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Let's say I have been studying an older theorem statement and its proof. I feel that it can be improved, e.g., I can make it a stronger double-implication theorem statement, with a different proof. Would I still need to cite the paper from which I first studied the theorem? Even though my work is completely organic and self-contained?

Thanks,

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    $\begingroup$ Wouldn't hurt to mention it as context to what you are improving. $\endgroup$ – gowrath Sep 29 '16 at 1:39
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    $\begingroup$ Yes, you need to cite it. If it's at all possible even to make a weak argument as to why you should cite something, you probably should be citing it. I know where you're coming from though. $\endgroup$ – Matt Samuel Sep 29 '16 at 1:40
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    $\begingroup$ @MattSamuel: Sounds a bit extreme? Should I cite Leibniz whenever I use the chain rule for derivatives too? After all that's why he invented the notation... $\endgroup$ – Mehrdad Sep 29 '16 at 6:41
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    $\begingroup$ @Mehrdad Wouldn't you cite Leibniz if you claimed a novel, improved chain rule and proof thereof? The question here was not about mere usage, but rather building upon. $\endgroup$ – dxiv Sep 29 '16 at 7:12
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    $\begingroup$ Especially with search engines nowadays, a reader of the old paper would be able to find your improvement by looking for papers that cite the old paper. $\endgroup$ – RemcoGerlich Sep 29 '16 at 8:41
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I've done everything in my research completely from scratch. I require no outside results to prove my theorems (I'm writing a blog about this, mostly because I don't have time to write papers; here is a link to the blog). My methods are new and almost unrecognizable if you're coming from the classical theory. But obviously I didn't come up with these things in a vacuum, and I searched and there have been others with very similar ideas. I read lots of stuff and synthesized it into new stuff that does the same thing but a little bit better. This is what every researcher does to one extent or another. Would you even have thought of this if you hadn't seen the past result? Probably not. So give them credit!

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    $\begingroup$ Thanks so much @MattSamuel, especially for noting that, "this is what every researcher does to one extent or another." $\endgroup$ – User001 Sep 29 '16 at 2:45
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    $\begingroup$ @user58865 No problem. $\endgroup$ – Matt Samuel Sep 29 '16 at 2:47
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    $\begingroup$ That edges with self-advertising already! :) $\endgroup$ – dbanet Sep 29 '16 at 17:53
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Adding this only because I think the point wasn't emphasized enough in the other answers, but it may actually hurt the credibility - or, at least, the perceived professionalism - of your paper if you did not cite the old result. An important part of research is to establish context and relevance, and anyone who happens to know or find the old result might (wrongly) conclude that you didn't carry out that part as expected if you didn't cite the prior work.

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    $\begingroup$ Notably, Einstein's relativity publications were extremely light on relevant citations, and one result of that has been historical controversy that continues to this day. $\endgroup$ – bright-star Sep 29 '16 at 14:55
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    $\begingroup$ I probably should've mentioned this in my answer, but having it in yours is just as useful, right? $\endgroup$ – Matt Samuel Sep 29 '16 at 16:37
  • $\begingroup$ @MattSamuel One could read it between the lines in your answer, too, but I thought it's worth having it spelled out loud and clear. $\endgroup$ – dxiv Sep 29 '16 at 17:23
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I'm not 100% sure, but you should always cite something if you can. If it inspired your result, you should be citing it.

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