For me, learning mathematics is a way of priming my imagination with patterns and tools that may or may not be relevant, but with the qualification that almost everything can find use if you look hard enough. I'm curious and like to think so having a library of abstractions is always satisfying. Just sitting down to figure out how math can apply to some simple object of meditation is usually fruitful.

You can get away speaking English with a relatively compact vocabulary. But reading broadly to enrich your vocabulary with new words and idioms allows you to describe events more fluidly, and perhaps in a way which inspires you into better ways of describing the same thing you could have described less poetry in the compact vocab set. In that way words let you change your perspective by affecting how you frame your sense-data.

Mathematics is the same way. If you want to work in a variety of domains, you're going to have to be agnostic ahead of time as to what tools might be useful, which is to say, have many tools.

You don't learn an English vocabulary by reading the dictionary, you read literature and see how those words are used in context.

Learning in a vacuum is hard for all but the most abstract thinkers.

I don't think I've ever read a math book that just went "Here is a list of definitions and the statement of some theorems. Have fun!" The problem is that math is usually built on top of more math. So the motivating examples given are often examples in mathematics, just in a different area.

For example, most category theory books talk a lot about the categories of abstract algebraic structures to get you an idea of what the things they're describing look like in "the wild." If you've never done any abstract algebra, it's like trying to use the Rosetta stone when you don't know Egyptian or Greek.

> Just sitting down to figure out how math can apply to some simple object of meditation is usually fruitful.

I personally find that bordering on impossible (and I still obtained a physics degree). I need a few examples of how a concept can be applied before it starts making sense.

At the moment I'm dabbling in image processing, and it wasn't until I had some visual explanations of morphology that it made a bit of sense. Now the maths has to follow on...

As a physics student in math classes, you should be more aware of the applicability of abstract theories, not less.