The paper argues that the rhombicosidodecahedron—a 62‑faced Archimedean solid—cannot be a Rupert solid, meaning no straight tunnel can let an identical copy pass through it. If true, this settles a conjecture first raised in 2021.

Jung says the calculations took about 38 hours on his laptop and were done with AI assistance. At the same time, other independent AI‑assisted proofs of the same result were posted on GitHub by Bence Hervay and Oscar Smith. Smith’s proof is formalised in the Lean proof assistant, while Hervay’s proof carries a commit date of Sept. 28, a week before Jung’s paper appeared.

Experts warn that even when AI writes code, the author must fully understand every part of the work. Oum Sang‑il noted that posting a paper creates a public record but does not guarantee its validity, and Seo In‑suk added that the author must be able to answer questions from others. Both stress that peer review is still required before the result can be accepted academically.

The case raises broader questions about how AI will change the way mathematicians conduct research. It shows that AI can speed up proof generation, but human insight and verification remain essential.