But what of the philosophy of mathematics! https://en.wikipedia.org/wiki/Philosophy_of_mathematics https://en.wikipedia.org/wiki/Philosophy_of_mathematics All

But what of the philosophy of mathematics! https://en.wikipedia.org/wiki/Philosophy_of_mathematics https://en.wikipedia.org/wiki/Philosophy_of_mathematics All intellectual roads lead to philosophy. Joking aside, I think we also run into problems with defining mathematics because its application and the thing itself are not really separable. One can have the philosophy of something, e.g. philosophy of mathematics, because philosophy as a method or type of intellectual excursion is not a single thing--you can go about philosophizing in many different ways, even if your topic is the same (e.g. logical positivist handling of philosophy of language vs. the ordinary language philosophers)--in the case of mathematics it is a field of study but it is more fixed as a method or tool of thought--there are several ways to go about philosophizing no matter what branch of philosophy you tackle, whereas with mathematics, while there are different branches of study, there is really only one mathematics--i.,e. there's only one way to go about mathematicizing correctly for a given problem, whereas there's not really a 'correct' way to philosophize about a given problem. I would define mathematics as a particular mechanism of human thought/a particular way we understand the world (the human mechanism of quantification and manipulation of said quantities) Of course mathematical realists will disagree with me.