I'll be applying to PhD programs in pure math this fall. However, my profile isn't that outstanding, so I'll most likely being going to a "mid" to "low" rank (as determined by US News Grad Rankings, for what it's worth). Ultimately, I'd want to do research as well as teach lower/upper division math classes. That being said, I know how overfilled the market is with math PhDs, so even those from top 10 schools don't have much of a chance getting tenure, at least, not super fast. That being said, I'm totally okay with being able to either just teach lower/upper division classes with no research, or doing research and teaching at a "No Name" or "low rank" school. I just love the idea of always learning new mathematics and contributing to it, no matter how small or insignificant it may end up compared to others', and I don't think it's absolutely necessary to go to a top 10 school to do that. I could be wrong though. So given my last few statements about be content with ending up somewhere that's not necessarily top rank, are my goals for teaching/research realistic?