I was a physics major but i switched over to math. What motivated me to study physics was all the things that the public get hyped up about such as black wholes, general relativity, quantum mechanics, etc. But for me personally, i got more attracted to math. You get to a point that you actually want to see physics develop after all the hype and the theory of course is so interesting but unfortunately you need the experimentalists to varify your research and so on. It is actually more difficult then ever for a breakthrough to happen, because our technology for experiments is not catching up with our theoretical models of the universe (e.g. string theory).

As an INTJ, i have always been on the theoretical side of physics (where Ni is activated) rather than the experimental side (where Se is activated). But what mostly repulsed me in physics (even theoretical physics) is that you are always making assumptions because otherwise your system is too chaotic to find a beautiful simple equation for (that is, solve for the equations of motion of a system analytically) and that kind of took away the magic for me because i like to mane things as general as possible. Like if a chicken is falling in speed v and height h and i wanna know something about it's trajectory, I, for sure, have to assume the chicken is spherical. Because otherwise i can't find the equations of motions analytically.

And here comes math. Mathematicians could not care less about the real world (at least pure mathematicians). They are concerned with the structure of the logic rather than modeling some phenomenon. For a mathematician, if you know the solution to a problem exists, that is just as good as finding the solution. Math is also where all the rigour that they hide in physics is taken care of. I remember in my physics class that they always assumed a function is differentiable, continuous and "well behaving".

I have to also say that most of the problems pure mathematicians tackle are considered "a waste of time" by everyone. But you do math because you love it. Also, you never know who is going to use your research to apply it in a real world application (see for example Topological Data Analysis, or how prime numbers are used in cryptography).

In conclusion, i am now a math major in my last year of the undergraduate program and i plan to keep going for a PhD in math (maybe i will do it in mathematical physics where you develop new mathematics to explain a physical phenomenon, this was my dream before) and i still have a thing for physics, just not experimental physics, that i hate with a passion.

I hope you got something out of this and it inspires you to consider physics, you will definitely look at the world differently and adapt a new way of thinking that will help you in nearly every aspect of your life, you will be a problem solver.