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"content": "<p>It's now one year from the release of "An aperiodic monotile" preprint. That year has seen an amazing outflow of mathematical and artistic work building on the hat, turtle and spectre aperiodic monotiles, and I'm very much looking forward to seeing what the future brings! In an update on the original work, "An aperiodic monotile" was accepted by a journal in December and is now awaiting publication, while a revised version of "A chiral aperiodic monotile", addressing referee comments on the first version, was submitted last month. I've started preparations for the Lean formalization of both papers and expect to continue with more substantive work on that formalization after IMO 2024; I don't think there will be any particular difficulties in formalizing the purely combinatorial parts of the arguments, but the link between the combinatorial and geometrical views of the tiles (Appendix A of "An aperiodic monotile") is likely to be rather more time-consuming to formalize (note that mathlib doesn't yet have either the Jordan curve theorem, which is likely to be of use, or Euler's theorem for plane maps, which is definitely needed).</p>",
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