How to learn math by self-teaching [Without books, or outside help]

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I'm thinking along the lines of attempting to explore mathematics by making my own discoveries as if it's the new frontier. As if I was a mathematician from 2000 B.C.

I know this sounds really strange but I'm curious - has anyone tried rediscovering mathematics? (who isn't an advanced mathematician) because I think it would be really fun.

If it matters - my most recent math classes were calc 2 and discrete structures.