Consultation regarding a study path

Hello Rabbi,
I am addressing you as someone who is familiar with both academia and the world of Torah, and deals with fields close to those I want to deal with.
Basically, what I want to do in life is a combination of philosophy and Torah/Torah thought. After two years in yeshiva (I came to yeshiva a bit late) I need to decide what my course of study will be starting next year. There are three options I’m considering:
A. Bachelor’s degree studies in mathematics and philosophy
B. Bachelor’s degree in philosophy and perhaps something related to Judaism with a teaching certificate, while simultaneously studying in a yeshiva
C. Continuing studies in a yeshiva only without a degree

There are three matters on which I would like to hear your opinion.

There are several things that motivate me to consider studying mathematics. One consideration is intellectual (I’m not sure I fully understand it myself, it’s a bit vague) – I think there might be certain intellectual questions that I would like to address that could require mathematical or scientific knowledge, which is knowledge that is difficult to access without a degree. Philosophical questions can also be thrown into these areas and I might not be able to deal with them properly without mathematical knowledge. Some of the problems that interest me concern areas such as probability, infinity, and game theory. Beyond that, regardless of philosophy, mathematics opens up a kind of window for familiarity and understanding of many intellectual areas, in other words, it is a very “basic” degree.
Another consideration is practical – I’m afraid of what will happen if I only deal with philosophy and Torah. Although I intend to deal with these fields eventually, it’s a gamble – there are few philosophy professors and yeshiva leaders in the world, and even if I were amazing in these fields, landing such jobs is sometimes tied to luck and not entirely dependent on me. Teaching Gemara in a junior high school or high school doesn’t sound like a big deal to me (I was exposed to it a little in a program I did at Herzog, it really didn’t seem particularly fun). Mathematics does allow for more employment in this context if I need to.
Added to this are small and not so important considerations, such as whether a degree in mathematics might give me more prestige within academia and maybe somehow help me advance in philosophy, etc.
Beyond that, I’ll mention that I like math and am pretty good at it, but overall my ambition is probably not to be a mathematician but to engage in the fields I mentioned – Torah and philosophy. I would be happy to hear your opinion on these considerations, as I will detail later in the email.

The second question is about studying philosophy at university. If I still decide to choose to go all-in on the path of Torah + philosophy studies, the question arises whether in order to know philosophy at a high level and participate in philosophical discourse, one must do it in an academic setting. I talked to David Enoch about this a bit, he said that he thinks academia is quite necessary to be a good philosopher, and reading alone is probably not enough. I also admit that apart from you, I don’t know a single person who has studied philosophy alone and not in an academic setting and is engaged in this field in a manner worthy of its name, and I have also encountered the opposite phenomenon – people who have studied philosophy alone and their philosophical skills are as good as those of a graduate existentialist. In light of this, do you think it is worth studying philosophy at university or do you think it is also possible to study philosophy on your own?

The third question is about studying Torah and a degree in mathematics. I am very afraid that while studying a degree in mathematics, it will be difficult for me to study Torah as much as I want. My plan is in any case to continue somehow in a yeshivah setting after my first degree, but I wonder if that is too optimistic and if it is worth building on it, given that I will probably be married by then and perhaps with a family, etc. Do you think I can build on the fact that even with an intensive degree in mathematics and afterwards I will be able to continue to study Torah seriously to the point of actually practicing it?

I have outlined several considerations in both questions here, I am not at all sure whether they are factually correct and what place each consideration should be given. I would be happy if you could express your opinion on these considerations – whether they are factually correct at all, and also how much place these considerations should be given from your perspective.