2D Motion - Physics 101 / AP Physics 1 Review with Dianna Cowern

Hello,
I am in high school and am primarily focused on pure mathematics, and would like to go into research in pure math. That said, i have a bit of a liking for physics as well. My whole focus is on pure mathematics, but i think in future my works might prove helpful in theoretical physics, so i am studying physics as well. Now my question is: how should i be studying physics? what should be the strategy? do i need to read or do i need to solve from books like University Physics by sears zamansky/resnivk halliday? I feel like solving physics is all about application of the things studied,  that said, if i contribute to physics,  i want to come up with new physics, new research. So should i be solving all those questions as i feel like they are not relevant in my case.
In my opinion, after i move into advanced mathematics,  i will be able to grab physics from there onwards, and spending ltim now solving these questions won't make much of a difference. Am i correct?
Does solving every question at this stage a prerequisite for coming up with new research in physics, or can a mathematician contribute directly at a later stage in physics, once he has all the math.