Eli5: Why mathematics not a science?
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Science uses inductive reasoning. You do an experiment on a limited number of samples, and based on the results you make an inference about the mechanics and the “rules” by which nature works.
Math uses deductive reasoning. We set the mechanics and the rules (called “axioms” or “postulates”) and, based on those rules, we draw conclusions about the behavior of numbers subjected to specific operations. We accept that these axioms are true (for example if a = b and b = c then a = c) and we use them as a premise for further reasoning. Math is, in a sense, entirely made up – but, it’s a system that has historically been very useful in analysing and predicting natural phenomena. We rely on it heavily because it’s always worked.
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