Most patterns eventually repeat themselves. But in the 1970s, mathematician Roger Penrose discovered a set of shapes that could cover an infinite plane without ever repeating. Known as Penrose tilings ...

If you walk through Midtown in New York City and look up, you’ll see a string of nondescript buildings towering over the street. Taken in as a whole, the buildings are mostly underwhelming—just ...

A quantum Rubik’s cube would be infinitely more complex than the traditional puzzle, but mathematical modelling shows it wouldn’t be unsolvable. In the summer of 2022, Noah Lordi and Maedée ...