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I work in computational algebra. The last seven months, I have been reviewing literature and reading some research in computational algebra, but till now, I've not been able to come up with any specific problem. For the first two years of my PhD, I did the course work.

Question : How much time does it take to come up with a specific research problem? Is there any way to speed up this phase of the PhD?

Please note that my research supervisor is helpful, I discussed this issue with him and he told me that it takes some time to come up with a research problem, but he did not tell me how much time it will take.

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At least in my experience, one's PhD adviser helps with finding a research topic, or even provides one. Depending on how mature and technical the field is, it might be very difficult to come up with a reasonably problem by oneself.

I suggest discussing the question with your advisor.

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Finding a thesis topic can be quite difficult. For example, I needed more than a year until I got into an interesting project where I was able to use my abilities and to find interesting research questions.

I was able to solve this issue by talking to my professor since he has a good overview of the state of the art. Thus, I would also recommend you to talk to your professor and other PhD students.

Another way might also be to read recent(!) research papers. Have a look at journals, conference proceeding. Think about attending an interesting conference and talking to other researchers there.

Even if you found a topic: Keep in mind that the beginning might still be difficult. It needs a lot of time and work to finally get familiar with a new topic, so do not give up too early.

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  • Reading papers can definitely be helpful, at least in principle. Many papers leave questions unanswered. Sometimes they specifically point them out, sometimes they are left hidden and only occur to you if you have enough understanding and insight to ask "But what if...". Of course, these questions need not be particularly accessible to a starting researcher, but sometimes you can get lucky (ie, the problem is "easy" for you because you studied bizarre thing Y which is perfect for it), and worst case you get some idea of what other people think is a good research question. – zibadawa timmy Jan 4 '18 at 8:00
  • If something remains unclear, it can also be very helpful to start a discussion with other PhD students of your institute. That may also help coming up with new ideas. In most cases it can be a nice idea to write to the author. Personally speaking, I am quite happy if someone reads my papers and is interested in my work. – J-Kun Jan 4 '18 at 8:03
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If you are a full time researcher, you may not have the luxury of an adviser to guide you, especially if it's a new field. But, as a graduate student, you should seriously discuss with your adviser what you have read and what you found interesting. They should be able to help you find that research topic.

Ask them to send you to a summer school or conference, where you would get the pulse of what's going on in your subject area. That's also the place to meet other people who might become later your friends and collaborators.

Apart from the adviser, you should talk to the people in your thesis committee, if you have one. If your department is a healthy place, they would be more than happy to help. Also, talk to other faculty and students about things related to the field you want to launch yourself into.

It is not sufficient to read a lot in order to come up with ideas of research subjects. From reading you may find out what are the main open problems in your field and what are the state-of-the-art methods. But, there is no substitute for hands on research experience. Without that, you cannot know if the thesis topic you propose is something doable or not.

Since you read a lot about computational algebra, try to find a review where they talk about open problems in the field. Pick one which sounds interesting and do some more literature search to see what you need to know to approach the subject. Then discuss that with your adviser, peers or other faculty that might be helpful. They should help you divide this problem into subproblems, and one of them might be your topic.

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In my experience: anywhere between one second and 5 years. Sometimes you don't start from the "specific". You will frequently start from a rather general problem (perhaps even just a feeling..."there's something interest going on here..."), and then you narrow it down to something more specific and tractable as you go along and understand why it needs to be narrowed down, and even how it can be narrowed down. To rephrase some advice my advisor gave me: "Theorems are produced by proving a long series of minor lemmas. You rarely ever just produce the theorem from the start. Instead you prove special cases of special cases and technical lemmas until eventually something bigger emerges." One of the most important skills to learn to be a successful researcher is not how to identify big, overarching problems and how to solve them, but how to dissect a problem into little pieces that you then attack and start assembling into the big picture.

If you've been given, or otherwise have, some questions and are having trouble thinking of how to even start on them, then start dissecting: come up with subquestions, special cases, identify what makes things "trivial", do some accessible/"easy" calculations, etc.

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