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I think that this (the MO question) is a good question (or can be made into a good question). It should be made, perhaps, a little more focused but I dont think that it represents a huge list of answers, and it can be quite a useful and educating list. (Also the proof-theory tag does not seem to belong there.) The Calabi-Yau example was not so convincing and it could be better to have a small list of good motivating examples.