how to guide AI in expanding human knowledge.
4. AI4S from a “Slogan” to a “Production Line”: A Fundamental Change in Scientific Research
The concept of AI4S has been around for years, but it has only become reality in 2026:
- Previously, AI was used as a tool (for calculations or literature searches); now, models like Claude can complete the entire research process independently—organizing intelligent agents, identifying problems, writing papers, and suggesting revisions to humans.
- Anthropic’s CEO states that AI should not be seen merely as a tool but as an intelligent entity capable of performing scientific work.
- This shift is transforming the research paradigm: In the future, scientists may collaborate with AI teams, or even let AI lead parts of the research while humans focus on setting the direction.
As the news concludes, “Perhaps Claude, like many of us, underestimated the speed of AI’s progress.” AI is evolving from a complement to research to an active participant or even leader in scientific discoveries, which will reshape the path of future scientific breakthroughs.