Chaim Goodmann-Strauss

The Monotiling problem and other questions

The famous Penrose tiles, the hat monotile Dave Smith discovered in 2023, and the very new, LLM-found, three-dimensional Chair44 are aperiodic: they shapes that can form tessellations, but only non-periodic ones. The discovery of aperiodic monotiles suggests the "Monotiling problem" (whether or not a given shape can form a tessellation) may be computationally undecidable. We'll survey a web of similar questions about monotiles.