>>12753827The problem with mathematics is that it's hard to get a general picture of what a particular field is about unless you delve deeply into it. So whichever fields you're intrigued by may appear pretty dull, while the fields you ignored can turn out to be fun once you get into it.
Keep in mind that different fields of mathematics can be very disconnected. Two mathematicians can have little in common if their area of expertise differ.
To get a vague impression of what math is browse through advanced lectures, seminars, arxiv papers just for the vibe of it to feel the culture without the intent to understand a lot, read mathematicians' biographies. This will give you a wider outlook on what it is all about.
Once you get to this layman level, it will be pretty obvious for you which books to read and you wouldn't feel like asking.
Curiosity about mathematical logic is a good thing in the beginning. You can unironically learn its fundamentals by watching youtube vids, reading blogs, wiki and stack exchange. You have to be comfortable with induction, the idea of cardinality (infinities coming in different sizes), Russel paradox, Cantor's diagonal argument, ordinal numbers, being able to express everything in terms of sets.
>>12753839"set theory and the continuum hypothesis"
This book would likely not fit you now even if you're an aspiring model theorist. Develop an intuition about set theory first by implementing it different contexts. Actually pretty much everything you really need about set theory is in the appendix of Munkres' topology.
Everybody has different taste, but you may give a shot at Allufi's algebra. It's a thourough text and I feel it's beginner-friendly. Also it familiarizes you with categories right away, which may play into your interest about the philosophy behind.
