AI discovers 3D shape that tiles space without repeating — SkimNews
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- Ioannis Tsiokos, a software developer with no mathematics training, used OpenAI's GPT-6 Astra model to discover a 3D monotile he calls "Chair44" that tiles space without gaps or repeating patterns.
- Tsiokos fed Astra the 2D problem's theory, theorems, Lean code, and reference papers, then asked it to find a 3D equivalent — and credits the model: "Astra found this, I didn't find the tile."
- Tsiokos also used AI to write the discovery paper and says he has published around 40 papers this way, with another 20 he has yet to release.
- Chaim Goodman-Strauss at the University of Arkansas called the paper "basically a piece of slop" but confirmed the result is valid and "incontrovertibly pretty," and has since published his own paper clarifying the work.
- Felix Flicker at the University of Bristol separately published a paper showing Chair44 can be simplified while retaining its aperiodicity.
- Craig Kaplan at the University of Waterloo — one of the researchers behind the 2023 2D aperiodic "hat" tile — called the new shape a valid solution while noting "all the usual deficiencies of AI-generated mathematics."
- The 2023 2D "hat" tile has already been cited in scientific papers spanning engineering to chemistry, including research suggesting hat-shaped building blocks could be more fracture-resistant than honeycomb-like structures.
Why it matters: Since the 2023 2D "hat" tile has already shown practical promise — papers suggest hat-shaped building blocks could outperform honeycomb structures in fracture resistance — a valid 3D aperiodic monotile could open similar research paths in materials science. The community's split verdict (valid result, "slop" paper) signals AI-assisted discoveries will increasingly need separate human-written follow-ups to gain traction.
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