If you don't understand how this is a human construct for human cognition and information processing, I don't have a way to explain it to you. I would recommend reading more about number theory and philosophy.

Reading about number theory helped me understand these concepts, and I recall having a similar resistance to the ideas at the time. Specifically set theory and "zero" as a proxy for the empty set, and "one" being the set that contains the empty set, etc...

Math is an imperfect mechanism for representing the physical realm, invented by humans for that purpose. It has truths that are only true in the mathematical realm and have no bearing or representation in the physical realm.

As an example, I suspect you'd have a difficult time pointing to a physical "real" example of the square root of negative one. It's called the imaginary plane for a reason.

> gives the impression that it is building fantasy castles in the sky

That's exactly what it is, as most mathematicians will tell you.

That doesn't imply however, that it's not useful.

Imaginary numbers (to continue the example) are quite handy for dealing with signal processing, among other things. Which doesn't change the fact that they are a human invention - one that stumped societies for hundreds, if not thousands of years (the Greeks struggled mightily with square roots for this reason, for them math and philosophy were not separate things). We only really got past it by inventing the symbol i and tossing all the gnarly stuff in it like a waste bin, because most of the time for practical applications it's factored out.

> absolute and objective truths

These are most appropriately the realm of religion, not of physical sciences.

This is not a fact and is the oldest debate in mathematics. All of it is just as likely (if not more) to be the way the brain models things than some objective truth of “reality.”