Sometimes wikipedia articles are not very helpful for learning. e.g. hyperfunction, can't they explain what it is without resorting to sheaf cohomology?!
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it drives me completely insane that the culture of mathematics is to provide definitions in this way, and even sometimes random examples, but never a concrete āhere is how and why this thing was created and here is what you can use it to do and why that is importantā
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honestly i try to write answers like that sometimes and sometimes i can do it but itās often exhausting because there are too many things
and like... lots of examples of concepts that were invented to do much more complicated things than the pedagogically natural and first thing
like a lot of linear algebra was invented to do functional analysis and solve differential equations and itās cool and useful to know that but pedagogically it makes more sense to start with much smaller finite-dimensional stuff first
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have always greatly appreciated your thorough math answers, so thanks for that! Re pedagogy: I think starting with simpler, motivating stuff is totally fine, but itās often done at an abstract distance, and the connective tissue to āHow I Would Actually Use Thisā is missing
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