July 21, 2026

Anthropic’s Claude Fable 5 helps disprove 90-year-old Jacobian Conjecture

A significant development in mathematics occurred as Anthropic employees Alpoge and Matthew disproved the long-standing Jacobian Conjecture, a 90-year-old problem in algebraic geometry, using their AI tool, Claude Fable 5. Originally proposed in 1939, the conjecture has intrigued mathematicians for decades, and its resolution reflects the growing trend of utilizing advanced AI models to tackle complex problems in pure mathematics. This instance highlights the collaborative potential between mathematicians and AI systems in advancing research in the field.

Alpoge: Levent Alpöge is a mathematician with expertise in algebraic geometry and number theory who has collaborated with Anthropic. Working with Akhil Mathew, he used Claude Fable 5 to produce a counterexample that disproved the Jacobian Conjecture. His recent work illustrates the role of AI assistance in tackling longstanding open problems in mathematics.
Matthew: Akhil Mathew is a mathematician who partnered with Levent Alpöge on a project involving Anthropic’s AI tools. Together they employed Claude Fable 5 to identify a verifiable counterexample to the Jacobian Conjecture proposed in 1939. This collaboration highlights effective human-AI teamwork in advancing mathematical research.
Anthropic: Anthropic is an artificial intelligence research company focused on developing safe and capable AI systems. Its Claude Fable 5 model was used by researchers to generate a counterexample disproving the Jacobian Conjecture. The company emphasizes applications of its models in scientific research and complex problem-solving.
Claude Fable: Claude Fable 5 is Anthropic’s Mythos-class AI model optimized for demanding knowledge work, scientific research, and autonomous reasoning tasks. It assisted mathematicians in autonomously discovering a counterexample that disproved the Jacobian Conjecture. The model is designed for extended, complex projects requiring high levels of capability and reliability.

AI in Mathematics: Frontier AI models are increasingly being applied to resolve longstanding open problems in pure mathematics.
Model Applications: Anthropic’s advanced models support ambitious scientific research tasks that extend beyond standard coding and analysis.
Research Collaboration: Mathematicians are partnering with AI systems to accelerate progress on conjectures in algebraic geometry.

AI tools built by Emerald Force

Built and supported by Emerald Force.

You might also like