In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

When counting squares in a grid, don’t stop at the smallest boxes; the bigger ones are hiding too. The rule is simple: In an n × n grid—where n is the number of squares both horizontally and ...

Parallel lines close parallel lines Lines which never meet and stay the same distance apart. Parallel lines are indicated by a pair of arrows. are two or more straight lines that remain the same ...

It is rare to read about “spectacular progress” or a “once-in-a-century” result in mathematics. That’s for good reason: if a problem has not had a solution for many years, then completely new ...