I think our sense of geometry comes from hunting (not body decoration). It's a little bit like mathematicians invent little "chains of reasoning" rather than "

I think our sense of geometry comes from hunting (not body decoration). It's a little bit like mathematicians invent little "chains of reasoning" rather than "mathematics", and that these chains are interesting and useful; even if their original assumptions turns out to be incorrect, the reasoning is still valid. In the marketplace/ecosystem of mathematics, people then choose the ones that they find most useful and/or interesting. I love the thought that when we meet aliens, they have utterly different mathematics from us, so it reveals how parochial our particular toolbox is. This has actually happened, in a sense, with Chinese mathematics. Apparently, their approach to "proof" was algorithmic rather than declarative - not just a different toolbox, but a different kind of toolbox.