I've read a lot about Russell and other Logicism advocates and their trial to reduce math to logic. But what does that mean? We know that all known mathematics can be reduced to Set theory, is that their goal? If not, what was their goal precisely?
I was told that their goal is to build mathematics using first order logic without any use of axioms. This seems weird, how can this be achieved?
I've studied mathematics and logic very well, so feel free to use whatever level of sophistication without an appeal to over-simplifying things for me to understand.