Question

Hello, Rabbi,
I am a yeshiva student. I became religious at age 20, and I am just about to turn 23, so only in the past few years have I had the privilege of studying Torah and philosophy, and during that time I have devoted almost all my time and energy to them (unfortunately, the 20 years before that passed mostly in intellectual idleness). Since the amount of time I have in the coming years to study without the burdens of life is limited, I am trying to manage it well and choose carefully what to study. Truthfully, what I would want to occupy myself with is exactly the subjects I mentioned—Torah and philosophy (especially the philosophical aspects within Torah). However, from my acquaintance with rabbis, even ones who are a million times wiser and more righteous than I am, I have gotten the impression that among those who do not have scientific or mathematical training there is sometimes more inaccuracy, lack of clarity, and so on in their philosophical outlooks. I assume that in my own personal outlook too there are such inaccuracies and leaps that stem, among other things, from insufficient familiarity with science and lack of training in scientific thinking.
Added to that, of course, is a strong curiosity to know how the world works (I have no idea whether such knowledge has religious value or not).
My questions are:
A. In the Rabbi’s opinion, is there importance to studying mathematics and science in order to arrive at a more correct understanding of philosophical issues in Torah (for example, why we believe, whether there is providence and what its nature is, etc.)?
B. In the Rabbi’s opinion, in order to arrive at a more correct understanding of philosophical issues in Torah (certainly for someone who wants to engage in them), is it worth investing something on the scale of pursuing a degree in mathematics/physics? Or is reading popular science books and the like enough for that purpose?