Imaginary Numbers Are Real [Part 1: Introduction]

For a small buffet of abstract math topics (with lots of exposition putting ideas into historical context and an emphasis on building geometric intuition) try Courant & Robbins "What is Mathematics?". Covers number theory, number systems, geometry, topology, optimization, algebra, and knots, among others. You could also play around with branches of math like Knot and Braid Theory, which are interesting in their own right, give insight into lots of different branches of math, and many interesting problems are still accessible to lay people. Number theory is also like this I think it can also be helpful to learn some things about the history of math and the historical context that different ideas came from. Here's a nice example covering complex numbers [this video] Maybe tangential to your ends, but the Crest of the Peacock is a nice book on non-European mathematical traditions, which provides some insight into how the process of establishing and validating mathematical knowledge works in other cultures. You might try books written by physicists or that are about mathematical physics (an author to look out for depending on your level is VI Arnold), since arguments will be of a more geometric or physical nature and appeal more to intuition. Stillwell is another author (not a physicist) that tends to write books that give context and geometric intuition You might like playing around with Pinter & Humphreys for Algebra, or Jänich for Topology (fantastic book for building intuition aro