The fact that you think I'm talking about the axiom of choice, demonstrates that you didn't understand what I'm talking about. I would also be willing to bet a reasonable sum of money that this topic did not come up in your Linear 2 course in physics undergrad.

The arguments between the different schools of philosophy in math are something that most professional mathematicians are unaware of. Those who know about them, generally learned them while learning about either the history of math, or the philosophy of math. I personally only became aware of them while reading https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav.... I didn't learn more about the topic until I was in grad school, and that was from personal conversations. It was never covered in any course that I took on, either in undergraduate or graduate schools.

Now I'm curious. Was there anything that I said that should have been said more clearly? Or was it hard to understand because you were trying to fit what I said into what you know about an entirely unrelated debate about the axiom of choice?

The proof is not a social construct.

The truth is.

The proof is a mechanism to reach that consensus, by convincing other mathematicians of a specific truth. That is all it is.

There is a naive idea that a proof is a purely mechanical series of steps that provides access to truth. Last I checked, this isn't so for the vast majority of proofs in math. Such a proof would be way too tedious to construct or check by mathematicians. And if it isn't checkable, how do we know it is actually true?

Automated proofs are a subfield, and (again, last I checked) controversial because they can often not be checked by humans.

So for example, if the proof doesn't convince other mathematicians, then it's not a a proof.

Or it might convince other mathematicians and later turn out to be wrong after all.

For more on the practical aspects of math, I highly recommend The Mathematical Experience.

https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav...

I read it in German:

https://www.amazon.com/Erfahrung-Mathematik-German-P-J-Davis...

I'm not who you are asking, but this book https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav... hits some of the philosophy of math. It's been a long time since I've dipped into it, but IIRC, it puts mathematical discoveries and exploration into more of a cultural and philosophical context. I could see this being sampled for a good crossover course that would cover humanities requirements for STEM, and STEM requirements for humanities.

My experience is that non-mathematicians like to have GED on their coffee tables as a conversation piece. The related book that mathematicians like is https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav.... (High school math is enough to enjoy it, but the more math you have, the more you'll get out it. All of the way up to the PhD level.)