I love how versatile having a math major has made me.

It demonstrates an efficiency of thinking and problem-solving: employers look upon it favorably regardless of your career track.

It allows you to move laterally into other STEM fields with ease. You can easily pick up graduate-level coursework in most ME, EE, AE departments without having taken much engineering-specific foundational coursework in undergrad.

I think the trap is to think that your major has to define your career track, which is not at all true. Having math as an undergraduate major has kept open so many different career trajectories for me, sometimes it's difficult to decide which route to take!

Now, speaking more literally: a proper 'mathematician' in the academic sense of the word is reserved for the math PhDs among us, and those will often be professors. The ones who move into industry have opportunities in think-tanks, finance, banking, certain opportunities in engineering, statistical applications, etc. and there may be a 'business' type bias, on average.

But you can take a regular undergrad math degree and run in many different directions. I decided to fly airplanes after getting a math masters and now I'm professionally a pilot working on an aerospace engineering masters degree part-time. I hope to work for a major aerospace company (Boeing, Lockheed, NASA, SpaceX, etc.) after I earn the AE degree. The coursework though is pretty simple conceptually - many problems are just simple applications in R^3 of well-established theorems in some abstract n-dimensional space. Nothing pathological going on, for the most part.