Big Advance on Simple-Sounding Math Problem Was a Century in the Making
There was just one wrinkle: Pasten had no exam to give his students. He instead had them write an essay on whatever topic they wanted. “This turned out to result in very high-quality work,” he said.
Pasten submitted his proof to Inventiones Mathematicae, one of math’s preeminent journals, where it was accepted in just over a month — the blink of an eye by the field’s usual publication standards. “It’s a lovely advance on something that hasn’t seen much progress for essentially 100 years,” said Cameron Stewartof the University of Waterloo. Mathematicians hope it will translate into advances on related number sequences, too.
Pasten’s technique also enabled him to make progress on certain cases of the abc conjecture, yet another question that deals with the interplay between addition and multiplication, and one of the most famous — and controversial — unsolved problems in mathematics. “New (and correct) ideas in this area have been scarce,” Granville wrote in an email. “The originality and promise of his methods deserve wide attention.”
