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phd_dead_or_alive
https://www.quora.com/What-would-a-PhD-graduate-advise-a-new-PhD-student
The easiest way is to refer scholar.google.com and search research papers of your relevant / interested / most viewed / most worked on topics, when we study latest relevant papers PLUS to readout Research Papers delivered in international conferences seminars, INSHALLAH you will have a superb n hot topic automatically.
Now it is well-known in all branches of learning, but in particular in mathematical learning, that the way to learn is to do, rather than to read. It is all too common to read through some material, convince oneself that one understands it well, but then find oneself at sea when trying to apply it in even a slightly different situation. Moreover, material understood only at a shallow level is easily forgotten.
https://www.site.uottawa.ca/~bochmann/Projects/how-to-do-good-research/index.html
https://cstheory.stackexchange.com/questions/25617/how-to-find-interesting-research-problems
https://terrytao.wordpress.com/career-advice/
https://www.cs.jhu.edu/~jason/advice/how-to-find-research-problems.html
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