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I have LW in my RSS reader. I can't see that you wrote the article until I open it in a browser.
This is a technical comment about the site. But yours is also the article that was interesting enough for me to care enough about who wrote it.
The rss seems not to have the by line. I don't know the proper place for this comment.
I'm interested to know if you think this is an argument for cosmic math. Even if you are not convinced by it I am still interested to know if it is arguing against your position of anthropic math.
Consider 'momentum'. It is a concept that comes straight out of math. The only reason momentum is named is because it is conserved. You have a system, you do some direct measurements, and combine those measurements into a derived measure of momentum, m1. You keep the system closed, but otherwise do a bunch of whacky stuff to the system and you meaure the momentum again, m2. You will find that m1-m2 = 0. If we go anywhere in the universe we will find the same observation holds true.
If we made contact with ET's that have progressed to primitive farmers however far humans made it before doing math. If we teach them to do the observations they will find the same phenomenon. If we left them to develop on their own then is there some part of that process that they would be incapable or unmotivated to do?
This may be my last contribution.
So you are comparing math to a pursuit that is clearly an exploration of the human mind like graphic design or other arts. But I am still fuzzy on the 'why'? I can share that wild crows, too, can count up to 4. But because I am not clear on your why I'm not sure how this observation will affect you. It shows that there are at least some part of math that are useful to non-humans. But perhaps you are referring to more sophisticated math systems like ZFC set theory, in which case the crows don't have a say.
Why does this matter? It felt like it was missing.
Is your question well formed? I'm not sure what a proof would demonstrate.
Have you considered the original purposes of math? My understanding is that it was for accounting, rather than elaborating on axioms.
Newton was the first to try to model the universe mathematically. Others had taken quantitative observations and even noted that specific things in nature could be modelled with math. But Newton was the one that sought and found universal laws that could be expressed in math, like his law of universal gravitation.