> The users of those mathematical tools (whether software implementors or people just calling some software library) usually don’t need to care about the detail

> The users of those mathematical tools (whether software implementors or people just calling some software library) usually don’t need to care about the details of the proofs Oh for sure, and perhaps this is just a confusion of terms but i think that's what the thread parent was speaking with "applied statistics". In academia, "applied math/statistics" can mean "I'm doing theoretical math with an eye towards applications but it still requires heavy mathematical machinery", but it can also mean "I'm using mathematical tools to solve empirical problems, and I'm never going to need to worry about Lebesgue measures".