Agreed. Axioms are created, everything else is a property of those axioms and 'discovered.'

Those basic axioms tend to be the most useful in our universe, but they were still 'created.' We often define or create other axioms, for example, taxicab geometries are imminently useful for modelling paths in cities. We created the rules for the taxicab geometry, as with Euclidian geometry, but we didn't create the properties that emerge from those rules.

I think maybe the confusion comes from a misunderstood analogy: people think 'if you build a castle of LEGOs, you created that castle; aren't maths likewise created?' The misunderstanding is that mathematical theorems and properties aren't like the castle, they're like the potential to build a castle from those given LEGOs. The child created the castle, but she only discovered the possibility of building a castle, which always existed as a property of those LEGOs.

Woah woah woah, deep cleansing breaths, friend. you've misinterpreted the quote you've used.

When he says

I'd be out of a job and miserable - who would I blame, myself, or them?

He's saying, in his theoretical situation "I just got fired for saying x in a context where i hoped to please people. This confused me, and as a result instead of having the desired reaction of regret and positive change, I would be radicalized into becoming angry and whatever subconscious bigotry i did have would become conscious and more fervent as I blamed x minority for my problems."

The worrying part about this interaction is that you've just done exactly what he was positing.

Not everyone who makes a racist joke is exclusively a racist bigot. There are all sorts of things that people say and do because of the innate human desire to be accepted by the group. This doesn't make these actions okay, but it does make explaining to that person why that action is not okay a reasonable first step. If there is evidence of systematic bigotry by that person, then that's a different story, but you've got to see that pattern of behaviour before you can make that judgement.

Like, when someone calls me "a transgendered", or "born a x", it's like, well, that's not strictly accurate, and you take an opportunity to educate in a neutral or positive setting. Or if someone says "I have a tranny friend", it's like, "i don't have a problem with that term, but you gotta know that there are a lot of people who have some serious issues with that term and you gotta be careful with a loaded gun like that in the future".

It's always best, when faced with a morally ambiguous comment, to first assume the best intentions of people, not just on the internet, but in real life as well. For one, not everything comes across properly in text without context and for two sometimes have legitimately no idea that something is offensive (this is far more common than you'd believe).

Getting angry on the internet is even more useless than it is in real life. real social change is the kind of work that requires the channelling of frustration and anger, and the tempering of expectations with time. You can spend your life angry and vitriolic, or you can put that energy into affecting useful positive change in your environment.