Researcher Used AI to Discover 3D Aperiodic Monotile
The Chair44 shape marks the first 3D aperiodic monotile, discovered in September 2026 using an AI model.
Updated on Sept. 28, 2026 in Mathematics
Live Poll
Do you trust scientific discoveries generated primarily by artificial intelligence over those by human researchers?
In September 2026, Ioannis Tsiokos identified a 3D aperiodic monotile dubbed Chair44 by tasking OpenAI's GPT-6 Astra with the problem. This discovery, which involves a single shape capable of tiling 3D space without repeating, follows the 2023 identification of a 2D aperiodic monotile known as the hat.
Why it matters
The discovery of an aperiodic monotile for 3D space explores long-standing mathematical questions regarding geometric tiling patterns. It represents an application of large language models to complex structural mathematics where the model processes existing theorems to generate new configurations.
Chair44 is a 3D monotile that maintains aperiodicity, meaning it tiles 3D space without forming a repeating lattice structure. This discovery builds on the 2D hat monotile identified in 2023, utilizing GPT-6 Astra to synthesize Lean code and existing mathematical laws into a valid geometry.
The players
Ioannis Tsiokos
A researcher who has authored approximately 40 papers utilizing AI models for mathematical discovery.
Chaim Goodman-Strauss
A mathematician based at the University of Arkansas who published papers clarifying the structural properties of Tsiokos's work.
Felix Flicker
A researcher at the University of Bristol in the UK who demonstrated methods to simplify the Chair44 shape.
The details
Tsiokos instructed GPT-6 Astra by feeding the model a corpus of mathematical theory, theorems, and Lean code—a formal language for writing mathematical proofs. The AI then analyzed the geometry of the 2D hat problem to extrapolate a 3D equivalent that satisfies the requirements of non-repeating space-filling. Subsequent research by Felix Flicker demonstrated that the initial Chair44 shape can be further simplified while retaining its aperiodic characteristics, a finding clarified by Chaim Goodman-Strauss.
Timeline
2023: Mathematicians identified the 2D aperiodic hat monotile.
September 2026: The discovery of the 3D Chair44 monotile was reported.
The Tech Race
The identification of Chair44 extends the search for aperiodic shapes from the 2D hat discovered in 2023 into three-dimensional space. This milestone represents a transition in mathematical research where AI assistants are used to derive complex geometric structures that have long evaded conventional analysis.
This development is currently limited to pure mathematical research and has no immediate application in consumer hardware or software products. Enthusiasts and researchers can watch for forthcoming papers from the author, who reportedly has 20 additional AI-assisted studies awaiting release.
The takeaway
The successful use of GPT-6 Astra to solve for a 3D aperiodic monotile validates the use of LLMs in formalizing mathematical proofs. Readers interested in the evolution of this geometry should monitor future publications by Tsiokos to see if these shapes hold structural properties useful for physical materials.
Further reading
For more background on geometric tiling and structural proofs, browse our Mathematics archive.
Source note: This article includes information reported by New Scientist.
Live Poll
Do you trust scientific discoveries generated primarily by artificial intelligence over those by human researchers?
