What is conducting Math research like? What is a typical day/schedule like?
Well, professors and grad students have a flexible schedule. There will be certain times that they have to teach or have a meeting or office hours. But in order to succeed, most of them will be working quite a bit. I guess it helps if you can be really productive when you do work.
But generally, between research and teaching, you'll be expected to do about twice as much as any normal human being can handle (and you'll wish you could do 100 times as much, given all the papers there are to read and so on), so you're basically set up to fail on some level, in most cases. You just have to find a way to cut some corners at minimal cost (example: not worrying so much about classes in grad school, unless they are going to help with quals because they don't matter as much as research). That's the system. You have to have exceptional self-motivation/self-control to make it in academia.
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