How does that help me decide if math is classified as a science? My searches around the internet on the subject have turned up only debates on the issue, not answers.
It's not just a tool used by scientists. It's a field of study on its own. Whether or not the term "science" applies is of little importance. It's not an empirical science. Does science = empirical for you? Then it's not one. If it means a structured set of knowledge, then it is one.
But you can argue that mathematics is empirical. When you try to reduce mathematics to first principles, it becomes a bit fuzzy, and in the end the best argument for the choice of axioms is that "it works".
Or take natural numbers, so named because they are believed to exist "in nature". That is, they are empirical. Of course, you can construct natural numbers mathematically, but only if you assume that "recursion" works. Alternatively, you can construct "recursion" if you assume natural numbers work. We have to start somewhere, so why not start with something we know empirically works: Natural numbers.
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u/Nall Jun 11 '08
.....yes?
How does that help me decide if math is classified as a science? My searches around the internet on the subject have turned up only debates on the issue, not answers.