How do I know if I'm smart enough to be an engineer? Which major should I choose?

Answered

To start out with, I want to echo @briannaf's comment about this not being a matter of intelligence or smartness. Engineering requires a set of skills that's different from say something like psychology or English, but the difference between those isn't a matter of "how smart" someone is. There are a lot of people who are very good at engineering but would struggle in a more humanities-focused major, and vice versa. So it's more about whether you feel comfortable with the skills you would need to use.

My feeling here though is that, if it's specifically Mathematics that you're passionate about, there are other ways to engage that than studying engineering. Math majors are fairly theoretical and actually kinda liberal arts-y in their vibe, so you would probably get much less of a "rat race" type of mentality there than you would in engineering. I'd also heavily consider looking into Statistics — Stats is a math-based major that gives you a wide range of skills and methods for understanding different problems, all of which should be extremely valuable to potential employers as well. Depending on things you might be interested in outside of math, you could also go in a more social-science-y direction with something like Economics — that's heavily math-focused, but involves a lot of other theory and adds in writing skills that wouldn't necessarily be developed in a pure math major.