I am a senior undergraduate and I am in the process of applying to physics graduate programs in the US.
Through my course of study, I've been excited about the interplay between physics and mathematics and studied mathematics up to graduate-level algebra, geometry, topology, functional analysis, etc. while pursuing a double major in mathematics.
I recently finished my first draft of SOP (Statement of Purpose). I stated that my experience in mathematics helped me grasp modern physics' mathematical formalism.
When I asked my colleagues to review my SOP, most of them said my mathematical background is "irrelevant and unimpressive," and they advised me to elaborate on my physics research experience.
I do have some research experience in physics, but it is rather weak. All I can say is that I attended the undergraduate research programs in both the physics and mathematics departments, and I wrote my theses there.
Admittedly, I didn't specialize in a specific research area in physics while pouring a lot of effort into completing a double major and exploring various subjects. Will this critically reduce my opportunities for being accepted to physics graduate school? What can I do to look appealing to admissions committees without exaggerating my experience?