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It's not just you, we are horrible at teaching advanced math. However, the reason for it is that advanced math is, as far as we can tell, just really, really, really hard. It's not that mathematicians don't care about teaching others (they very much do, and they try their best to get their understanding across to others), or that Wikipedia authors are particularly bad at clear exposition (they are, if anything, above average). Quite simply, we know of no royal road to understanding mathematics, you have to put in many hours to bite it in very small pieces. Here's an example: https://en.wikipedia.org/wiki/Homology_(mathematics) It has motivation, examples, and even actual numbers (though they're really just 0 and 1. most of the time). In my opinion, it's very good and clear exposition, for an encyclopedic article. However, I strongly suspect that people without enough mathematical knowledge (and "enough" in this case is something in the neighborhood of "enough to obtain an undergraduate degree in Mathematics") will simply not get anything about it beyond "it's about number of holes" (and that's not even remotely close to the whole picture: homology theories are important and useful in context of things with no "holes" to speak of). If you think otherwise, but not know what a quotient group is, you're just fooling yourself. This is something I observe on HN a lot: people don't understand advanced mathematics, and are dumbfounded by the fact, trying to blame weird notation mathematicians insist on, or lack of motivation/examples/pictures etc. I never see people here do the same with advanced physics ("if the Standard Model is so standard, why can't they briefly and clearly describe what it is" is not something I ever see), molecular biology, or material science. People seem to know their limits and understand that really grokking these fields requires many years of deep study. I think it's because many people on HN have good experience learning mathematics at school: it was something they always grasped really easily, and were easily able to figure out how to calculate derivatives, integrals, get matrices into normal forms etc. I don't want to rain on anyone's parade, because these things are still relatively difficult, and it does require more intellectual ability and effort that probably 3/4ths of the population aren't capable of. However, relative to advanced mathematics, undergraduate calculus is really rather trivial stuff. Point is, if you don't understand modern advanced mathematics, you shouldn't get any more disappointed than you are about not being able to play violin. These things just don't come easy. |