Teen’s Claude-coded proof claims rhombicosidodecahedron is not Rupert
Awaiting review
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Expert-checked
- Importance
- 3 of 5
- Last verified
- 14 October 2026
Your AI and this story
- GPT-6 Astra158 days after its cutoff
- Claude Opus 5.597 days after its cutoff
- Gemini 4 Argon188 days after its cutoff
- Grok 4.7127 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 97 days before it.
Key facts
- Preprint: Gihyo Jung, ‘The rhombicosidodecahedron is not Rupert’, Zenodo 10.5281/zenodo.23159625, Oct 5, 2026 (about 7.8k views by Oct 14); code at github.com/swiri0921-bit/rhombicosidodecahedron-not-rupert
- Abstract: settles a conjecture of Steininger and Yurkevich, who built the first convex polyhedron without the Rupert property (the ‘Noperthedron’, arXiv 2508.18475, 2025). Because of the solid’s symmetry, the standard subdivision method does not work alone, so the paper adds three new local certificates
- Method (README): implements Steininger–Yurkevich’s global and local theorems; outward-rounded interval arithmetic with rigorous sin/cos; exact identities in Q(√5); LP (HiGHS) used only to find witnesses, all re-verified; cell cover of 211,680 cells (1.23e7 leaves) with 0 failures; a second implementation in exact rational arithmetic. About 38 hours of computation on a laptop
- Background: Steininger and Yurkevich conjectured (2021) that the rhombicosidodecahedron is not Rupert; their 2025 Noperthedron methods did not suffice for it. Benjamin Grimmer (Johns Hopkins) had told Quanta that two weeks of computer search on it ‘just seems to resist any attempt’
- AI use (press, not in the Zenodo record or README): Jung told JoongAng Ilbo he used Claude ‘to generate code for solving a difficult mathematical problem and then reviewing the results’; Korea Daily says he also used AI to check the proof and help write the paper. His Reddit post topped a Claude coding forum on Oct 10
- Jung says he chose the topic without an adviser, admits he cannot independently verify every detail, and says another study reached the same conclusion by a different method around the same time (not named; not found)
- Korean experts (JoongAng): Oum Sang-il (IBS Discrete Mathematics Group): posting ‘establishes a public record of when it was released’ but ‘does not guarantee the validity of its contents’; Seo In-suk (SNU): the author must understand all details and answer questions; Choi Kyu-dong (UNIST): lack of training and a paper’s value ‘can be distinct’
What happened
A convex polyhedron is “Rupert” if a straight tunnel can be cut through it large enough for a congruent copy to pass through (Prince Rupert’s cube puzzle, c. 1693). For decades every convex polyhedron tested turned out to be Rupert, until Jakob Steininger and Sergey Yurkevich proved in 2025 that a purpose-built polyhedron, the Noperthedron, is not. They had earlier conjectured that the rhombicosidodecahedron (20 triangles, 30 squares, 12 pentagons) is not Rupert either, but their methods did not settle it.
On Oct 5, 2026 Gihyo Jung posted a computer-assisted proof of that conjecture on Zenodo, with a GitHub repository of certificates and two independent checkers. Korean newspapers (Korea Daily, Oct 13; JoongAng Ilbo, Oct 14) reported that he is a ninth grader and that Claude wrote the code. Neither the Zenodo record nor the README contains an AI disclosure; the AI role is known only from his interviews.
Why it matters
If it holds, it is the second named non-Rupert polyhedron and the first Archimedean solid shown not to be Rupert, from an author with no formal training working with a coding agent. The Korean debate centres on authorship: whether a paper counts if its author cannot check every step himself.
What is disputed or not yet verified
| Verification | unverified claim (computer-assisted certificates published with code; no peer review or independent check reported as of Oct 14) |
|---|
Sources
6 sources from 6 sites. Numbers match the chips in the text.
6 sources: 3 primary, 3 press
Primary
- Zenodo: G. Jung, The rhombicosidodecahedron is not Rupert (Oct 5, 2026)zenodo.org, paper
- GitHub: proof code and certificatesgithub.com, code
- Steininger & Yurkevich: A convex polyhedron without Rupert’s property (arXiv 2508.18475)arxiv.org, paper
Press
- Korea JoongAng Daily: 15-year-old claims AI helped crack 300-year-old math puzzle (Oct 14)koreajoongangdaily.com, press
- Korea Daily: Rupert’s Hypothesis — South Korean middle schooler tackles 300-year-old math problem using AI (Oct 13)en.koreadaily.com, press
- Quanta: First shape found that can’t pass through itself (Oct 2025)quantamagazine.org, press
Changes
- Filed (Google News: Korea Daily and JoongAng Daily); verification status pending