Comment by nitsuaeekcm
12 hours ago
For those who aren't familiar with the great but tragic story of Principia and Russell's quest for the foundation of math (spoiler: there is none), there's a really great graphic novel called Logicomix https://en.wikipedia.org/wiki/Logicomix I haven't read it in probably ten years, but it's one of those books and stories I spend an inordinate amount of time thinking about, for whatever reason.
The foundation of math is (mostly) ZFC.
It is not. The foundation of math is contested -- but afaik it is widely held that HoTT is the, erm, hottest contender to the throne https://en.wikipedia.org/wiki/Homotopy_type_theory
There is not a single foundation - you can choose. The differences are rarely important for working mathematicians though. Most know enough of ZFC to get by and ignore foundations tbh
Most foundations are in a sense equivalent. In that sense, "ZFC" is as good a choice as any. I think there might be some confusion around the different meanings of the word "foundation": A foundation is a formal system that suffices, somehow, to encode virtually all of known mathematics. The reason why people (including me!) are interested in other "foundations" like HoTT is because they try to build the same mathematics as ZFC from a different set of building blocks, despite them eventually arriving in the same place. In the case of HoTT, it reduces mathematics to homotopies and fibrations, while also making those weighty-sounding concepts seem easy. If you're interested in homotopies, fibrations, cohomology theories etc. then HoTT is a really helpful way to better understand those concepts.
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