How can I use my mathematical background when applying to physics PhD program?

Question

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?

Well... · Accepted Answer

I actually think the problem isn't that your math classes are off-topic. I know lots of Physics PhDs who double majored or minored in math.
The problem is that you're focusing an awful lot on your coursework in your SOP. Your classes really shouldn't be the focus: anyone reviewing your application gets that information from skimming your transcript. Most professors in physics departments are familiar with the classes you took by their titles and already know how they would relate to physics research, so making it a centerpiece of your SOP is a waste of space. You can give the double major at most one paragraph to tie it into your goals.
You should talk about your research more. It doesn't necessarily have to be impressive, but your ability to function as a researcher is more important to your promise as a PhD student than how many upper div math classes you took.
A double major will not totally make up for a lack of research experience in a grad school application. Succeeding in classes is a different skill set than succeeding in research.

How can I use my mathematical background when applying to physics PhD program?

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