There is no consensus as to what is the true and correct philosophy of mathematics. People are going to disagree about that, just like they disagree about almos

There is no consensus as to what is the true and correct philosophy of mathematics. People are going to disagree about that, just like they disagree about almost every other part of philosophy. But there are books which give you a survey of different views, such as Shapiro’s “Thinking about mathematics” — which surely will bring you to “I know a bit about the philosophy of mathematics”-level. During my time as a master student in mathematics we used to have a joint seminar with students from philosophy where we would take turns reading and presenting topics from philosophy of mathematics. I think it was useful for everyone, and it wasn’t difficult to organise and didn’t take much time (2 hours per week during one term).