Hi Plan 9. I loved your movie.
In applied math, an intelligence must care about a particular "2" and another particular "2."
The invention is in discovering properties of the objects which are being added, and how those complicate the equation.

In pure math, the = sign after 2+2
will obtain an answer of "4" by definition.
The definition will remain true since there IS NO DIFFERENCE between the definitions 2+2 and (+) 4. There is not a DIFFERENCE; there is AN EQUAL SIGN.
I think pure math is just the discovery of combinations which are true by definition in proportional relationships all the way to the frontiers of infinity (as we know it).
Affectionately,
Mike