> At some point, you will hit a rock that nobody you know, even really smart people who have done this their whole lives, can jiggle. What do you do? Keep work

> At some point, you will hit a rock that nobody you know, even really smart people who have done this their whole lives, can jiggle. What do you do? Keep working. Or leave it, come back after some time (hours, days, weeks, months... even years). > Are people who do that basically experts at the little problems? Or is it like coding, where you can design a fairly large system and rely on the parts to come together one way or another? Because when I read a math text, it seems really quite dense with things that require a lot of details to be correct. If it's a house of cards spanning a hundred page thesis, how brittle is it? I haven't worked too much in pure math research, but from my understanding it's a process of adding details. You have something you want to prove, and a base you start from. You have an intuition of what you need to be true in order to prove the thing, so start developing those proofs too. In the way you'll find you need certain conditions, and you might find that certain concepts reappear so you find it helpful to define them. > Because when I read a math text, it seems really quite dense with things that require a lot of details to be correct. If it's a house of cards spanning a hundred page thesis, how brittle is it? While technically it is a house of cards (i.e., if a proof is wrong everything that depends on it fails), most of the time you won't find such fundamental errors. Maybe a proof has some missing details that can be amended, or the same statement can be proven another way, or the theorem needs just tiny changes or extra conditions to be fixed.