9th grader uses Claude to prove 2021 geometry conjecture with 12.3M-case computer check
Gihyo0921 · reddit · 2026-10-10
A ninth grader, working with Claude, claims a proof of the 2021 conjecture that the rhombicosidodecahedron cannot pass through a copy of itself—following last year's discovery of the Noperthedron, the first known such convex shape.
Key points:
- The standard method breaks down due to the solid's 120 symmetries; they identified 4 singular configurations, located them exactly using sqrt(5), and proved new theorems to handle them.
- The final verification splits all orientations into 12.3 million boxes checked via interval arithmetic (immune to rounding errors), taking about 38 CPU hours.
- Claude did much of the math arguments, code, and paper writing; the student chose the problem, steered direction, and verified everything—a full re-check by Claude caught several real mistakes.
- Bence Hervay and Oscar Smith independently proved the same result with different methods and are cited; conjecture co-author Sergey Yurkevich endorsed the paper, due on arXiv Monday.
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