I'm not a mathematician by training (engineer) but I'm endlessly fascinated with the discipline. I keep hacking away at books on real analysis, functional analysis (plus convex analysis for my optimization stuff), measure theory and sometimes abstract algebra. It's incredibly hard self-learning this stuff patchwork, but it's rewarding on the rare occasion that something sticks.
Recently while trying to sus out the differences between closedness, completeness, compactness, etc for the umpteenth time, I ran into this historical paper on the origins of compactness. It was fascinating seeing all these names and dates mentioned in one place. It made the whole thing seem slightly less mythical and more, er, human.
It also taught me that there were, in a sense, competing definitions of similar concepts, and some won out eventually. This got me wondering: was the development of math as we know it today inevitable, or could it have gone a completely different way? In my mind, this contrasts sharply with the idea that math formalizes certain fundamental truths about nature.
Thoughts appreciated!