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

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 ...

Gerd Faltings proved a conjecture that had been unsolved for six decades, using connections between numbers and geometry.

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 ...