Maths in my view (and not speaking for the wife) is simply a way of creating models of reality. It's analogy, metaphor. One apple for me, one for the wife, one each for the kids.... how many's that? Let's set up a correspondence between apples, people, and fingers. That many! Let's go out and find that many fingers of apples, then we know we've got enough. Thank goodness we've only got two kids who can eat apples.

But then there's maths for maths sake, mathematica gratia mathematicae. That's creating new relationships. And every now and then, someone who's both good at thinking about relationships between things and maths, finds that maths describes a relationship between things that we didn't know how to quantify before.

The relationship was always there; now we can describe it, and make predictions. Next apple season, we've got another kid who's old enough to eat apples. Now we need more fingers. Thank goodness I've got a thumb.