[Tainnor]

That's not a "mathematician" thing, it's a US thing. US universities, for some reason, insist on teaching mathematics twice, once with lots of handwaving and then at some point you get to do a "proof-based course".

In Europe (at least in certain countries, can't speak to all of them), maths lectures will typically be abstract and proof-based from day 1 - at least for maths majors (but frequently for CS and physics students too). Other majors, such as economics and maybe engineering, may get their own lectures that tend to be more hand-wavey because they don't necessarily need the axioms of real numbers to take a derivative here and there.

My linear algebra course was algebra and proof based to the extent that maybe a little bit more geometric intuition would have helped.