how 18% gray is mathematically calculated?

Searching around there are so many different answers to this question that I think it’s a subject that confounds everybody. Here’s what i understood (and i hope more experienced people on the forum will give better answers than mine and correct my errors).

It has to do with our eyes perception of light. What our eyes perceive as the middle point between white and black is a not the shade of gray that reflects the 50% of the light (as the logic would presume but that would look too bright for us) , it’s a shade of gray that reflects the 18% of the light (so, it’s not the “real” middle gray ,  it’s perceived in this way). That shade of gray is the zone V of Adam’s Zone System and in theory should the shade of gray cards used for exposure.

In a real generic scene there are brighter spots that reflect a lot, darker ones that reflect less and everything in between and the average of all of them is more or less a 18% reflectivity (again, to our eyes) , at least in theory and apart from scenes with an extreme lighting conditions. So exposing correctly what reflects the 18% allows to create what we perceive as the natural light of our world and being in the (perceived) middle of black and white should allow to expose correctly also the highlights and the shadows.  The camera metering system, if i understood correctly, treat everything as 18% and indicates 0 when the 18% is correctly exposed.

I hope i didn’t write too many wrong informations, ah ah!