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.
Time & source
Times shown in UTC
Display time zone: UTC
Local time zone unavailable; showing UTC.
PublishedOffset at this time: UTC+0Oct 10, 2026, 13:10 UTC
IngestedOffset at this time: UTC+0Oct 10, 2026, 16:00 UTC
- Published
- Oct 10, 2026, 13:10
- Ingested
- Oct 10, 2026, 16:00
- Source type
- Dev community
- Tier
- Community
- Source status
- Healthy
Tier is a per-source editorial setting, not a per-item score.
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.