Which even amplifies the observation. Not only is the process of proving a theorem more complex than it looks in retrospect, but the whole process of deciding

Which even amplifies the observation. Not only is the process of proving a theorem more complex than it looks in retrospect, but the whole process of deciding whether a theorem or even a whole field of math is even useful or not can be driven by chance over a time span of decades. What is now "topology" was kicked around for many years with many approaches before a general agreement that open sets formed the most useful basis (heh). Advanced textbook authors regularly have to cut topics from subsequent editions of the book, because what seemed promising 30 years ago turned into a dead end. So math is far from the discrete list of topics and answers that it seems to be when you're picking out classes in your syllabus.