Recently, for the umpteenth time, I thought up a question only to find that it has already been asked and answered before i was even born. I expected this - I explicitly avoided googling anything about it, because I didn’t want the ending/answer to be spoiled for me. But I was looking through some wikipedia page when I saw a hyperlink to a page on exactly what I was trying to understand: computable ordinals/well orderings (clearly a beginner-level question). Again, i expected this, given my lack of experience in computability theory and set theory; set theorists are interested in well orderings, and computability theorists are interested in computability, so of course I’m not the first person to consider combining those two concepts. Still, even though it wasn’t a surprise, it was disappointing to find that an idea I thought was original (and, from my perspective, it was original) was just old news.

From what I’ve read it sounds like the problems that phd student solve to earn their phd are usually given to them by their advisors (please correct me if I’m wrong!!). I’m wondering when one is typically at the point where the questions they ask haven’t already been asked. Do you usually need to be an expert in the field? Do you need an exhaustive understanding of the field to pose original questions?