A software dev with no math degree cracked a 3D shape mathematicians spent decades dreading to visualise — using a chatbot.

AI finds 3D shape that fills all space with a never-repeating pattern

Software developer Ioannis Tsiokos, who has no mathematics background, used OpenAI's GPT-6 Astra model to discover Chair44, a 3D aperiodic monotile — a shape that tiles three-dimensional space forever without ever repeating a pattern. He fed the model the underlying theory, theorems and Lean code, and the AI also drafted the paper describing the find. Craig Kaplan of the University of Waterloo calls the shape a valid solution but says the paper has the usual clarity problems of AI-generated mathematics; Chaim Goodman-Strauss of the University of Arkansas called it "basically a piece of slop." The 2023 2D "hat" tile had already appeared in engineering and chemistry research.

Source: AI finds 3D shape that fills all space with a never-repeating pattern — New Scientist

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