AI Assisted Discovery of 3D Aperiodic Monotile
Researcher Ioannis Tsiokos used AI to identify a 3D aperiodic monotile known as Chair44.
Updated on Sept. 28, 2026 in Mathematics
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In September 2026, researchers reported the discovery of Chair44, a 3D aperiodic monotile found by Ioannis Tsiokos using OpenAI's GPT-6 Astra model. This unique shape fills space without ever creating a repeating pattern.
Why it matters
Aperiodic tiles provide essential insights into geometric tiling theory, building on the 2D hat monotile discovered in 2023. The use of advanced AI models to solve complex mathematical problems marks a significant shift in how researchers approach theoretical discovery.
Ioannis Tsiokos utilized GPT-6 Astra, feeding the model comprehensive mathematical theory, research papers, and Lean code. He has published approximately 40 papers using AI, with another 20 currently in development.
The players
Ioannis Tsiokos
He is a researcher who has published approximately 40 papers using artificial intelligence tools.
Chaim Goodman-Strauss
He is a mathematician based at the University of Arkansas who published a paper clarifying the work of Tsiokos.
Felix Flicker
He is a researcher at the University of Bristol who demonstrated that the Chair44 shape can be simplified.
The details
Tsiokos instructed the AI to search for a 3D equivalent to the 2D hat problem, resulting in the Chair44 shape. Subsequent research by Chaim Goodman-Strauss and Felix Flicker helped clarify the geometry and simplify the shape while maintaining its aperiodic properties.
Timeline
Mathematicians identified a 2D aperiodic hat monotile in 2023.
New Scientist reported the Chair44 discovery in September 2026.
Deeper Dive
The discovery of Chair44 extends the research trajectory established by the 2023 discovery of the 2D hat monotile.
While primarily a theoretical breakthrough, the identification of aperiodic shapes may eventually influence structural engineering or material design. Future research into the properties of 3D aperiodic monotiles could lead to stronger building materials or new manufacturing techniques.
The takeaway
The successful application of AI to solve long-standing geometric puzzles highlights a new era of computational mathematics. This discovery suggests that AI models will play an increasingly vital role in exploring complex theoretical landscapes previously inaccessible to manual computation.
Further reading
Learn more about advancements in Mathematics.
Source note: This article includes information reported by New Scientist.
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