While I like most of your points, I've got to stand up for our brains (or mathematics, depending on who you think is getting shorthanded there :)).

I would say the exact opposite of "our brains are not wired for [math]": mathematics is the simplest expression of our ultimate thought ("brain") processes.

It is only hard because it is so abstract and builds on a large corpus of what has already been constructed, but it was "designed" exactly after how our brains operate.

For a layperson, proving even the basic arithmetic might seem like magic, but once you go through the simple exercise of defining everything in terms of "One" and "Successor(One)" and compare that to how we teach our kids numbers, it's clear mathematics matches exactly how human brains operate.

Then again, I concede that not everybody's brain is "wired the same way," but I am sure there are plenty of us for whom mathematics is just natural: the only problem being the fact that majority of people have not been exposed to true mathematics.