Over the next decade, mathematicians tinkered with the concept and got the number in the set down from tens of thousands of shapes to just a couple. But all the time they were searching for The One — an answer to the "einstein problem." Some scientists were working hard just to prove that no such single shape existed.

In November 2022, David Smith, a self-described "shape hobbyist" from East Yorkshire, England, announced that he had likely discovered an einstein in the form of a 13-sided tile he called "the Hat," because it looks vaguely like a fedora.

Smith, a retired printing technician, spent a lot of time at home cutting shapes out of paper and experimenting with them. He knew the mathematical theory behind what finding the einstein would take, and one day he found something very promising. He contacted computer scientists and a mathematician he knew, and they set about trying to prove it.

In March 2023, they posted a preprint, much to the astonishment and excitement of mathematicians the world over. But in the midst of this discovery, Smith found another einstein: "the Turtle."

It turns out, "the Hat" and "the Turtle" are just two in a family of einstein tiles, created by adjusting the lengths of the sides of the shapes in relation to all the others.