This is more of a thought experiment than a problem. I just want to know how ethical is it.

Suppose a student discovered a very cool theorem/result that would yield a very good academic paper in a very good journal. But the student know that the admission to the graduate program in his country is based only on a written test (which they are expected to ace), so publishing now will not be beneficial. So, is it ethical for him to save the paper for the rainy day in the future by publishing it under a pseudonym (hence the world will not miss out on the knowledge)?

A generalized version of this problem would if you are overproductive in a certain year, then is it ethical to anonymize the production above the bare minimum and use it in the future when you are going through a lean phase?

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    I don't get it. How do you intend to save a paper for future by publishing it under a pseudonym? You want to publish it later again under your real name? That would be unethical, autoplagiarism and scientific misconduct. You can just not publish it for the time being, sure. And what does studying to a test have to do with anything of this? – user68958 Oct 6 '19 at 11:09
  • Publishing under an anonymous name is appalling ethics. Imagine if that was possible. It is bad enough the fakenews sites. The amount of anonymous submissions would be appalling. – Poidah Oct 6 '19 at 11:46
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    We already have a question on the ethics of pseudonyms in general, see academia.stackexchange.com/questions/5408/…. @Poidah, I guess I would say that not everyone agrees with you. – Nate Eldredge Oct 6 '19 at 13:06
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    In mathematics where there can be minimal or little consequences of the discovery can be is very different from cancer research or research into health, where lives can be at stake. Saving it for a lean phase seems silly especially when theorems are unlikely to have any discernable impact. Publish it later runs the risk of the theorem being published by others rather than world "missing out on the knowledge". – Poidah Oct 6 '19 at 16:49

Pseudonymous publication, while unusual, is not particularly problematic from an ethical perspective. A famous example is Nicolas Bourbaki, a highly influential mathematician who never existed. Anonymous publication is more problematic, because then there is nobody taking responsibility for a work.

The practical value of your proposal, however, seems dubious at best. You cannot time-shift a publication by claiming it later: all that you would be doing is adding the publication to your past.

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    Actually, Bourbaki is a group, not an individual. – Buffy Oct 6 '19 at 12:04
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    @Buffy Of course: and because the group assumed a single pseudonymous identity, that's consistent with what I have written. – jakebeal Oct 6 '19 at 12:11
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    There are more pseudonym examples at mathoverflow.net/questions/45185/…. It's a long and distinguished list. – Nate Eldredge Oct 6 '19 at 13:04

I see no ethical issues here, you can do what you like when you like with your ideas.

The only issues are practical. No "very good journal" would publish an anonymous or pseudonymous paper such as this. They require a real corresponding author who literally puts their name to the work and who can answer comments, criticisms, etc. Also, I don't see how publishing it without your name will bring you any future benefits.

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