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Disclaimer: The following story is written based on my knowledge of high school mathematics and a little bit of Mathematical Girl.
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Until now, I had always thought that mathematics was a set of rules that transcended human society, like the laws of physics. It was something akin to technological determinism, and I found beauty in it.
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However, recently (at the level of high school mathematics), I’ve started to realize that it’s not quite like that. Through Mathematical Girl, I learned that mathematics is just one system among many. As for the general “mathematics” system, I had the impression that geometry was based on the real “space,” while algebra was something more abstract or higher-level. But I discovered that even algebra is ultimately based on the physical world. For example, when I traced the proofs of formulas related to complex numbers, I ended up at the Pythagorean theorem (which is based on the physical world?). In other words, algebra and geometry are connected through discussions about complex numbers.
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In the first place, integers are based on our human ability to recognize discrete quantities. But I wonder if physics also becomes discrete when you delve into it. Or maybe the concept of quantity itself is based on our human perspective?
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Lately (as of November 2020), I’ve been feeling a bit disappointed. Maybe I was idolizing something that doesn’t actually exist, haha.
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If I delve into something like abstract algebra, will I eventually arrive at a different kind of mathematics?