Gerd Faltings, mathematician who proved the Mordell conjecture, wins the Abel Prize at age 71

"Since the beginning of math, people have been looking for a rarified subset of these solutions—rational points on the curve, where the coordinates are integers or fractions. These special points have rich and complicated relationships that belie a hidden order that mathematicians aim to uncover."

"He proved that if a curve's equation has a variable raised to a power higher than 3, then it must have a finite number of these points. Only lines, quadratics (such as circles) and cubic equations could have an infinite number."

"Near the beginning of my career, I got the Fields Medal. And near the end, I'm getting the Abel Prize. It's a nice duality."

Gerd Faltings, a 71-year-old German mathematician, received the Abel Prize, a lifetime achievement award for mathematics. He is renowned for proving the Mordell conjecture in 1983, now called Faltings's theorem. The theorem addresses rational points on curves—solutions where coordinates are integers or fractions. Faltings proved that curves with variables raised to powers higher than 3 possess only finitely many rational points, while lines, quadratics, and cubic equations can have infinitely many. This proof is foundational to arithmetic geometry. Faltings previously won the Fields Medal at age 32, making the Abel Prize a fitting capstone to his distinguished career.

Read at www.scientificamerican.com