Learning mathematics for its own sake

Hello Rabbi,
I know that I want to major in Torah/Halakha and philosophy. However, I still have the desire to pursue a degree in mathematics (along with philosophy), even though it is a major investment of time and effort, and I have no plans to work in the field. The considerations are roughly these:
A. Learning for its own sake, meaning it’s something that seems to me to have value in knowing in itself. That also interests me.
on. The instrumental value of getting to know very creative and interesting forms of thinking that are not really found in other fields, which could perhaps influence the study of Torah/philosophy/anything else.
third. This opens up access to engaging in the entire world of real-world topics (statistics, logic, probability, perhaps physics) that might interest me in certain contexts, even if not as a central concern.
Beyond that, I would like to point out that I suspect that much of the desire to study mathematics stems from the explanation (which the rabbi himself mentions from time to time) that truly smart people study mathematics/physics, and are not content with philosophy or even Talmudic study.
In fact, deep down I’m a little skeptical about the considerations I’ve raised. One moment they seem logical to me, and the next moment they seem not serious and simply stem from the psychological reason I mentioned above or something like that. In the Rabbi’s opinion, are the considerations I’ve raised above real considerations and should have weight, or are they just nonsense, a waste of time that will cause me to have much less time to study Torah over the course of 3-4 years?