Gerd Faltings, a number theorist at the Max Planck Institute for Mathematics in Bonn, Germany, has won the 2026 Abel Prize, ...

The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

It’s a puzzle that’s baffled experts since the 1950s, but now a solution for the Diophantine equation has finally been cracked. The problem asks if all whole numbers could be expressed as the sum of ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

Your mathematics teacher at school will have told you that you can only solve a set of simultaneous equations if there are as many equations as there are variables, but that is because they don’t ...