You should probably read contemporary philosophy, then! Formal logic is a central tool of most analytic philosophy, to this day. The more logic-oriented side of philosophy typically merges seamlessly into maths.
It's not limited to analytic philosophy, either - continental thinkers like Badiou have sustained engagement with set theory - it's very traditional, actually.
Well, it really depends on what you're interested in. The Stanford Encyclopedia of Philosophy is actually very good, and contains a bibliography at the end of every article. Philosophy is very diverse in terms of subject matter - and my experience is that people are very different in terms of what questions they find engaging.
It's not limited to analytic philosophy, either - continental thinkers like Badiou have sustained engagement with set theory - it's very traditional, actually.