At the college level physics is almost completely math. It's not the formulas; it's how you look at them. And what they "mean" to you. Linear Algebra, Functi

At the college level physics is almost completely math. 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".