AI helps topple decades-old geometry problem
A famous 30-year-old geometry conjecture has been proved with minimal assistance from AI. The conjecture, proposed by Michel Talagrand, asserts that simple convex shapes can be formed from chaotic point assemblages in high-dimensional spaces. Talagrand, who received the 2024 Abel Prize, expressed his astonishment at the proof's revelation.
- ▪The conjecture states that simple, orderly shapes will emerge from chaotic point distributions across multiple dimensions.
- ▪Michel Talagrand proposed the convexity conjecture in 1995 and initially doubted its validity.
- ▪The proof was recently published, marking a significant milestone in high-dimensional geometry.
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| Original publisher | Scientific American |
| Canonical URL | https://www.scientificamerican.com/article/sensational-proof-topples-decades-old-geometry-problem/ |
| Publication time | Tue, 19 May 2026 16:25:14 +0000 |
| Retrieval time | 2026-05-19T16:29:57.870Z |
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May 19, 20264 min read Add Us On GoogleAdd SciAm‘Sensational’ proof topples decades-old geometry problemThe sudden resolution of a well-known conjecture highlights the growing adoption of AI as an assistant in high-level mathematicsBy Joseph Howlett edited by Lee Billings yuanyuan yan/Getty ImagesLove math? Sign up for our weekly newsletter Proof PositiveEnter your emailI agree my information will be processed in accordance with the Scientific American and Springer Nature Limited Privacy Policy. We leverage third party services to both verify and deliver email.
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