## The Importance of Being Wrong (and in the Right Way)

When I was an undergraduate, one of my math professors […] explained to us the difference between a useful wrong proof and a useless wrong proof. When attacking an unsolved problem such as the Riemann conjecture, a useful wrong proof was wrong; but for reasons nobody expected. Finding the flaw in the proof taught you things about the problem you didn’t previously know. By contrast, a useless wrong proof was wrong for obvious reasons. It didn’t teach you anything new about the problem.