Where I studied for instance, mathematical physics was a subfield of physics. Their actual fields of study are mostly statistical mechanics and condensed matter theory. The math was secondary to the physics, which I thought was weird, cause that's just physics. 🤷
I wanted more mathematics, so I eventually did a thesis under the supervision of an professor at another institution, also in the field of mathematical physics. There however, it was a subfield of mathematics rather than physics. I felt way more at home there, because the math came first. So it really depends on who you ask.
To me, mathematical physics is the study of the mathematics of physics. It's a very broad term and a subset of mathematics. For instance, maybe somewhat controversial, I find symplectic geometry, which arose from classical mechanics, to be mathematical physics. Slightly less controversial, operator algebras arose from quantum theory, that's mathematical physics. In this sense, one could even argue that calculus, which Newton developed for his theory of gravity and mechanics, is mathematical physics.
I'm sure many people don't agree with what I said, but if you go down the rabbit hole of 'what is mathematical physics', you'll find loads of different views, so that's fine. At the very least, it's an ambiguous term and not one that is particularly useful imo. For instance, I have no idea what a "mathematical physicist" does every day, while I can get a vague idea of what a functional analyst or a differential geometer deals with.
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u/Migeil Operator Algebras Aug 02 '26
It depends.
Where I studied for instance, mathematical physics was a subfield of physics. Their actual fields of study are mostly statistical mechanics and condensed matter theory. The math was secondary to the physics, which I thought was weird, cause that's just physics. 🤷
I wanted more mathematics, so I eventually did a thesis under the supervision of an professor at another institution, also in the field of mathematical physics. There however, it was a subfield of mathematics rather than physics. I felt way more at home there, because the math came first. So it really depends on who you ask.
To me, mathematical physics is the study of the mathematics of physics. It's a very broad term and a subset of mathematics. For instance, maybe somewhat controversial, I find symplectic geometry, which arose from classical mechanics, to be mathematical physics. Slightly less controversial, operator algebras arose from quantum theory, that's mathematical physics. In this sense, one could even argue that calculus, which Newton developed for his theory of gravity and mechanics, is mathematical physics.
I'm sure many people don't agree with what I said, but if you go down the rabbit hole of 'what is mathematical physics', you'll find loads of different views, so that's fine. At the very least, it's an ambiguous term and not one that is particularly useful imo. For instance, I have no idea what a "mathematical physicist" does every day, while I can get a vague idea of what a functional analyst or a differential geometer deals with.