requesting a book recommendation

Would anyone here be willing to recommend me a decent book on different philosophies of mathematics (eg formalism, intuitionism, etc)?  I've been searching amazon and I'm having a difficult time distinguishing what's worth the purchase.  I'm looking for something relatively rigorous in its details.

I have some background in predicate calculus (mathematical logic - I've read through the proofs of Gödel's theorems and briefly touched on second-order logic), set theory (I'm familiar with ZFC as well as basic ordinal and cardinal arithmetic), and a tiny bit of category theory (products, equalizers, duality, etc).  I wouldn't mind reading something that reviews those things, as long as the main subject is the philosophy and it's aimed at someone with an undergraduate background in math.

Thanks to anyone who bothered to read this.

It's more about algorithms. Equations that utilize other equations within variables, going numerous depths for the purposes of simplifying what would otherwise be complicated and arduous computer work.

You might notice that we no longer utilize binary, but something called C++ or compiler code.

Long-division is the process of jumping different levels of math to form one formula to create an algorithm.

And no, it's not what you've learned in grade-school.