Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

Has one of the major outstanding problems in number theory finally been solved? Or is the 600-page proof missing a key piece? The verdict isn’t in yet, but the proof, at least, will finally appear in ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

A mathematical problem more than 300 years old gets a formal proof with the help of computer formal verification. A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

A Russian mathematician may have finally cracked one of the most famous problems in mathematics: the Poincaré conjecture, a question about the shapes of three-dimensional spaces. If his work is ...