In physics, your solution should convince a reasonable person. In math, you have to convince a person who's trying to make trouble. Ultimately, in physics, you're hoping to convince Nature. And I've found Nature to be pretty reasonable.
Frank WilczekIf you don't make mistakes, you're not working on hard enough problems. And that's a big mistake.
Frank WilczekAn ordinary mistake is one that leads to a dead end, while a profound mistake is one that leads to progress. Anyone can make an ordinary mistake, but it takes a genius to make a profound mistake.
Frank Wilczek