I don’t know. I read and writ a lot of math (where “obvious” is probably most likely to be overused) and I do try to double-think every time I write it down. But when reading, it means to me “this statement SHOULD be obvious, if it’s not, then you’re missing something and you should probably reread what just happened.” If it doesn’t say that and just states the result I am less likely to give it a second thought, perhaps ironically. If they don’t say “obvious” then maybe they’re quoting some theorem I don’t know and that often isn’t very relevant unless I need to know every detail of this. If they do say “obvious” then they’ve at least judged that theorem (or definition or whatever) to be sufficiently basic as to be worth my while learning. Not only that, but if I think something seems obvious and the author thought it was sufficiently obvious to call it obvious, then I’m probably not missing anything subtle!
I don’t know. I read and writ a lot of math (where “obvious” is probably most likely to be overused) and I do try to double-think every time I write it down. But when reading, it means to me “this statement SHOULD be obvious, if it’s not, then you’re missing something and you should probably reread what just happened.” If it doesn’t say that and just states the result I am less likely to give it a second thought, perhaps ironically. If they don’t say “obvious” then maybe they’re quoting some theorem I don’t know and that often isn’t very relevant unless I need to know every detail of this. If they do say “obvious” then they’ve at least judged that theorem (or definition or whatever) to be sufficiently basic as to be worth my while learning. Not only that, but if I think something seems obvious and the author thought it was sufficiently obvious to call it obvious, then I’m probably not missing anything subtle!