Graduate study and research in theoretical physics

Question

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 theorical 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? 

Comments

Dirac studied Electrical Engineering before moving on to Theoretical Physics. In contrast, Harish-Chandra, Dirac's student hated the lack of rigour in Physics and eventually moved on to Mathematics. The key is that courses don't determine your future, it has a lot more to do with what you enjoy and are comfortable doing.  Gaps in one's education can always be filled as and when necessary or discovered.

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How to Learn Math and Physics by John Baez.

Answer 1

Certainly the advice to learn independent of courses is valuable. Searching out the great texts and studying them will almost always prepare you better than a course. I speak from an American perspective where course evaluations and various other pressures invariably force programs to diverge from what is intellectually optimal. Unless, you are at some elite school...  I think this advice applies to both math and physics.

That said, we need to either solve original problems and publish papers of substance or, the more standard path, we earn degrees. My opinion, it is much easier to learn higher math online than physics. The trade craft of physics, it is communicated in person far more effectively. In my experience, the physics I learned in person I probably would not have learned as well from books. Physics has customs and traditions which are easier to absorb when amongst physicists. Mathematics also has such customs, but, I think is better defined.

So, I would advise seeking out physics degrees while studying math in parallel, perhaps partly just as independent study. At some point, you may have to switch to a math degree as you go on, but to begin, I think physics needs some face-to-face interaction.

A bit on my background: I earned a B.S. in math and physics. Then, for graduate school, I found a theory program in physics where I could take a course on string theory. For 2 years I took most graduate physics courses, earned a M.A. in physics, and more importantly, I gained some understanding of physicsy supermath. The thing that really helped me was not a course, rather, I chose to prepare a seminar where there was threat of questions from professors (gulp...) Thankfully, a string theory student who was further along got me started and after a few hundred hours of spinor index calculations I felt like I understood something. I gave the seminar, survived, and as it happens, it served to form the basis for my PhD work in math (which was a lot of fun). There are many paths to take and the possibilities for study seem endless, so, pick something, and enjoy the journey.

Comments

Thank you.

Answer 2

You can checkout now how easy you learn from the material freely available on the web.  If you cannot grasp a concept or technique from one source, try another one - the same stuff is repeated on the web in different variants over and over again. If you can't follow because terminology is used that you aren't familiar with, pick up another source where the lacking concepts are explained. http://scholar.google.com is an important search tool.

After some experience with this mode of learning you might want to pick for a degree the part that is less easy to learn in this way, since you get extra help. On the other hand, it may be more interesting to pick for a degree the part that you understand more easily, since you'll get further there.

In any case, one learns well only what one is really interested in and where one puts enough effort in.

I studied math because I liked rigor, and learnt all physics from books and papers (not so easily because the lack of rigor makes it often more difficult to interpret); others do it the opposite way.

Comments

Thank you for your advice Professor.

Answer 3

I guess this is a problem in some countries. For example in Spain or in Greece undergraduate education is basically 50% mathematics in the first 2 out pf 4/5 years which lasts an undergrad degree. UK's problem is that degrees are too short while USA's problem is that you take many different courses from other subjects. Despite that if one looks at BSc thesis from German or Dutch undergrad students one is amazed by the advanced level of training in just 3 years. This has lead me to conclude that you basically learn what you read and not what you do in your courses.

Personally I have never had a course in Algebraic Topology and I understand it better than my Electrical Circuits course. It is good to have some guidance of course (and this place is a good one to ask for it). I would say that if you want to become a physicist do physics. If you want to become a mathematician do maths. This does not mean you cannot do research in the boundaries of these two fields and alternates slightly between each other. 

I had this problem my self too some years ago. I chose physics and I do not regret it. It takes some time and effort but the advanced mathematics come into the game at some point and it is totally rewarding being able to work in the interplay between these two subjects. I just finished my master thesis in AdS/CFT and started, just a week ago, a new project in 2-algebras something completely different and abstract unless you are a mathematical physicist. Anything you choose, I promise it will be a lot of fun!

I really hope this helps!

Comments

Thank you for your answer.