Today I spent hours reading about recent developments regarding the Continuum Hypothesis and Set Theory. Where would I even start with these topics? My undergraduate professors all considered foundational questions to be something noone did anymore.
I earned my BA in Math in 2001. However, as a returning student I needed to focus on completing my general studies. My math electives were waived by my department chair based on my previous actuarial exams. I don't know if I could motivate myself to work through a textbook of proofs. Nor could I evaluate my own work in that regard.
I had one introductory course in Set Theory as an undergraduate. Also, I scraped through Real Analysis, Group Theory and Ring Theory. Perhaps a few other proof based undergraduate courses.
I'm not sure if this is a helpful insight. I had difficulty relating to my classmates because I am not a Platonist. And I am not particularly fond of numbers. I think in terms of patterns and structures. Also, I consider math a development out of our cognitive capabilities of abstraction, not any sort of description of reality.
Thank you for reading!
:) I think your lecturers are pretty clearly wrong, then. Many people are involved with foundational issues, and there is literature. (Often, by the way, they may be paid by departments of philosophy, as opposed to departments of mathematics.) I have a somewhat similar background in math. Why should you not be able to work through textbooks? I think that's what they are meant for. In any case, do you know st.openlogicproject.org? I am working a bit with this book, I think it's not to bad, you may give it a try, it's for free. Otherwise often Potter (2004) is mentioned. And, depending on your interests, you may want to have a look at the new proof theory book from Mancosu-Galvan-Zach. For in proof theory, that's where it get's foundational, as far as I understand. In any case, you may also be inspired by reverse mathematics, category theory and/or type theory. Last but not least, do you know the Oxford Handbook of philosophy of mathematics and logic? May give you some background for your more philosophical questions..