Eli5: Why mathematics not a science?
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Some people think it is. They call it a ‘formal science’. Others do not. This is because the definition of ‘science’ is contested. Some people think a science must relate to the material world and be testable with experiments. Ultimately, this is just semantics.
A related idea is ‘do humans invent mathematics, or do we discover it’. This is a complicated question that the answer is probably ‘discover’ but might be invented in part. If we do, in some sense, discover mathematics, then it is reasonable to consider it a science.
Regardless, they are intimately linked.
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