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I am trying to come up with more ideas for math research. It's hard because I don't know which problems are doable or interesting to other mathematicians. My former thesis adviser doesn't seem to have any ideas. I've been attending some online seminars, but even then it's hard to know who is working on what.

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    How many times have you posted some variant on this question? What are you expecting different in an answer this time?
    – Bryan Krause
    Commented Aug 22, 2023 at 21:30

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Talk to a lot of people. Share ideas. Visit other institutions. Go to conferences and meet people.

Keep a notebook of potential research ideas. Revisit it often. Update it often. When you have a thought about some older idea, add it to the page(s) for that idea.

In math, think about variations on a theme. What has been done? What is similar to that that might be valuable. How can variations in definitions and axioms lead to new things. Lots of advances in math have been just this sort of thinking.

Dive deep into some problem areas and seek insight there. What is really going on that isn't obvious from the proven theorems?

What would it mean for something to be "sort of true"? "Sort of continuous"? Higher dimensions, lower dimensions, fractional dimensions??? Can I apply ideas from "that" field to "this" field?

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