I would, in plain language, say that ‘math needs evidence’ is true.
It seems reasonable to think that the study of the natural numbers was the earliest math. I’d imagine that reaching the idea of abstract numbers itself required a lot of evidence.
And mathematical practice since seems to involve a lot of evidence as well. A valid proof seems to exist in the perfect Platonic world of forms and I’m very sympathetic to the sense that we ‘discover’ proofs and aren’t ‘inventing’ them. But finding proofs, or even thinking of searching for proofs seems both necessary in the abstract as well as practically required.
I have been explicitly instructed by math professors to play with new math, e.g. gather evidence of how those systems ‘work’, with the context that doing so was necessary to develop general understanding and intuition of that material.
I would, in plain language, say that ‘math needs evidence’ is true.
It seems reasonable to think that the study of the natural numbers was the earliest math. I’d imagine that reaching the idea of abstract numbers itself required a lot of evidence.
And mathematical practice since seems to involve a lot of evidence as well. A valid proof seems to exist in the perfect Platonic world of forms and I’m very sympathetic to the sense that we ‘discover’ proofs and aren’t ‘inventing’ them. But finding proofs, or even thinking of searching for proofs seems both necessary in the abstract as well as practically required.
I have been explicitly instructed by math professors to play with new math, e.g. gather evidence of how those systems ‘work’, with the context that doing so was necessary to develop general understanding and intuition of that material.