I didn’t take Paul Sally’s math class when I was an undergraduate. I wish I did; unlike most professors, Sally was clearly devoted to teaching first and foremost. A rare trait amongst academics (alas). Be sure to read this Q&A as well. The interviewer was Supriya Sinhababu, and the key passage, in my mind, is the following:
SS: You’ve said that people view it as a “badge of honor” to not be good at math.
PS: Yeah, well. Ignorance is bliss.
SS: You’ve also said that they’d never say the same thing about not knowing how to read. I was wondering why you think it’s become socially acceptable to not be good at math, and what can be done about it?
PS: …First of all, to actually be good at math you have to practice, you have to take it seriously, and you have to be willing to spend time working at it. And all of these are very difficult for students and for humans in general. And they don’t understand that you should never confuse activity with achievement. Many people spend a lot of time early in their math careers, early in their math days, in the classroom, working at it extensively, saying, “I worked three hours on math last night.” Well, if they didn’t achieve anything, that’s activity, that’s not achievement…. And if you don’t get it right, you have failed.
…If you’re working on a certain project in a lab, and you set up the protocol correctly, then whatever the results, you can publish them. “I did this in the lab, and this is what happened.” But see, in mathematics you can’t do that. You have to set out to solve a problem or prove a theorem, and by the time you get through, if you don’t have a proof, you cannot actually publish your results, making apologies for your inability to prove the theorem. You simply have to confess that you couldn’t do it….
Requiestcat in pace.