[crazygringo]

> what it is that mathematicians want from math: that the primary aim isn't really to find out whether a result is true but why it's true.

I really wish that had been my experience taking undergrad math courses.

Instead, I remember linear algebra where the professor would prove a result by introducing an equation pulled out of thin air, plugging it in, showing that the result was true, and that was that. OK sure, the symbol manipulation proved it was true, but zero understanding of why. And when I'd ask professors about the why, I'd encounter outright hostility -- all that mattered was whether it was proven, and asking "why" was positively amateurish and unserious. It was irrelevant to the truth of a result. The same attitude prevailed when it got to quantum mechanics -- "shut up and calculate".

I know there are mathematicians who care deeply about the why, and I have to assume it's what motivates many of them. But my actual experience studying math was the polar opposite. And so I find it very surprising to hear the idea of math being described as being more interested in why than what. The way I was taught didn't just not care about the why, but seemed actively contemptuous of it.

[Ar-Curunir]

Math-for-engineering and math-for-math courses are very different in emphasis and enthusiasm. Many engineering students tend to not care too much about proofs, so the "get it working" approach might be fine for them. Also, the math profs teaching the "math-for-engineering" courses tend to view them as a chore (which it kind of is; pure math doesn't get a lot of funding, so they have to pick up these engineering-oriented courses to grab a slice of that engineering money).

[losvedir]

I guess, what university and what level of math was that?

I majored in math at MIT, and even at the undergraduate level it was more like what OP is describing and less like what you're saying. I actually took linear algebra twice since my first major was Economics before deciding to add on a math major, and the version of linear algebra for your average engineer or economist (i.e.: a bunch of plug and chug matrices-type stuff), which is what I assume you're referring to, was very different. Linear algebra for mathematicians was all about vector spaces and bases and such, and was very interesting and full of proofs. I don't think actually concretely multiplying matrices was even a topic!

So I guess linear algebra is one of those topics where the math side is interesting and very much what all the mathematicians here are describing, but where it turned out to be so useful for everything, that there's a non-mathematician version of it which is more like what it sounds like you experienced.