[throwaway_bad]

It's easy to gain physical intuition because you can often explain one physical phenomenon in terms of another physical phenomenon that you have much more real life experience with.

But with mathematics, "intuitive" analogies are all in terms of other mathematical objects! You can't build intuition if you don't even know what they trying to abstract over.

In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated.