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What's the actual difference between what a Mathematical Physicist and a Theoretical Physicist do?

When I look at the curriculum from some Applied Mathematicians from the maths department at my university, the areas on which those work in look quite similar to the one some Physicists from our Physics department work in.

Allow me to make an concret example: There's one professor of mine, mathematician, whose research is centered in General Relativity, more specifically, QFTCS (Quantum Field Theory on Curved Spacetime), and some others. That's exactly the line of research some physicists have.

So how to properly differ what they do? That may be a very trivial or naive question, but, nevertheless, it's something that I really do need to understand. If anyone could help, I'll be grateful. Happy holidays for everyone!

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    I do not hear the term "mathematical physicist" very often, but my guess is that the difference is little to nothing.
    – Anonymous Physicist
    Dec 23, 2021 at 16:36
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    Don't expect hard walls between fields, where a person does only X and another only Y with no overlap.
    – Buffy
    Dec 23, 2021 at 16:42
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    Essentially the same question is on the physics site. physics.stackexchange.com/questions/56293/…
    – Terry Loring
    Dec 23, 2021 at 18:33
  • Buffy’s comment is spot-on. At some point, whether as a formal student or otherwise, you get a quick, maybe nasty, glimpse of what’s actually happening. You’re there, things are less clear than you’d like, yet here you are. I wish you nothing but the best in your endeavors!
    – A rural reader
    Dec 24, 2021 at 5:09
  • For me a mathematical physicist is a researcher doing mathematically rigorous work on questions originating from physics. The lines are (for me) quite blurry. Mathematical physicists can be found in both math and physics departement.
    – Severin Schraven
    Dec 24, 2021 at 21:51

2 Answers 2

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Where the dividing line is drawn is very likely to vary from institution to institution. I used to work in a "Department of Applied Mathematics and Theoretical Physics", and there, "Theoretical Physics" was understood to consist of High-Energy Particle Physics, General Relativity, and Cosmology, while the physics-y bits of "Applied Mathematics" included experimental and theoretical Fluid Mechanics, Biomechanics, Planetary Science, realization of Quantum Computing, and Glaciology.

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There’s quite a bit of theoretical physics contained in “others”.

There is a lot of fascinating theory work in condensed matter theory, including statistical mechanics - beautiful results on spin chains, Ising model etc, antiferromagnets. Robert Laughlin or Leo Kadanoff stand out a names with international recognition, as is Jun Kondo.

These days there is also a lot of work in quantum information theory, with Alexei Kitaev a shining example of a theorist working in this area.

So theoretical physics is much broader in scope than the mathematical physics done in math departments. The topics you list get a lot of public attention because they capture the imagination of many, but there is lots of good stuff in theoretical physics at large.

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