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For example, if (hypothetically speaking) I am stuck on proving a theorem, is it okay to ask my academic advisor some help for next step? My approach has been, "this is what I have tried, I am stuck here...can you point out how I can continue". But the amount of time that it takes the professor to reply is stressing me out, I am afraid that he is getting exasperated at my question.

What makes thing a bit worse is that the prof says flat out he likes people who are able to solve problems independently. But he also has a reputation of being a fast replier to student emails regarding problems arising in his course. I wonder what he expects of me.

So what is considered appropriate to ask your advisor without pushing him to the limit of having to solve the problem himself. Ultimately I am worried about looking totally incompetent. Is there some way for me to not appear totally incompetent?

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    You should not worry whether you look incompetent. At the end, it is unimportant. You should worry whether you are competent --- if professor always can answer your questions quickly, then you probably getting stuck at relatively easy bits. You should ask yourself and your advisor what you can read, which problem sets you can practice on, etc, so that you can learn the skills that you lack.
    – Boris Bukh
    Commented Mar 14, 2015 at 2:28
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    I'd describe this situation as a research problem as opposed to technical problem. To me, technical problems are instruments not working, lack of tools (and importantly, money to buy tools and supplies - which would always require asking the supervisor). Commented Mar 14, 2015 at 16:31
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    Why not ask him what he expects of you?
    – Davidmh
    Commented Mar 14, 2015 at 17:14

3 Answers 3

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Your approach to asking -- "this is what I have tried, I am stuck here...can you point out how I can continue?" -- is the right one. Without knowing how difficult of a problem you have gotten stuck on, and how often you ask for help, it is very hard for us to judge how your advisor will interpret your request.

That said, in general I very much appreciate it when my graduate students and postdocs let me know when they get stuck on some step of a research project. My students and I are collaborators after all, and if I can help them get going again, or alternatively if I can recognize that we've been heading down a dead-end, this is very much to everyone's benefit.

Of course, they should not be coming to me with trivial problems: "I can't get this expression to format properly in LaTeX" or "I don't know how to compute the Jacobian matrix for this function", nor would I want to get these requests on a daily basis. But if a competent student has made a serious effort to solve a problem and is still stuck, I'd like to know about it and to help if at all possible.

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    +1 Moreover, this is the right approach when asking anyone for help with a problem, not just your advisor.
    – JeffE
    Commented Mar 15, 2015 at 11:29
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First you should ensure that your question is not trivial (as @Corvus noted).

Are there other graduate students in your group? Talk to them. Bounce ideas off them first. There may be senior PhD students or the like in your department who may be excellent resources for certain types of material.

When you have exhausted some of these avenues, you can and should discuss the roadblock that you have with your advisor. It is quite possible that your advisor may also need time to digest the question and provide an answer or provide some direction. Remember that your advisor is your collaborator and that you are tackling a research question and so others may be as stumped as you are. Even if you believe your advisor is extremely capable you should bear in mind that faculty members have so many tasks to attend to that the fraction of time available to think deeply about your question is quite limited. This may be another reason for delayed responses. A PhD student may have a course or two to tackle but will have -- or is expected to have -- sufficient time to think deeply about a problem.

One more possibility is to discuss your problem with another faculty member in your department who may not be working on the same problem but may have the relevant background to quickly set you on the right path.

A professor responding quickly to questions in a course is quite different because she or he is already an expert on the material, likely set the question or has answered it in the past. So a swift response to student doubts in those cases does not contradict slower responses to open questions.

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To offer perhaps a different perspective here, I wouldn't have hesitated to discuss something like this. Yours likes people who are able to solve their own problems. I'd perhaps pose the question though, that perhaps he also values those who know their own limitations and seek advice from others.

As the other answers stated, it's always good to talk to other students or post-docs. This may be for specific advice, or simply as a form of "rubber duck programming" - there is significant learning and new understanding by explaining something in fundamental terms to a metaphorical (or physical) rubber duck sat in your desk. If your colleagues are not experts in the field, even discussing the problem in broad terms may help you spot something you didn't spot before.

To give an example, I once was stuck in knots, trying to work out a complex concept in some code I was writing. I ended up discussing the problem in fundamental terms with my coworkers in the office. The process of explaining it to them (non experts in the topic) made me really think about the problem I was facing and its context. That led me to have the proverbial brainwave, and find a new angle of approach to the problem I hadn't considered.

In saying that, as I said earlier, I never hesitated to discuss things with my advisor. In fact, we would generally try to talk for at least half an hour per day. Of course that wasn't all seeking technical advice, rather dealing with ongoing business and updating each other on any progress or interesting ideas or discoveries. Obviously this depends on your advisor, but in my experience, advisors value independence, but also recognising your own limitations. I would rather a student I'm supervising came with a problem, than struggled and made no progress for weeks or months.

You asked how to avoid appearing "totally incompetent". What I advise is that you prepare a brief summary of what you've attempted. Be able to concisely explain the problem, and your initial analysis of how to solve it. Then be able to state the problem you're experiencing, and what you've tried to work around it. Did you refer to any other works or books (if so, mention this)? Putting a bit of effort into the question shows that you have put the work in, and understand the problem, but need some advice. Don't expect your advisor to immediately solve it, but perhaps they will give a few pointers or ideas. The first few words I mutter after being posed with a problem are often scribbled down quickly by students, who then go away to decipher them and try them out - often the initial thoughts from someone uninvolved with the problem help to solve it or offer a new insight or way of thinking.

I would add though that often it takes me a while to look through a complex problem. And I am often bad at replying to emails when my initial reaction is to delve straight into the problem! Replying to class-related questions is typically much easier (they are generally based on established theory and can be answered with reference to slides, notes or books. Failing that, the explanation is usually familiar). For ongoing, leading edge research, that's obviously not possible. Don't panic - in the cutting edge of research, even the most experienced professor doesn't know the answer immediately. Otherwise it wouldn't be the cutting edge!

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