I agree. Let me add another item to the author's list: 7. Most problems have no solution. Doing undergraduate mathematics you can always be sure that every que

I agree. Let me add another item to the author's list: 7. Most problems have no solution. Doing undergraduate mathematics you can always be sure that every question is well posed and has an answer somewhere. Once you start doing research, this is not the case at all. Problems without solutions are so prevalent, that asking the right question becomes the interesting thing, not the finding of the answer.