AI finds 3D shape that fills all space with a never-repeating pattern
A 3D shape that can tile 3D space, leaving no gaps and never forming a repeating pattern, has been discovered using an AI model. The researcher behind the findings, who has no academic background in the area, says his work has angered professional mathematicians
In 2023, mathematicians discovered a 2D shape known as "the hat" that can tile a surface without gaps and without creating a repeating pattern, which they called an aperiodic tile. This finding has since been applied in various scientific fields, such as engineering and chemistry. Now, Ioannis Tsiokos, a software developer with no formal mathematical background, has utilized AI to discover a 3D version of this shape, which he calls Chair44.
Tsiokos fed the 2D problem to OpenAI's GPT-6 Astra model, asking it to find a similar solution in three dimensions. The AI, Astra, found the 3D shape without Tsiokos' intervention. While Tsiokos acknowledges that he didn't discover the tile himself, he has published a paper on his findings and has used AI to write several other mathematical papers.
However, some mathematicians, like Chaim Goodman-Strauss, have criticized the paper, calling it "basically a piece of slop" and stating that it does little to clarify or explain the result. Despite the criticism, Felix Flicker, from the University of Bristol, has published a paper showing that Chair44 can be simplified while retaining its aperiodicity.
Craig Kaplan, one of the researchers behind the previous 2D aperiodic tile, acknowledges the paper's deficiencies but confirms that Chair44 appears to be a valid solution.
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