Philosophy of Mathematics

"Philosopher says math is philosophy" isn't proof that math is or needs philosophy.

I think you need a refresher on the philosophy of mathematics: https://en.m.wikipedia.org/wiki/Philosophy_of_mathematics.

It's not a matter of legitimacy (which is a social construct) but of foundation. Russell, Brouwer and Hilbert believed that mathematics must be based on a solid philosophical foundation so that it leads to some "Truth." I am not saying this is the only way to think about the philosophy of mathematics -- in fact, my original comment said just the opposite -- but it was very much at the center of the mathematical world in the early decades of the 20th century, and is still a matter

Would it be wrong to call philosophy "abstract {math|logic}"?

Fair. I like Polyani so I shall put a Polyani quote here which I feel goes to your point: Mathematics as a purely formal system of symbols without a human being possessing the know-how for dealing with the symbols is impossible (1969) the wiki page I found it on is the Brouwer-Hilbert controversy (constructivism vs formalism, which seems a reasonable laymans take on a component of your point) and says: Despite the last-half-twentieth century's continued abstraction of mathematic

What is constructive mathematics for the layman?

Not really. One could argue some math is innate and we are just rediscovering it. See the disconnect between natural language and math which happened early 20th century because of material implication bringing vacuous truth, leading to "impedance mismatch". Medicine is still using counterfactuals precisely because of weirdness introduced by Russell in order to make all Boolean values defined for inference.

You may be looking for mathematical philosophy: https://plato.stanford.edu/entries/philosophy-mathematics/

It doesn't matter what you consider yourself. Or who is doing to considering, despite your efforts to emphasize that.The proofs are math. We've already established that math is sound. This discussion is not about the merits of math, we're talking about philosophy. Things like "The transfer of understanding from one person to another is not automatic. It is hard and tricky. Therefore, to analyze human understanding of mathematics, it is important to consider who understands

Enthusiasm doesn't imply skill. - I love discussing natural philosophy, I believe I'm good at explaining these ideas, but I have no shortage of evidence that I am in fact very bad at explaining things. I am probably not special.Either way, I can speak in a strict fashion which sort of jives with formal logic. I referenced Hilbert's program and the assumption that mathematics has a foundation: <a href="https://en.wikipedia.org/wiki/Foundations_of_mathematics#