> I'm skeptical of this logic. I think nobody would be able to learn mathematics if they had to keep it all in their head at once.
That's what functions are for.
> Instead we learn some, we internalise it, and then we can appreciate the new notation
Those new notations are functions, simplified abstractions of more complex processes that allow us to think in larger concepts and not sweat the details.
> Mathematics is beautiful. If anything, it's programming languages that have the catching up to do.
Perhaps, perhaps not.
I'm skeptical of this logic. I think nobody would be able to learn mathematics if they had to keep it all in their head at once. "Unobfuscated" maths, i.e. maths that has every single logical deduction written out from first principles so that you can (to use your words) "execute it", would be impossible to understand because, fundamentally, we are not computers.
Instead we learn some, we internalise it, and then we can appreciate the new notation that encapsulates what we have learnt before without exposing us to the underlying complexity that we simply don't need to solve higher problems.
Mathematics is beautiful. If anything, it's programming languages that have the catching up to do.
Edit: more generally, the blog post seems to be a case of "when all you have is a hammer, everything looks like a nail" -- if you spend all day programming, then it might make sense to try and relate mathematics back to something you're more comfortable with. That doesn't mean that it's the most sensible way for everyone else to learn mathematics.