I'm a 9th grader and I used Claude to prove a geometry conjecture: the rhombicosidodecahedron can't pass through a copy of itself
A 9th grader, with the help of Claude, proved a geometry conjecture that the rhombicosidodecahedron cannot pass through a copy of itself. This follows mathematicians' 2021 conjecture and the discovery of the Noperthedron, the first convex shape with this property. The proof involved overcoming challenges posed by the rhombicosidodecahedron's 120 symmetries, identifying four singular configurations using sqrt(5), and developing new theorems to address these complexities.
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发布当时偏移：UTC+02026年10月10日 13:10 UTC
收录当时偏移：UTC+02026年10月10日 16:00 UTC
- 发布
- 2026年10月10日 13:10
- 收录
- 2026年10月10日 16:00
- 来源类型
- 开发者社区
- 档位
- 社区
- 信源状态
- 正常
档位是按信源手工设定的编辑判断，不是逐条打分。
Last year, mathematicians found the first convex shape that can't be pushed through a hole in a copy of itself (the "Noperthedron"). In 2021 the same researchers conjectured that the rhombicosidodecahedron, a classic Archimedean solid, also can't do it, but nobody had proved it.
- The existing method breaks down because of the shape's 120 symmetries. We found 4 "singular" configurations where it fails, located them exactly using the number sqrt(5), and proved new theorems to handle them.
- The final computer check splits all possible orientations into about 12.3 million boxes and verifies each one with interval arithmetic (so rounding errors can't fool it). It takes about 38 CPU hours.
- Claude did a lot of the heavy lifting: math arguments, code, and writing the paper. My job was choosing the problem, deciding the direction at each step, and checking everything. When I asked it to re-check the whole proof from scratch, we found and fixed several real mistakes.
Being honest: two other researchers (Bence Hervay and Oscar Smith) independently proved the same result around the same time with different methods, and my paper cites both. Sergey Yurkevich, one of the researchers who made the original conjecture, endorsed my paper for arXiv. It should go live on Monday.
The GIF shows the simpler case: a dodecahedron CAN pass through itself. The rhombicosidodecahedron can't.