On Mon, Jul 6, 2015 at 2:09 PM, Dan Asimov <asimov@msri.org> wrote:
There are several different mathematicses that would each have its own definition, including at least the following:
1) The human culture of any field that uses mathematics to study something
2) The human culture of mathematicians studying pure math (the study of deriving rigorous results from rigorous rules*)
Unless you want to exclude Gauss, Euler, and Euclid from this culture, I think you need a different definition (or a slightly different mathematics 2A, that also requires its own definition) that includes the study of the same subject in ways that do not meet modern standards of rigor. Andy
3) The study of deriving rigorous results from rigorous rules per se
4) The body of past, present, future rigorous results from rigorous rules
5) The body of past, present, future rigorous results from axiom schema of any cardinality
This last one besides being interesting in its own right includes, e.g., all exactly definition of the integers, satisfying Platonists of all stripes
—Dan
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