>But I think most mathematicians teach and learn math because they think it's cool, not because it's useful
That's exactly the point I'm making. That's math for math's sake - which is perfectly okay if you're actually studying math, because in that case it's what you signed up for in the first place.
The problem is if you study something else (for example, Computer Science, or Physics), and are thrown into the exact same math lectures, with no one telling you how all that fancy math is actually useful for anything but doing even fancier math. Only after the mentioned experiences at my internship, where I had the chance to work and talk with people who actually do applied math did I see the point of it. What I think is that mathematicians - and I don't mean this as an accusation - are often unable to understand that while math for math's sake works fine for themselves, it's not really the best approach for people who want to actually apply math to their own field of science.
That's exactly the point I'm making. That's math for math's sake - which is perfectly okay if you're actually studying math, because in that case it's what you signed up for in the first place.
The problem is if you study something else (for example, Computer Science, or Physics), and are thrown into the exact same math lectures, with no one telling you how all that fancy math is actually useful for anything but doing even fancier math. Only after the mentioned experiences at my internship, where I had the chance to work and talk with people who actually do applied math did I see the point of it. What I think is that mathematicians - and I don't mean this as an accusation - are often unable to understand that while math for math's sake works fine for themselves, it's not really the best approach for people who want to actually apply math to their own field of science.