1.3 may be a more useful answer than 2.

I responded elsewhere with this:

"One of my biggest revelations in mathematics was in statistics, when, after the class (including me) worked unsuccessfully for a couple of hours to integrate an equation, the instructor (who I'm sure was laughing at us) walked up to the board, converted into a different coordinate system, and integrated the now very easily integrated equation in about thirty seconds."

Imagine you're an alien, for a moment, whose mathematics don't have any of the trigonometric functions - no sine, no cosine, no tangent. Whenever they're called for in their mathematics, they do a fourier transform of an infinite series of aperiodic waves, although they would never understand them -as- aperiodic waves, but as simple equations. This is an equally valid way of representing the trigonometric functions - but there would be a lot of very intractable mathematical problems.

Before you call that ridiculous, we didn't have set theory until the 19th century; it permitted the solution of a lot of mathematical problems we had, until then, been struggling with. Set theory overcame a lot of the problems arithmetic had struggled with. New mathematical models have arisen since then, such as category theory.

It's useful, therefore, to recognize arithmetic as a model, and one we may have a bias for, in consideration that another model might be more useful. More specifically, it's useful, when building AI for example, not to build into it a requisite bias for a particular model, if your goal is to permit it to solve problems which we have thus found far intractable; you may be building into it the very structural problems which have made it intractable for us.