For me as a graduate student, there are some papers out there that really stand out among the others. Some of them are really meaningful and inspiring.
Is it polite or even acceptable emailing the authors of a paper you enjoyed reading?
Sometimes I think some people would be happy for knowing that a student got inspired about the work they did. But at the same time, I think this could be taken as a weird/spam/useless e-mail.
Answer
Is it polite or even acceptable emailing the authors of a paper you enjoyed reading?
Yes! Who doesn't like getting a compliment about work they did? Nobody, that's who. On the somewhat rare occasions it happened to me, I was delighted. And I don't think it matters how famous the author is -- trust me, no one in academia is so busy that they will not enjoy receiving fan mail.
The only caveat I would make to the above advice is that the email should be 100% genuine in its intent to express your admiration of the authors' paper and achieve no other purpose. Do not appear to have a hidden agenda or ulterior motive of any kind. Do not start telling the email recipient elaborate stories about yourself, ask leading questions about jobs or collaborations, etc., and for heaven's sake don't attach a CV. Keep it short. And please don't make up a technical question to have an "excuse" for sending the email -- in my opinion, aside from being dishonest, this runs the risk of coming up with a question that is clearly lame and inauthentic-sounding, which may spoil the whole effect. On the other hand, if you do have a genuine question, even a vague one like "that formula in section 3 is amazing, how did you think of it?", go ahead and ask it, but be considerate of the recipient's time, and make it clear that you would be extremely grateful for a reply but that you are not expecting one and that the recipient should feel free to ignore your email if they are too busy.
Here is an example of how I would go about phrasing such an email:
Subject: your awesome paper (no reply necessary)
Dear Prof. Goodpaper,
I hope you'll excuse this unsolicited email from a grad student. I recently read your paper "Traveling salesman optimizers in pseudo-logarithmic time". I'm writing to let you know that I was simply blown away by how good of a paper it is. Not only was it an incredibly clear and fun paper to read, but I was also really inspired by the clever ideas. In section 3, your definition of the class of problems solvable in pseudo-logarithmic time really captures the essence of the kind of algorithmic complexity that was previously studied only in a few special cases in the Jones-Truckey paper you cited. And your idea of taking the Mellin transform of the recurrence relation to get the asymptotic behavior of your TSP optimizer was also very inspiring -- I've never seen that trick anywhere, and was wondering how you came up with that idea. I'm currently working on a problem involving an asymptotic analysis in a graph connectedness problem that has a somewhat similar structure, so I'll definitely try to see if the same technique could apply.
Anyway, thank you again for the inspiration, and thank you for reading this. If you have any references to other papers you wrote or other books or papers by others on pseudo-logarithmic time problems that you think I should look at, I'd be very happy to hear about it. However, I realize you're very busy, so please do not feel obliged to send me anything or to reply to this email at all.
Sincerely,
[your name]
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