[0] https://en.m.wikipedia.org/wiki/Benacerraf%27s_identificatio... [1] https://plato.stanford.edu/entries/philosophy-mathematics/#W...
> If you don't know why set theory is important, it is because set theory is the foundation of all of mathematics.
Nitpick maybe but the types and categories people might prefer sets as "a" foundation instead of "the"? These 3 things are the most useful, get the most attention, and have benefited from the most serious efforts. But IMHO one of the cool things about math is that if you're willing to squint and work at it, then many alternative foundations are possible. For example Conway's surreals[2] hint that you can get numbers/sets by starting with even games as a primitive. I can't quickly find refs, but the visualizations here hint that starting with graph theoretic axioms can lead to sets instead of vice-versa and I think people have worked on that too. Who knows whether alien math builds everything else up starting from geometry or probability, etc.