What does “a few days” mean in the following context? In response to me sending a short paper to a professor for review, he said:

Sorry, I'll look ..but might take me a few days".

Is this a polite decline or is there a real good chance he will look at it?

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    Is there a particular reason why he should look at your paper? Is he your supervisor or have you worked with him on the paper or was he interested in the topic? Profs are very busy (students underestimate that), so it is good if there is a special incentive here. – Captain Emacs Dec 11 '16 at 16:21
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    Did he say exactly this words? If he said "I'd look at this" then it implies no, he won't look at it. But 'i'll look at this' implies yes to me. And 'a few days' could be one week, btw. – Quora Feans Dec 11 '16 at 21:05
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    I think it means "I'll do this when you remind me in one or two weeks" in practice. – user18072 Dec 11 '16 at 23:16
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    This might depend on location. In many Asian cultures, one never gives a negative answer (you might lose face, if told that that he will never look at it). – Mawg says reinstate Monica Dec 12 '16 at 11:32
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    @Mawg Very much so. For an example in the other direction, in more direct cultures like for example Dutch culture (and I assume German culture as well) the intended meaning of the professor is even more likely to be exactly what he says. – Jasper Dec 12 '16 at 14:02

Of course it’s impossible to be sure, but if the professor didn’t intend to do anything about your paper, I consider it likely that he would not have answered at all or that he would have answered that he lacks time. The latter would have been the polite decline – there is nothing polite about saying that you will do something without ever intending to do it.

What is uncertain is whether and when the professor actually does as he intended. Many professors are notoriously busy and underestimating when they will find time to do something. Moreover, they may be disorganised and just forget about it. Depending on how urgent and important this paper is to you and whether you delay anything waiting on the professor’s response, I suggest to write a polite and short e-mail stating when you would need the response and that you understand if he would reply that he is not able to respond to your request up to that point.

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We're not mind-readers. Keeping that in mind, my guess is that a professor at a top-ranked university is a reliable person and, therefore, wouldn't make empty promises.

If you need his feedback within a particular timeframe, you should politely ask him if he could send it within this timeframe, rather than wait for his feedback to happen.

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He is a mathemetician. He knows what words mean. If he had meant 'sorry, I don't have time to do this sort of thing' he would have said so.

8 pages is short in some ways. But it's still 8 pages. I hope you took care to start with a few lines of précis. Then a busy man can reply on the lines of "Do you add anything to X's recent publication on this topic? If so, please let me know and I'll study your work more deeply."

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In all likelihood what it means is

"I'm very busy right now - I've just read your email and want to move onto other emails. I mean to come back to your paper and read it when I have time, which will probably be in a few days' time"

And then he subsequently forgets/ doesn't have time/ doesn't feel like reading your paper. So "few" subsequently has a high probability of meaning "infinity", even if it didn't before hand.

If he has forgotten a gentle reminder may help - but if it is either of the other possibilities it will merely be irritating. Critical evaluation of papers isn't the most fun past-time in the world - if he doesn't have much to gain from the exercise, and he is otherwise busy, you are probably all out of luck. It can sometimes be quite difficult to get supervisors to read students' papers - and that's when they are going to be listed as co-author!

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Famous professors' email inboxes are constantly overflowing with papers they genuinely want to read, recommendation letters they need to write, and administrative tasks that they have to take care of. I would say the meaning of "a few days" is "as soon as I can".

Since you have e-mailed him twice already, I would not do so yet again. Unless you submitted the paper for publication at a journal this professor edits, he is under no obligation to respond.

You said that you asked him "if the proposition there makes sense". I warn you that this is a bit awkward. It is perfectly fine (and indeed I highly recommend it) to send your work to scientists whom you think may be interested, and to ask for comments. But in most circumstances, it's a bit impolite to ask scientists whom you don't know to check your work.

All that said, I think it's more likely that you'll get a favorable response than not. It is December 11 today, and at most US universities final exams are concluding right about now -- which keeps most professors very busy with helping students and grading exams. Very possibly the professor in question has postponed everything which is (to him) not urgent, but fully intends to reply once exam season is over.

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You can't make a conclusion. If you don't hear his response you may send a followup email after few days (2-3 weeks) and if he reply the same I will consider it a polite decline.

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Take it at face value but interpret it in the context of the academic calendar where he works. You wrote "top 10" so my guess is you and the professor are both in the U.S. At many U.S. universities, grades have to be turned in somewhere around one week from now, I'm guessing.

You could try writing again about three days after grades are due at his university.

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As someone who has completed a PhD, I have had a lot of responses like that. Every time, it literally meant it may take a while for them to look into it. In some cases, quite a while, if they're a professor or lecturer you can't really underestimate how busy they are (and then all of a sudden they may have time). If they're not your supervisor then you're probably not their priority, but I would take what they say at face value, they need some time.

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The prof sent you a polite reply, and you should certainly thank him. You can use your thank you note to clarify the situation. Something like "Thank you very much. I look forward to hearing your thoughts, and there is no rush" (if there isn't, in fact, a rush) would give him the opportunity to clarify any misunderstanding.

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