I am a mathematician but I want to be an engineer

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I am doing a ph.d in math, but I really want to be an engineer.
I am doing a ph.d in numerical analysis and simulation with a minor in stochastics.
My dream after I finish is to get a job in one of the following industries:

My three main areas of interest are:
0. anything aerospace, I just love flying
1. energy infrastructure, I think it is a very exciting problem
3. AI and robotics, it's cool

I of course would prefer to keep working with math, not doing research per se, but using the latest research and implementing new methods and such.
That's why I say I want to be an engineer instead of a mathematician.

I also want to make good money.
Do such jobs exist?