What kind of degree (maths or physics) is more suitable if one's objec

[phmat]

maths or physics degree for theoretical physics?

In my country

1. on the one hand, I feel that BSc degrees in physics do not provide adequate mathematical
training (that is to say, you've to study nearly-all maths rigorously on your own because only 3 courses in analysis and 1 in geometry and linear algebra are offered), but offer a broad physics overview (that is to say, lots of actual physics courses) and even 2-3 theoretical physics courses (special relativity, statistical mechanics, quantum theory, non-linear physics, etc);

2. on the other hand, maths degrees provide the mathematical training but are weak when it comes to learn actual physics (there are only 2 general courses at a basic level of understanding and 2 courses in mathematical physics (mechanics)).

It is, however, possible to take some extra courses (although it is extremely difficult: for example, take special relativity and quantum mechanics as a math degree; or a couple of extra geometry courses as a physics degree. This does not provide complete math training nor complete physics training, though.

That having been said, what kind of degree (maths or physics) is more suitable if one's objective is to do good research in mathematical and theoretical physics?

 

[homeomorphic]

Mathematical and theoretical physics is not specific enough to say. Generally, I would tend to side with physics if you want to do physics, but math would be better if you want to work on physics-inspired math, rather than physics itself.

 

[phmat]

Can you make an example of what you mean by physics-inspired math?

 

[homeomorphic]

Topological quantum field theory, for example. That's what I studied in grad school, and it was still fairly far from physics, at least in my case. I learned a decent amount of physics, but only enough to vaguely grasp what quantum field theory had to do with what I was doing, not that I was specifically working in terms of path integrals. Probably, I would have done just as well if I hadn't known any physics--I didn't really use it explicitly, although having a basic familiarity at least the idea of Hilbert spaces and operators in quantum mechanics does provide for better motivation.

 

[micromass]

That having been said, what kind of degree (maths or physics) is more suitable if one's objective is to do good research in mathematical and theoretical physics?

Definitely physics, without a doubt. Most mathematics you see in a math degree isn't all that useful for physics, even theoretical physics. Sure, things like analysis, functional analysis, topology, differential geometry have their uses. But getting an intuition for physics is way more important if your intent is to do physics later. The math is the easy part of physics, the physical intuition is what is important.

Einstein was not very good at mathematics. There were many better than him, such as Hilbert, Poincare, Levi-Civita, etc. But he had an amazing physical intuition, which enabled him to be one of the greatest physicists. Other physicists are better at mathematics, but if you don't grow that physical intuition, you will never get there as a physicist, no matter how well you know your math!

https://www.youtube.com/watch?v=obCjODeoLVw

 

[homeomorphic]

In my own case, I sort of would have preferred to do a physics PhD, but I was afraid of all the ugly calculations and, ironically, the lack of physical intuition in physics, so I went for math and tried to work in as much physics as I could with it, but in math departments, it's rare to find people who are enough of a physicist to be suitable for such a thing, although you might luck out and find someone like John Baez in a math department to work with (unfortunately, he doesn't seem to be doing mathematical physics anymore). Also, at the time when I applied for grad school, I was more rigorous and more abstract than I am now, so it made more sense back then, in a way, but I probably would have been happier in physics because I don't care that much about complicated math, unless it's telling me something of philosophical or scientific significance that adds to my understanding of the world around me. I took a couple physics graduate classes, and they weren't bad.