Ever since Penrose found a two-shape aperiodic tiling of the plane in 1975, mathematicians have wondered if a single shape would suffice. We got our answer on March 20th when Smith, Myers, Kaplan, and Goodman-Strauss published their discovery of The Einstein Hat, the first known aperiodic monotile.

What they actually discovered was an infinite family of aperiodic monotiles. See the neat animation at this timestamped link. There's a Hat, there's a Turtle, and there's an infinite number of other combinatorially equivalent tiles that also tile aperiodically.

This market will resolve YES if a new (combinatorially distinct) family of aperiodic monotiles is discovered by the close date. I will wait for a peer-reviewed result before resolving.