Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Do you know what the dominant word of the day is? It’s conjecture. Mr. Dictionary says that conjecture is an opinion or conclusion formed on the basis of incomplete information. Sounds reckless and ...