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I have read that references in scientific papers should be no more than 2-3 years old, since such fields move fast, and no more than 10 years for arts or related fields:

A good rule of thumb is to use sources published in the past 10 years
for research in the arts, humanities, literature, history, etc.

For faster-paced fields, sources published in the past 2-3 years is a
good benchmark since these sources are more current and reflect the
newest discoveries, theories, processes, or best practices.

However, I believe that's subjective, so how old is it for a reference to be "too old" to cite?

References can be as old as they need to be to cover the material. I had some that were more than 30 years old. But if all of your references are "old," people are going to want to know why.

You must also be sure you cover the most current research in your field. A few in my own dissertation were for material published in the same year as my own work.

The link given in the comments and the revised question seems to be directed toward undergraduate research assignments, and the "ten years" reference is a part of an example assignment, not a requirement given by the Shapiro Library. The key idea in the link is that references must be "somewhat current."

For a thesis or dissertation, one must cover the field, including both early and very new research.

There is no rule about the age of citations. For example in my PhD-thesis I quoted some math-papers from 1600s that were originally written in latin (but those were exceptions).

Much more relavant than the year is the content of a citation and that you cover the relevant literature.

Also, you might want to include a few (relevant!) citations from recent years in order to show that you did your reading not just at the beginning of your thesis and then ignored everything afterwards.

A group of researchers published this very interesting paper:

The nearly universal link between the age of past knowledge and tomorrow’s breakthroughs in science and technology: The hotspot

From a pure data science perspective, they try to understand how the distribution of reference age affects the forward citations of an article. They analyze all publications (~ 28 million) in Web of Science published between 1945 - 2013.

Unfortunately, they do not show an aggregated histogram of age differences between a publication and its references. But in Fig. 1 we see the mean (0-50 years) and variance (0-4) for all published papers and it is all over the place. So the take away might be to cite what you want.

However, they echo in their paper the comments and answers that you got here. Impactful and hopefully good research seems to differ from the "cite what you want" approach. If you want to increase the likelihood of your work having an impact you should base your work on recent advances but also be aware of well-established theories or overlooked ideas from the past. They show this in the paper by finding a hotspot of highly cited papers that have a low mean age distance to their references but a high variance in age distance.

Here is a link to the paper (super interesting):
http://advances.sciencemag.org/content/advances/3/4/e1601315.full.pdf

Your rule has a large fraction of exception that you should always consider. Make sure you cite the relevant papers for your claims and that you cite the papers which were the first introducing the idea. Don't cite a textbook for ideas just because they are recent. Instead, try to find and cite the original works.

If you cite an idea originating back to Aristoteles it does not make sense to use a recent source. The idea is that old! Also, if you want to prove your claim, that some method was used in the 70s, it's useful to cite papers written in the 70s.

There's no limit on how old they can be. In biology people often cite Darwin (1859) and geneticists who work on pedigrees can cite government records from hundreds of years ago. Work involving theology may cite the Bible. Historians cite original documents from thousands of years ago. Sometimes a fun game is to see what the oldest citation you can get away with is. Plato or Aristotle is often a safe bet.

Generally, you are supposed to cite the oldest paper that made a discovery, as the credit belongs to them. When in doubt, you can cite one old and one new paper.

However, your work must be in the context of contemporary scientific literature. If you cite a 50 year old paper for a theory, you better make sure the theory has not been disproven in another paper published 30 years after. If you say the state of the art in a field is a paper published 10 years ago, it would look really bad if somebody brought up a 5 year old paper that advanced it further. This is why citing old material is risky: You can't easily tell that it's still current. If a paper came out last monday, chances are pretty low that somebody refuted it in that time.