Majoring in Physics vs Mathematics (Pure)

Question

I am a third-year UG student enrolled in a five-year BS-MS dual degree program. I just got the opportunity to personalize my courses and pick a major at the start of this semester. I went with a physics major, with four core physics courses and two pure math courses (Linear Algebra and Real Analysis).

Lately, I have been second-guessing this decision. I like both physics and math a lot. But I am unsure of what I wish to do. Having chosen physics as my major, I'm uncomfortable about the fact that I'm giving up on getting into the field of pure maths - a kind of FOMO? I have been pondering over switching majors, not because I'm not enjoying physics, but because I feel like I might want to pursue pure math professionally and study physics in my own time.

I have talked to some of my seniors who have been in a similar situation in the past, and also professors. But I still feel like I'm just going in circles thinking about this. I want to know what some of you people think about my present situation, and what you would suggest.

Here's some more information:

-> I've roughly been a B/B+ physics student and an A math student. (Silly slips in the computation work involved in physics pulls my grade down often)

-> I'm seriously considering applying to grad school for a PhD in either Theoretical Physics or Pure Mathematics.

-> I have to say that my pure math classes have been the most enjoyable out of all my classes, and I'm able to digest everything too. I love looking at mathematical structures, and at how deductions follow from axioms and other deductions to give rise to a wonderful structure of logic.

Things have been complicated in physics, however. In my experience, at times, physics professors and sometimes even textbooks are terribly "hand-wavy". They're too wordy, and it just feels like they're avoiding giving you an accurate description of what they're talking about. I can remember way too many instances of when something could've been explained in an objectively better way if the other person would just try to be precise with their words.

This becomes very frustrating sometimes because I end up spending so much time trying to decode what the other person is saying, only to find out that it wasn't too complicated and could've been told more clearly and in fewer words too. On a side note, in my case, the best reference material for when I don't understand something in physics has been Wikipedia. Concise, precise, and technical.

Sorry about the rant :') And please bear in mind that this doesn't mean I don't like the subject of physics.

-> My reason for wanting to do physics has been the same as that for math - I like studying it, and I can absolutely imagine pursuing it further. "Studying" physics (in the sense of majoring in it in college) is certainly frustrating, as I have described above. Still, the subject matter is wonderful regardless, and I am thoroughly amused by it.

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Sorry if this post has been wordy and confusing. It has probably been because I'm extremely confused myself. Any advice/analyses will be much appreciated!

Answer 1

I am in a very much similar position to yours. I first did my bachelor's in physics, then switched to math, did a bachelor's there and am now studying physics for my master's. I ultimately decided to stay in physics because what fascinated me most was how nature can be described with the tools of mathematics and finding these instances. Pretty much what is described by Eugene Wigner in his famous essay The unreasonable effectiveness of mathematics in the natural sciences.

I can very much relate to your feelings of lacking precision in how physics lectures are held or how some physics books are written. You are certainly not alone with that feeling among theoretical physicists and most of them do strive towards bringing their work into a consistent framework. It is however not the main goal since the ultimate test in physics is experiment and not a proof, so theoretical physicists will sometimes do something just because it "works", i.e. fits the experimental results.

If what you are ultimately interested in is the rigorous mathematical framework behind physics, you are probably better suited to mathematical physics. You will however have to accept that you are rarely at the forefront of physical discovery and rather in the background solidifying existing theories. One of my professors when asked about mathematics vs. physics once told me something that stuck with me and went roughly as follows:

If the obstacles in theoretical physics are rivers and solving them would mean crossing the river, then theoretical physicists are trying to jump over them, using slippery stones and sometimes getting wet whereas mathematical physicists are those building the bridges afterward.

This metaphor is of course limited and there are important instances where mathematical physics has provided important new insights that weren't there previously, but I felt that I could suffer the occasional mathematical crudity for the price of learning to explore nature with math and therefore opted for physics.

Answer 2

Looking at the end goal for your academic career being a PhD in either Theoretical Physics or Pure Mathematics; I'd say take a a heavier load on your mathematics courses, like:

• Complex Analysis
• Partial Differential Equations
• Ordinary Differential Equations
• Real Analysis (involving metric spaces)
• Functional Analysis

The above will provide a solid mathematical foundation for a career in theoretical physics. You can then also add the following, if time permits;

• Graph Theory
• Group Theory

Hope this helps!