Is mathematical physics theoretical physics?

Question

I was reading about mathematical physics on a university website and they said "an education in theoretical physics is..." appearing to imply mathematical physics is theoretical physics. Is this the case? I want an education in theoretical physics or the closest thing to it. The problem is I live in New Zealand and the universities here don't teach it other than this one potentially.

Answer 1

Both deal with theory rather than with experiments. The most striking difference is the level of rigour being put in. For example: In theoretical physics you solve differential equations, in mathematical physics you solve them as well, but you also prove that the solution exists and is unique or, if it is not unique, you consider all possible solutions and try to give them physical interpretation.

Theoretical physicists sometimes use mathematical notions which are ill defined, for example, the Gauss integral with purely imaginary exponent. They don't care that much about mathematical rigour (but, obviously, still much more than an experimental physicist would do), use the mathematical tools, if they seem useful intuitively, and deal with new physics. Mathematical physicist would rather deal with the problem of making the Gauß integral with imaginary exponent well defined by considering some suiting limit.

But it's not like mathematical physics are just cleaning up after theoretical physicists, which left some mathematical mess while pushing forward the understanding of physics. While making things rigorous, often new questions emerge, dealing with them might give a better understanding of physics.

Answer 2

Mathematical physics

• In the most general sense mathematical physics means mathematical methods used in physics (i.e., those parts of mathematics that are actually useful in physics applications). E.g., one may be interested in developing new methods of solving sine-Gordon equation and analyzing its solutions - without actually changing the physical situations where equation arises and its applicability to such situations.
• As @user1379857 mentioned in the comments, sometimes mathematical physics simply means theoretical physics, as opposed to the experimental physics
• In some places mathematical physics has more specific meaning - e.g., in Russia the title is common to the books and courses dealing specifically with the second order partial differential equations.

Theoretical physics

• In the most general sense it is doing physics with equations, rather than in a lab, i.e., as opposed to experimental phsyics. Sometimes computational physics is treated as a separate branch as well.
• The term may more specifically address to the high energy physics, particle physcis or cosmology, thus excluding the theoretical fields that are considered "more mundane" although not necessarily less complex -such as condensed matter theory, quantum optics, etc.