delooper wrote:Various types of set theories can provide a foundation for mathematics but there are also people who prefer alternative foundations so I don't think it's right to say mathematics is founded on the principles of logic and set theory. More than anything I think foundations are largely useful as pedagogical devices, as they make learning a subject easier, as they're more like little machines that you get to open and inspect, part-by-part.
Desiato wrote:Sadly and frankly, that's not true. I dare say that anyone that tries starting to learn mathematics with rigorous foundations is doomed to not get anywhere.
Note that what most mathematicians would consider among "foundations" is set and model theory, and that's a vast and extremely abstract field that is pretty much impossible to study without a more or less solid idea how math works before even starting to learn it.
In fact, I know several mathematicians with a master's degree (well, technically, an older German semi-equivalent called "Diplom") who have no clue about this topic that goes beyond "AoC is scary".
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