Well, wouldn't the same be true for using language? Language follows a grammar, uses established vocabulary based on an underlying set of characters or speech forms; why would anyone follow the rules?

Formalists in mathematics argue that mathematical structures are very much conventions, which could perhaps be otherwise (indeed alternative axiomatizations or even alternative axiom systems are often a subject of mathematical interest), but there are certain quite widely used conventions that have shown value in our studies of the world and/or of mathematical practice itself. Learning the Peano or Zermelo/Frankel axioms is acquiring a very useful vocabulary for the practice of a certain way of number or set theory, and we say this encapsulates a productive way of thinking about things without demanding that they are the only right way to learn to multiply or to perform abstract operations on collections of objects.

Well, wouldn't the same be true for using language? Language follows a grammar, uses established vocabulary based on an underlying set of characters or speech forms; why would anyone follow the rules?

Formalists in mathematics argue that mathematical structures are very much conventions, which could perhaps be otherwise*, but there are certain quite widely used conventions that have shown value in our studies of the world and/or of mathematical practice itself. Learning the Peano or Zermelo/Frankel axioms is acquiring a very useful vocabulary for the practice of a certain way of number or set theory, and we say this encapsulates a productive way of thinking about things without demanding that they are the only right way to learn to multiply or to perform abstract operations on collections of objects.

* indeed, alternative axiomatizations or even alternative axiom systems are often subjects of independent mathematical interest