Do not do engineering.
Unless you've accidentally derived advanced math theorems while you were doodling or at least won state math and physics competitions, do not do engineering.
Math and physics fields are made up of tiny handful of people with unimaginable natural talent orders of magnitude above the rest, and thousands of bright, hardworking people who will never get anywhere no matter how hard they try. Fermi said there are two types, of physicists: the very best, and those who shouldn't be there at all.
Any other major gives you a chance to significantly improve your abilities. I was always an extremely driven self-studyer as a kid. I learned all the physics and most of the advanced calculus I would ever know by the time I was 15. 6 years later when I finished engineering school I was almost exactly where I was in 9th grade in terms of mathematical ability.
Chances are, no matter how smart you are, you will not be an amazing physicist or engineer, especially aerospace engineer. People who rise to the top in engineering are a random bunch. They are increasingly involved in much denser math than their predecessors, and are cursed by the same problems as beautiful celebrities: Their assets are genetic and not the result of work ethic, so they become self-destructive slackers. They are also are less able to apply their work now than in the 1960s, which makes them bitter and depressed. Von Braun and Korolev were the last applied physics/engineering people to actually build something groundbreaking(if you like aerospace you know who they are). Since then, Aero-engineering has kind of lost its white-hot status.
Considering the future of engineering, the coolest things that may be built in our lifetimes are more powerful ion engines (if NASA had a reason to really try) or hydrogen gas particle nuclear fission engines (if everybody stopped being afraid of the word 'nuclear'). Even if all these happened amd antimatter engines were to be built, who would build them? Chances are, not you, but a few guys in a small elite team like C.K. Johnson's Skunkworks. Unless you're one of the best mathematicians anywhere right now, chances are you won't be on a team like that. Reality sucks.
Very true. Nuclear energy is an excellent way to go. Problems with current nuclear generation might stem from the fact that they haven't built a new plant in DECADES. Massive liquid propane storage tanks provide a greater threat to you than a nuclear plant ever will.
As for the rest of what you said, maybe that might apply to aerospace engineering. For other engineering fields however, they are certainly in high demand. I work at an engineering firm with civil engineers and mechanical engineers (I think I'm the only ChemE there). While engineering is definitely an insanely difficult major, it certainly does not require you to be a child prodigy. Sure those prodigys will end up designing the future ion cannons and cold fusion systems of tomorrow, but there are certainly a lot of intelligent engineers out there working on systems most people probably will never hear of.
I'm not allowed to go into too great of detail, but lets say that I work on modeling systems that have been developed that serve to recycle the catalysts used in oil refining. Wanna see oil prices really skyrocket? Try buying new batches of catalyst every time a certain amount of oil is refined. The systems that I've been working on are going to be used in one of the biggest refineries in europe.
Now don't get me wrong, my job is boring as all holy hell and is part of the reason why I'd rather go into medicine. My point is that there is a lot that engineers do for the world that people don't realize. Its certainly true that you're going to encounter a lot of genetically smart people out there, and I've certainly run into people who study about a quarter of the time I do and get higher grades.
Chances are, no matter how smart you are, you will not be an amazing physicist or engineer, especially aerospace engineer. People who rise to the top in engineering are a random bunch.
If by "amazing" you're talking about being the next Stephen Hawking and having your name recgonized by millions of people then yeah maybe this is true. Being an amazing engineer at the top of the bunch is not limited to the random prodigy that surfaces every now and then. Innovations are constantly made, but the engineers who make them are hidden behind the corporations they work for. They still get compensated very well, they just don't get the name recgonition and worldwide acclaim. Odds are you aren't going to find that in any field.
And don't dismiss mathematics so quickly. You don't need to be a theoretical mathematician who sits in front of a chalkboard deriving formulas all day. Especially if you go towards the field of applied mathematics there are many different job opportunities available with excellent compensation.
Example: The job of an actuary. Generally works for an insurance company (but could work for other companies as well) in the field of risk management. To do this you need a bachelor's degree in math or applied math or statistics; No masters, no PhD. The hardest thing is passing the actuarial exams. Those tests get exponentially harder. With each exam however, your paycheck gets higher:
http://www.actuarysalarysurvey.com/
Not bad for a simple bachelor's degree in math, and you don't even have to be a genius at the top of your field either.
