Mathematics what is the difference between science

Science is discovery. A scientist axiomatizes statements using evidence. "This apple is red" becomes a scientific fact with an event or experiment that documents the reality that backs it. Scientists then build statements that predict facts without having to directly observe them. "All apples are red" would be an example of a predictive statement, and hence a theory. A green apple would easily prove it wrong so "apples fall from trees" would be a better theory.

Mathematics is computation. A mathematician solves problems and derives proofs by applying mathematical axioms to mathematical statements. Truth can only be translated, and never generated. Both sides of any equation are equally true. But this allows a mathematician to juggle the truth without ever breaking it. Mathematics describes the various shapes of any given truth.

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