Eli5: Why mathematics not a science?
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“Science” generally refers to a system where you make predictions based on how you think the world works, then test your predictions, then, if necessary, update how you think the world works.
“Math” usually involves assuming that a few starting rules are true, then seeing what else you can prove/disprove based on those assumptions. There are multiple different self-consistent systems of mathematics that aren’t compatible with each other, but still work because they start by defining different things to be true. So a lot of the time, “new” mathematics comes from people picking new things to assume to be true, then finding out what kinds of problems this way of thinking can help solve.
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