Physicists are often split into two groups: the experimentalists and the theorists. Now in my third year, I very much consider myself part of the latter group. This had been very clear to me since the beginning of my studies here, which is why I took the Mathematics course in my second year as my third option (next to the two Physics modules) and am taking both theoretical physics classes offered this year. For me I find it very enjoyable to work with physics without ever having to set up an experiment (this is a decision I made, most people here don't decide to go down this route).
The typical reason someone gives you as to why they study physics is "they want to know how the world works" etc. For me, physics is a pool of problems that I want to solve with more abstract maths. The fact that one can describe something real (or at least potentially real) in terms of mathematical notions is fascinating. And again, I don’t mean the first thing that might come to one’s mind, differential equations. Sure, most things fall back to them but either you know a cool trick to solve the one in question or you plug it into a computer and let it do its magic – no interesting math involved there. No, I mean there are many large areas of mathematics that can be used to describe fundamental physics. The theories developed rely on the understanding of the mathematics behind it which in turn lets you predict things that no simple observation of the world, experiments, would do.
Let me give two examples: for general relativity the underlying construct is the field of differential geometry. On the opposite scale of physics though, you need group and representation theory to understand quantum field theory. And who knows what ideas one will have to draw on to combine them all into a unifying theory???
Physics allows for a huge spread of interests to come together and work on problems that at first may seem uncorrelated but will eventually merge together. Together with all sciences it is one section of the big picture of the world around us that we are trying to figure out and every scientist is working on a different tiny pixel in this picture. For every interest there is a different region of these pixels in which one belongs. Mine is in the grey area between physics and mathematics.
So why didn't I study mathematics first with physics on the side? Because I'm interested in describing physics in terms of maths, not finding new mathematical theories for its own sake. And for this I felt I needed to get a bigger picture of physics first. A degree in physics gives you the summary of everything that has been done already and then slowly lets you zoom in towards the areas that attract you. It gives you the orientation you need to see which problems there are and where they are coming from.