Re:Mathematicians don't care about foundations
by adgjlsfhk1 on Saturday December 20, 2025 @05:11PM
(#46340113)
you're kind of coming at this backwards. it's not that someone doing analysis doesn't care about whether all functions on reals is continuous, it's that if you hand them a foundation where that's true, they'll disagree with whether your foundation is correctly modeling functions/real numbers.
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Re:Mathematicians don't care about foundations
by black_knight on Saturday December 20, 2025 @05:52PM
(#46340423)
At which point we would have an interesting debate! I could tell them all about how this foundation will give them a more nuanced view on continuity!
Re:Mathematicians don't care about foundations
by johngossman on Saturday December 20, 2025 @06:09PM
(#46340558)
I suggest you go meet some PhD mathematicians and have that discussion.
Re:Mathematicians don't care about foundations
by black_knight on Saturday December 20, 2025 @06:25PM
(#46340666)
Having a PhD in mathematics myself, I have been surrounded by such and had this discussion a few times. Some even like the ideas suggested!
I would say the most common counter argument is cultural: Classical mathematics is the norm in the field, hence one must use it to participate in research in this field.
But that seems to me a rather intellectually unsatisfying argument, if one cares about the meaning of the work.