“Another thing he talked about that’s actually useful, and this is my favorite one, he said that blackboards smudge productively, which is just a great line. You know, you’re writing on a blackboard and oops, you make a mistake, you can rub it out with your hand, or you rub it out with an eraser. And it’s really easy to do. But it’s really hard to do it completely; you can’t get rid of it entirely. There’s always a little bit of a smudge and you write over it. And I’ve always thought that was a bad thing. And he argues that for mathematics, and particularly mathematics research, it’s a good thing because a lot of math research involves taking existing concepts and applying them in new ways. And so if you’ve written an existing equation everybody’s familiar with and then rubbed out a part of it and written something new over it, there is a visual sign that you have taken an existing concept and tweaked it, which is sort of like a reminder to the people in the audience that this is how you approach it. This is not some new thing you’ve brought down from on high, it’s an alteration of an existing one.”

— Why Do Mathematicians Love Blackboards So Much?