Almost complete agreement here. There seems to be a 'shortcut mentality' among some hackers - the idea being that if you are faced with a difficult subject, beg

Almost complete agreement here. There seems to be a 'shortcut mentality' among some hackers - the idea being that if you are faced with a difficult subject, begin with the assumption that standard learning material is padded with lots of useless filler material, and hence conclude you can save time by going for the more summarised stuff. I think this is not generally a bad strategy in many subjects (business comes to mind), but mathematics is different. There really is no 'royal road' to any subset of it. There are shortcuts, sometimes, but every shortcut you take (with the exception of clever mathematical tricks, which count as solid learning here) deprives you of the opportunity to make a small but significant improvement to your logical problem-solving apparatus. And that is probably a greater waste of time than anything else: shallow learning. Again, this is possibly not a bad strategy in many subjects, but again mathematics is not one of those.