Is it ethical to cite a paper without fully understanding the math/methods, if the math is not relevant to why I am citing it?

Question

I'm writing an article for a university assignment, and I am essentially looking for sources to support fairly surface level points. Two of the points I am searching for is evidence of diffusion models being used in the modern day, as well as how diffusion models work on a surface level.

To describe my question better, this is the paper I'm looking at in question: https://arxiv.org/abs/2209.00796

I can easily answer the above two points using the above paper. However, I cannot fully understand the equations in the paper, just the general gist of how the math works, enough to confidently know that I will not accidentally twist the authors' words.

Would it be ethical if I cited the paper?

Answer 1

Yes, it is ethical to cite the work of others when you don't completely understand it. You depend on the fact that it has been vetted by others; the reviewers who approved and possibly improved it.

But you put yourself at risk, also, by doing this. If it turns out that the original has errors that impact on your work then your work is called into question.

But some papers are correct in some ways but not in others. If you understand the parts you actually use, then you are pretty safe. But there isn't an ethical question in any case.

Note, however, that arXiv papers may not yet have much vetting, making it risky to depend on claims you don't understand. But if you use it, you have an ethical obligation to cite it.

Caveat: Knowingly reinforcing the work of cranks is a different matter. It is better for scholarship and the advance of knowledge if they aren't cited in a way implying acceptance of incorrect, especially damaging or dangerous, ideas. I doubt that is the issue here, however.

Answer 2

In my opinion, it is not a matter of ethics but a matter of peer-review and how research progresses.

As pointed in the comments to your question, there is not enough time. It is not reasonable to assume that every researcher in a quantitative field understands the details of every paper cited, since otherwise research would not progress. It takes time to understand other's ideas, but it takes even more time to develop, structure and redact your own ones. Therefore, you should only focus on key aspects that are important to be understood for your own research work.

That being said, this does not mean that you are carelessly taking any risk, because we have two powerful tools for avoiding that: peer-review and citations. With peer-reviewed papers, there is some guarantee for the content of the paper (in most cases, of course there are exceptions of bad review policies at certain conferences and journals). If the paper is not peer reviewed and just a pre-print, such as the one you link, then another good indicator for the quality of its content are the number of citations and the context in which they appear, which in your case are 52 for now.

If a paper does not meet any of the above criteria, I'd be cautious and review it myself. But this is rarely the case, specially at the level of university assignments, it can happen when doing a M.Sc. or Ph.D. thesis.

Of course, there might be exceptions to this, in my own field there was one popular paper with an algorithm available in the most relevant software packages, and 10 years later another paper came showing that the algorithm was mathematically incorrect (on a detail, but it impacted results). But those are also rarities and occur at research-level (note that another paper was needed to explain the issue, that is, an ordinary university student would not be expected to spot it).

Answer 3

Buffy's answer and caution is on point. To add one thing: one way to mitigate the risks associated with the citation is by being very precise about the citation wording. What are you citing the paper for? Often it is a simple statement that you actually need, so you can simply state exactly that. For instance:

• If the statement you need is "recently, researchers have investigated X", you can say that, and you will never be wrong :) This is very common in academic papers.

• If you need the paper for a particular finding, you can say, e.g.: "In the context of ABC, researchers found that X have an impact on Y." This is also fairly safe: you caveat that the researchers found ABC, not that it is necessarily true.

• Sometimes, you need a definitive and not qualitative statement: e.g., "we know that every Foo is a Bar, so we choose to implement only Bar..." Here you need to be really sure you are right and that your definitions match theirs.

• Finally, even if you need something definitive, there are cases where you don't actually know for sure that it is true, and sometimes you can say this. For instance: "Recently, researchers found that the effect Y is primarily due to causes A and B, though we are not aware whether this finding was due to any extraneous factors." Hedging like this doesn't look great, but if it is really impossible for you to figure out something from the earlier paper, sometimes hedging is the safest and most honest thing to do.

What's more dangerous than any of the above scenarios is if you cite for a large body of an existing paper that you haven't read: e.g. copying results tables or calculated data. Here it is generally wise to exercise caution and just replicate the result(s) yourself.

In any case, if you say exactly what you know from the paper (and nothing else), then even if (worst case scenario) the paper is later turns out to be wrong for some reason or even retracted, you won't have to change your paper at all.