This is completely off. At the college level physics is almost completely math. Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.
One way to explain this might be that physics isn't about doing math, but using math to do computations. Meanwhile, math is about abstract ideas and rigorous proofs. Physics doesn't care about wondering if an integral is a well-defined concept, nor does it care about the real numbers being uncountable. Similarly, maths looks at the formulae in physics and thinks those things are way to complicated.
Our lin-alg course is joined physics and maths. The older physicists complain about all the proofs needed there. Mathematicians lament the lack of rigor in the same course.
Just like mathematicians can turn the results of 'unsolved problems' into axioms and go on with their lives.
It's not the formulas; it's how you look at them. And what they "mean" to you.
Linear Algebra, Functional Analysis, and Abstract Algebra aren't exactly 'measurement-based' subjects.
Right; but those are just the ABCs, is it were.
Physicists and astronomers, by and large, are interested in a broad range of mathematical subjects -- but generally as tools, just enough therein to make sense of what's coming out of their particle detectors and their telescopes.
Pure mathematicians, meanwhile, are into things like the Langlands program, or Inter-universal Teichmüller theory. And they constructions they consider aren't the mere means to some end, grounded in the prospect of obtaining some better understanding of the physical world. They are, rather, the end goal in itself.
Or if you will, the "music".