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 “here is how and why this thing was created and here is what you can use it to do and why that is important”
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honestly i try to write answers like that sometimes and sometimes i can do it but it’s 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
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like a lot of linear algebra was invented to do functional analysis and solve differential equations and it’s cool and useful to know that but pedagogically it makes more sense to start with much smaller finite-dimensional stuff first
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 it’s often done at an abstract distance, and the connective tissue to “How I Would Actually Use This” is missing
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Prime example: matrices as taught in pre-college education
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