Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "

Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "Mathematics, Form and Function". It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided by understanding of where mathematics has ended up in the modern age). The false-historical expose is fantastic. The goal becomes less to express things as accurately and comprehensively as modernly possible—which you'll experience as you take on graduate level books or modern papers—but instead to demonstrate large-scope intuition for why whole fields evolved as they did and how they are all intermingled.