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Oct 30, 2020 at 23:27 comment added Timothy Chow @user1504: I'd agree that the paper qualification isn't needed, but what one does need is the ability to find and/or create problems, discern what problems one can fruitfully work on (and what problems should be set aside), solve them, write up the solutions well, and get others to recognize the value of what one has done. For most people, going through the process of getting a math PhD under a good advisor provides invaluable training in these matters. The OP has some research experience, but it sounds to me that he or she hasn't quite reached the point of being able to function as a postdoc.
Oct 30, 2020 at 19:11 comment added user1504 Second, I'm not sure a math PhD is required to do math research. The math community really is a community (and so much of its lore is oral). To take part in math research, especially in a paid capacity, means to join this community. A PhD is one way to achieve this. But so is a postdoc or a visiting position. The key thing is doing work and talking to people. Start now, if you're going down this road.
Oct 30, 2020 at 19:10 comment added user1504 I want to second the advice to finish the PhD (if that is feasible). First, you may find yourself needing a job at some point -- life is unpredictable -- and a PhD is far more useful for this purpose than an ABD.
Oct 30, 2020 at 15:58 comment added Dave L Renfro (+1) (and more if I could) for your 3rd and 4th paragraphs. Of course, the OP shouldn't make it as "in your face" explicit as this, but what you've suggested shows the kinds of things the OP may later (when finished with math Ph.D.) want their application materials to advocate for and provide evidence of. And these things certainly would be useful for getting into a math graduate program.
S Oct 30, 2020 at 13:20 history answered David White CC BY-SA 4.0
S Oct 30, 2020 at 13:20 history made wiki Post Made Community Wiki by David White