Extremely hard, I think, but I may have a high bar for what constitutes useful progress (in general; FAI research might be an exception but you don't need to pursue graduate study to get in on that). My impression is the following. Most academic research seems more or less useless, and that's no less true of mathematics than other fields. There are probably too many research mathematicians at the moment. The incentives are aligned pretty strongly towards research and away from other arguably more useful-at-the-margin activities like exposition, synthesis of previous research, meta-research, and so forth. Research mathematics also seems highly competitive relative to other areas where math-related talent has applications (e.g. programming, maybe finance).