New shape makes TIME’s Best Inventions of 2023 list

Earlier this year, Cheriton School of Computer Science Professor Craig S. Kaplan and his international colleagues David Smith, Joseph Myers and Chaim Goodman-Strauss discovered a single shape that tiles the plane — an infinite, two-dimensional surface — in a pattern that can never be made to repeat.

Now, that shape has been chosen by TIME magazine as one of the best inventions of 2023.

Of the new list, TIME’s editors write: “The result is a list of 200 groundbreaking inventions (and 50 special mention inventions) — including the world’s most powerful supercomputer, a game-changing entertainment venue, and a new shape — that are changing how we live, work, play, and think about what’s possible.”

The shape is known to mathematicians as an aperiodic monotile or an "einstein", a pun that takes its name from the German words "ein" and "stein" that mean "one stone".

Also called the hat by the researchers because of its resemblance to a fedora, the shape tantilized mathematicians, tiling enthusiasts and the public alike, solving a nearly 60-year-old problem in tiling theory, a branch of mathematics that explores geometric shapes that cover a plane without overlaps or gaps.

“It’s an honour to be included in TIME’s list,” says Professor Kaplan. “It’s a rare privilege to have been involved in research that doesn’t just represent an important step forward in what we know about the mathematical universe, but has also captured the public’s imagination. I can only hope that our work will continue to inspire new ideas in mathematics, art, science and engineering.”

Banner: Professor Craig S. Kaplan stands in front of a wall of hat-shaped einstein tiles in the newly renovated Computer Graphics Lab in the Davis Centre, the building that houses the Cheriton School of Computer Science. Photo courtesy of Joe Petrik.