I know a PHD in math that claims math is invented by ourselves and not any universal true. So well, depends who you ask.
Also some of these programming utilities may outlive some math proof. Time will tell
Of course they are universal truths. We may have made up the rules/abstractions/symbols to represent the underlying but a proof will hold in any part of the universe. Infact, math will hold in any universe. You could change every fundamental physical property of the universe and those proofs will still hold.
Those are wild claims that you can't possibly prove. They are typically assumed to be the case to the extent that we even think about them but in the end are largely unanswerable philosophical questions.
It’s not a claim, it’s a pretty self apparent fact. To wrap your head around this, as the simplest example 2+2=4 doesn’t change anywhere or under any different physical law. It’s as universal as you can get. There’s nothing philosophical about this.
It is a claim, and you can't test it. If physical laws varied between galaxies you wouldn't know unless we were able to measure it. So the current bound on physical phenomena is whatever the resolution of our observational data is, coupled with our models that match it.
How are you going to get observational data for a different universe? Does such a thing even exist? What is its nature? You're operating well outside the bounds of human knowledge.
What you are actually saying there is that you can't imagine 2+2 being anything other than 4. That's perfectly reasonable but it's not the same thing.
There is no circumstance where 2+2 does not equal 4. It is a literal fact.
At the most fundamental level, you can only have a discreet or a non-discreet universe. If it’s discreet, there are countable things and 2+2 = 4 is true. In a non-discreet universe there are no countable things, but the universe itself is countable. If the universe were non-discreet and infinite, you could still count the infinities so it’s still true.
You are making a number of assumptions there seemingly without realizing it even after I explicitly called it out. I'm not sure what to say other than to suggest that there's an entire field, analytic philosophy, concerned with such matters.
You literally can't prove that you aren't a brain in a vat so I have no idea how you expect to make sweeping claims about the fundamental nature of reality. It is certainly convenient and practical to take certain basic assumptions as fact in order to go about higher level tasks but that does not make them so.