> except that for programmers it's possible (and advantageous IMO) to deeply understand way more than they actually do, which seems less clearly true in number

> except that for programmers it's possible (and advantageous IMO) to deeply understand way more than they actually do, which seems less clearly true in number theory. But that's not true for programmers either. How often do we look at the compiler or interpreter and check each opcode to make sure the right transistor gets turned on at the right time? The fact that number theory papers are 50-100 pages long may be an indication they're missing some useful level of abstraction, but then again if they're already operating at the most abstract level limited by the human mind then maybe that's why the papers are so long.