@studentguy - Aeronautical science at a school like Embry Riddle isn’t the same thing as, say, aeronautical engineering at an engineering school. It’s not as hard as actual engineering, and doesn’t contain the high level foundation math, physics, chemistry, etc., theory that is part of an engineering degree. If one intends to be an engineer, most employers require an actual engineering degree.
I suppose you can take graduate courses in aerospace engineering if the school permits you to do so. If you want to work in aerospace engineering, you really need the degree, not just a few courses. Some schools may admit students without an engineering degree to their master’s programs in engineering, but I assume you are talking about undergraduate. If you know you want to do engineering work in case the piloting doesn’t work out, definitely go for the engineering degree.
Math is in demand in the financial and tech industries - companies that do significant research and development have mathematicians. Math majors can also work in actuarial science and accounting (though one needs to have a certain amount of accounting courses to sit for the CPA exam in most states). Chemists find employment in chemical companies, pharmaceuticals, and industrial research (my friend in college got his bachelor’s and master’s in chemistry and was hired by one of the major drug companies. He later got his PhD in organic chemistry and is now their VP of research).
I don’t think it’s that easy to get into an airline piloting job despite the airline industry doing better now than it did say 25 years ago. I had once considered giving up engineering and going into airline piloting, but after thinking about it I decided I liked going to work at 9, being home at 5, not having to travel much, and my comfortable chair and desk. To qualify for a first officer on a Part 121 (scheduled) airline you must have an ATP rating. This requires 1500 hours (there is now an “entry level” ATP that requires 1200 hours). You must also now have Level D (full motion/visual) simulator training on a jet or other transport category aircraft to get a multiengine ATP rating. Unless you can get into an airline program that pays for this training after you get your commercial, multiengine, and CFI ratings at Embry Riddle or Purdue, etc (which you have to pay for), you will incur six figure debt in student loans even before getting that airline job. That should be a non-starter, IMO.
My advice - have a viable marketable backup outside of aviation (unless it’s aerospace engineering).
Full disclosure - Ph.D., Electrical engineering, engineer for a Fortune 500 aerospace manufacturer, PE, hold commercial pilot certificate, and aircraft owner.