>>8791655I'm no math PhD but /adv/isor.
Being a math PhD and becoming a mathematician is just to do post-graduate research, so you're only sitting there thinking what new thing you could create and teach at the undergrad level.
Nothing is getting applied in the real world, unless you're working on something like mathematical physics maybe.
Also you're an AppMathfag, you'll be fine with just the MSc.
There exists AppMath PhD but it's not worth it.
You always gotta think what you will do with your major though, you can't study appmath just for the sake of it, but I'm sure you already know what you want to do.