On a mild autumn day in 2016, the Hungarian mathematician Gábor Domokos arrived on the geophysicist Douglas Jerolmack’s doorstep in Philadelphia. Domokos carried with him his suitcases, a bad cold, ...

Last August, 30 years after the Rubik’s cube first appeared, an international team of researchers proved that no matter how scrambled a cube got, it could be solved in no more than 20 moves. Although ...

An engineer noted for his ability to visualize three-dimensional structure was having coffee and doughnuts. Before he dropped a sugar cube into his cup, he placed the cube on the table and thought, ...

Geometry also predicted that if you fragmented a flat surface randomly, it would break into rough rectangles, and if you did the same in three dimensions, it would produce rough cubes. But for any of ...