A technique I have found that works well is read a lot of paper and their citations, but don't dive deep. Each paper usually provides some easy to grasp insigh

A technique I have found that works well is read a lot of paper and their citations, but don't dive deep. Each paper usually provides some easy to grasp insight (far too little per paper, but that is elitism for you) that you can use to get a good picture of the field. Reread papers to grasp more insight. Once you have a good overall picture, find some area/problem that really interests you, you like the math, and isn't covered well and bone up on the math techniques. Do your research and present. Showing up at thesis defenses is good too. Learn a lot from the back and forth with advisors. The key is to understand at a high level why the different math techniques are being used without actually understanding all the details. This won't be sufficient for your own work,but at least you'll have a good idea how your part fits in the scheme of things.