I mainly disagree with this:

The way I see it, the brain is a computing device, so the above statement is a priori wrong.

Secondly, the article is sloppy in its expressions. It equates mathematical representability to computability, which I disagree with. As Gibran and others already pointed out, even mathematical problems without closed-form solutions can have numerically approximated solutions to whatever precision computer capacity allows. That's the beauty of computing: A simple algorithm can calculate a result that otherwise transcends closed-form symbolic expression. min(x,y), for example, is easy to construct as a coded function but impossible(?) to construct as a mathematical symbolic function of x and y.