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Yeah, I think you're right. There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever
by __MatrixMan__ 5y ago
Yeah, I think you're right.
There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it.
I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.
- smus 5y agoMaybe it's the differential structure itself? Or an (over?)emphasis on the study of functions from space to space instead of the study of the space itself? Or the specificity of calculus (the study of one specific space) instead of the generality of topology (thinking about a lot of spaces and comparing them to each other)
- __MatrixMan__ 5y agoHmm, I'll have to ponder those. Specificity seems closest. Whatever it is, it's not a rational critique. Despite the discomfort, I'm also fascinated by it because one should not have an emotional response to specific types of math, but I very much do. Something about the homework in Real Analysis left me feeling angry. Not because it was difficult or presented poorly, but because it was somehow... untrustworthy? As if my betters had decided which ideas were the good ones and the only thing left for me to do was optimize along the one dimension that they had assigned me. I realize that this is nonsense, but I can't seem to shake it.
- smus 5y agoI think it's totally good and human to have preferences for one sort of math over another :)