Earlier quoted context omitted.
I think you're missing the point. Mathematics isn't a natural science, and that's what I was trying to point out. There is a term for doing science on human constructs - it's called social science. Is your thesis that mathematics is a social science? > Humans are part of nature. Human constructs are part of nature. Humans physically are part of nature, sure. Human constructs are not considered to be as far as classif…
I am not sure why you are using the phrase "natural science", is there any other kind? Lets revisit with the wikipedia definition: Science (from Latin scientia 'knowledge') is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. That seems pretty general and all-inclusive to me. Any knowledge about humans; or societies; or the stuff human…
The argument here for math to be a science is very tortured and contrived, but if it has any even technical validity then it makes the argument for math as a social science.