15-year-old Korean posts AI-assisted proof that a 62-faced shape can't pass through its own copy

A South Korean ninth grader says he used Anthropic's Claude to prove that a 62-faced solid cannot pass through a hole in an identical copy of itself, a claim not yet peer reviewed.

Jung Gi-hyo, 15, a student at a middle school in Gimpo, Gyeonggi Province, posted the paper, titled "The rhombicosidodecahedron is not Rupert," on the research repository Zenodo and the code-sharing platform GitHub on Oct. 5.

"I wrote the paper by using Claude to generate code for solving a difficult mathematical problem and then reviewing the results," Jung told the JoongAng Ilbo.

He said he chose the topic and direction of the research himself, without a professor or other adviser, and that the calculations took about 38 hours on his laptop.

A Reddit post in which he shared the paper topped a forum for Claude users on Oct. 10, according to the newspaper.

A solid is called Rupert if a straight tunnel can be cut through it wide enough for an identical copy to pass through. The name comes from Prince Rupert of the Rhine, who won a late-17th-century bet that a cube could pass through a hole in another cube of the same size, Quanta Magazine reported.

Mathematicians had widely believed that every convex polyhedron has the property. Jakob Steininger and Sergey Yurkevich disproved that in August 2025 by constructing a 90-vertex solid with no such passage, which they named the Noperthedron.

Jung's paper takes on a narrower conjecture the pair raised in 2021: that the rhombicosidodecahedron, an Archimedean solid whose faces are 20 equilateral triangles, 30 squares and 12 regular pentagons, is not Rupert either.

At least two other proofs of the same result have been posted on GitHub. Bence Hervay's computer-assisted proof carries commit dates of Sept. 28, a week before Jung's paper appeared.

An independent audit of Hervay's proof, run on Oct. 8 and 9, found no mathematical gap but stated that it was not a peer review. Oscar Smith's proof is formalized in the Lean proof assistant.

"I am not at a level where I can independently verify every detail of the paper," Jung said. "But another paper reached the same conclusion around the same time through a different approach, so I believe the conclusion itself is unlikely to be wrong."

An illustration of a rhombicosidodecahedron, the 62-faced solid that Jung Gi-hyo’s paper says cannot pass through a copy of itself. Photo generated by AI with Python scripts

Online reaction was split. Some commenters marveled that a middle school student could take on research in such a specialized field, while others questioned whether he understood what he had written.

The paper must still pass peer review before it can count as an academic contribution.

"Posting a paper on a research repository establishes a public record of when it was released, but it does not guarantee the validity of its contents," Oum Sang-il, chief investigator of the Discrete Mathematics Group at the Institute for Basic Science, told the JoongAng Ilbo.

"The author of a paper must understand every aspect of the work and be able to answer questions from others," Seo In-suk, a professor in the Department of Mathematical Sciences at Seoul National University, told the newspaper. "Even when AI is used in research, the author must personally understand and strengthen the arguments for the work to be recognized as a complete academic achievement."

Jung's claim comes weeks after OpenAI said on Sept. 8 that one of its AI systems had resolved the Navier-Stokes problem, one of seven Millennium Prize Problems that each carry a $1 million award from the Clay Mathematics Institute. The institute considers a solution only after it has been published, has stood for two years and has won general acceptance among mathematicians.

Choi Kyu-dong, a professor of mathematical sciences at the Ulsan National Institute of Science and Technology, told the JoongAng Ilbo that Jung's paper was an interesting case showing that an author's formal training and a paper's academic value can be separate matters. "The question now is how such changes will affect the way mathematicians conduct research," he said.