> If you actually read the article

Needless.

> The insights one can gain from this pure math definition are still very much useful for real world programming tough (e.g. memoization), you just have to be careful about the slightly different definitions/implementations.

I agree completely here. But I think that undermines some of the earlier claims. The math definition only serves as inspiration, we're not using the math definition when we memoize. And the important part you need for that inspiration is a lot narrower than full equivalence.