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There are so many assumption that were hammered into me in high school (and below) that I find hold back my thinking, rather than help me. I kind of feel like t

by mstade 10y ago

There are so many assumption that were hammered into me in high school (and below) that I find hold back my thinking, rather than help me. I kind of feel like the education I received was full of hacks to get me past whatever test was coming up, rather than truly teaching me. I've spent years playing what feels like catch up to actually truly learn the things I thought I knew – a lot of high school mathematics included.

fl0wenol 10y ago
What was not obvious to me, and took a lot of higher math to get to, was that in the grouping of N=>I=>Q=>R=>C, at each stage you're pulling in a more complete mathematical representation (counting, rings, fields) until you're algebraically closed, and while you could go higher, you start losing properties you like again, like commutability over multiplication. Complex numbers are that nice saddle point, which is an interesting thing to ponder. I wish there was more focus on these "why" aspects in at least the optional advanced math or physics you could get in HS. It helps put some things in perspective.