Should a theoretical physicist learn maths like a mathematician?

[lawlieto]

I'm currently doing my undergraduate physics course at university, and I'm quite confident I'd like to be a theorist in the future. We have separate maths lectures from maths students, and most people have an attitude towards maths which could be summed up as "only learn what you need to know, you're not a mathematician." We mainly learn application, and never really care about where things came from, or why they're true, but this just got me to the point where I'm asking myself if my maths knowledge is good for anything else other than solving exam questions. The books we're recommended are obviously "maths for physicists" books, and don't really explain any maths, but focus on how to solve problems. Our maths lecturers are physicists, but most of them were astrophysicists doing research, so I'd imagine they don't need to rely heavily on things like the abstract part of linear algebra, hence giving students the impression that we can get away with dodgy maths.

So my question is, should I learn "real maths" from our maths department notes, from actual maths books, and also topics which are not on my specification but help my understanding of maths? Should a theoretical physicist learn maths like a mathematician?

 

[BvU]

http://www.staff.science.uu.nl/~gadda001/goodtheorist/index.html

 

[PeroK]

So my question is, should I learn "real maths" from our maths department notes, from actual maths books, and also topics which are not on my specification but help my understanding of maths? Should a theoretical physicist learn maths like a mathematician?

If you have an hour to spare, you might like to watch this:

http://www.cornell.edu/video/richard-feynman-messenger-lecture-2-relation-mathematics-physics

My two cents worth is that you can't learn it like a mathematician, but that is different from your maths being dodgy. You are ultimately using maths as a tool. You don't need to be able to make your own tools, but the better you understand your tools the better you may use them. So, it's a balance that you'll have to strike.

 

[lawlieto]

If you have an hour to spare, you might like to watch this:

http://www.cornell.edu/video/richard-feynman-messenger-lecture-2-relation-mathematics-physics

My two cents worth is that you can't learn it like a mathematician, but that is different from your maths being dodgy. You are ultimately using maths as a tool. You don't need to be able to make your own tools, but the better you understand your tools the better you may use them. So, it's a balance that you'll have to strike.

Thank you for your reply, so I definitely have to improve on my understanding of maths, it's just that I'm not absolutely sure where the "borderline" is.

I'll definitely watch the video after my exams next week.

 

[Crass_Oscillator]

Absolutely not. Math is not physics, and the way mathematicians think is useless for doing science or engineering. However it is very useful for doing mathematics; if you want to be a mathematical physicist, operating at the interface of the disciplines, you need to think more like a mathematician.