Ein Stein - Aperiodic Monotiling

Ein stein (lit. "one stone") is a geometric shape proven to be capable of tiling a plane aperiodically (i.e. by never repeating a pattern).
Aperiodic tiling is one of the most interesting debates in math, with scientists (including Dr. Roger Penrose) trying to narrow down the number of different shapes for this kind of tiling. In 2023, a group of scientists proved that a shape alone, proposed by an amateur mathematician, could get the job done.

https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/