Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy). However, they can also be pretty free with t

Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy). However, they can also be pretty free with their assumptions (which can be wild, though if reasoned from carefully usually turn out to be useful even if nobody anticipated that they would). People working with mathematicians probably spend a lot of time wondering why they're so persnickety about some things most people would consider obvious ("but how do you really know 2+2=4?") but sometimes not so much about whether the constructions they're working with actually reflect a particular concrete reality.