Changing major after BS and MS in CS and double major in Physics for PhD in Mathematics

Question

Before telling about my background, I'd like to say that I did look at several similar questions, but neither involved my case (at least, not as far as I could see).

Now the background: I majored in Computer Engineering. I have expected more of Computer Science, but it was mostly business-oriented coding education (maybe I am being a little too harsh on this). So in my second year, I applied for a double major in Physics, thinking it might be more satisfying. In fact, I did enjoy Physics more than CS (or, CE in my case), and found it much more challenging and meaningful.

However, I ended up finishing my main major (CE), before Physics, so I applied for MS in CE in the same university, feeling the workload might be too little otherwise. I got accepted, and am currently enrolled in this program while taking 2-3 courses left from undergraduate Physics program. (My subject in MS is Computer Vision.)

But one thing I noticed over these years is that, for Physics I do not feel like I have the right mindset (seems that I lack a practical approach to things), and CE feels a little meaningless. Considering that I focused on Mathematical Physics, and more of the mathematical stuff in CS, I thought maybe Mathematics is the right place for me. But I cannot yet tell if I genuinely want Maths, or just whining about what I have at my hands.

So I have two questions, actually:

1. What are my chances if I apply for PhD in Number Theory?

2. Do you recommend changing the field? Can you share other people's experiences in similar cases?

For the application part, I must add that I do not have an outstanding transcript in neither of my majors (around 3.4 GPA in both fields -Physics might be around 3.5 too), although I did get a paper published which was about relativistic quantum mechanics.

Edit: This question is different from what is suggested as duplicate as this particularly involves the case of a double major background. Specifically, whether the case of double major suggests the admission committee a versatility in working different fields or not. So I do not think this should be regarded as a duplicate question.

Edit2: Experience in proofs
I have taken Discrete Mathematics and Formal Languages and Abstract Machines, in which we mostly used induction to prove things. Apart from that, in the mathematical methods courses we have gone through the proofs of Stokes' theorem, divergence theorem, etc. Although I mostly can understand a proof reading through it, and working out some things that seem off, I would not say that I am good at mathematical proofs, nor that I am much experienced with them.

Answer 1

What are my chances if I apply for PhD in Number Theory?

Every PhD program has different requirements and the admission's committee evaluates different aspects of a candidates application. So there is no real answer to your "chances" of be admitted if you apply for a PhD program in Number Theory. However, with that said, if you can show rudimentary course work and experience in Number Theory, that can work in your favor. I do have close friends who majored in Business, Political Science, etc. who took the minimum requirements for medical school admissions (basic bio, chem, physics) and were admitted because they were able to distinguish themselves from the rest of the applicants. The same situation applies here. You may not have an extensive background in Number Theory, but that's not to say you won't be admitted to a PhD program and be great at it!

Do you recommend changing the field? Can you share other people's experiences in similar cases?

You need to follow your passions for where you want to take your career. I have had friends who pursued what they thought was their "dream" career, only to recognize that it was not at all what they had imagined - and wasted all that time thinking that it would change, that if they put in more effort than it would be exactly what they imagined it. On the other hand, I've also had friends who took a job that wasn't what they had wanted/dreamed and it turned into a great career and they absolutely love it! It all depends on what you want your future to be.