Harvard Mathematician and Claude Disprove 100-Year-Old Carathéodory Conjecture
新智元 · wechat · 2026-08-20
Levent Alpöge (Harvard/Anthropic) and Claude have disproved the century-old Carathéodory conjecture and the Loewner exponent conjecture.
Key Findings
- Explicit Counterexample: Alpöge and John-Paul Smith constructed a specific function g₂. The resulting convex body has an umbilical point with exponent 2 at the origin.
- Disproof: An exponent of 2 violates the Loewner conjecture's limit of 1. Additionally, this C∞ smooth convex body possesses only one umbilical point, refuting the Carathéodory conjecture's requirement of at least two.
AI's Evolving Role
- This follows Alpöge's previous collaboration with Claude to disprove the 3D Jacobian conjecture.
- The event highlights a paradigm shift where AI acts as an "intuition supplement" for mathematicians, solving long-standing problems through human-AI collaboration.
Related event: Claude Helps Disprove Century-Old Carathéodory Conjecture(2 posts)→
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