Citing different papers which use different notation for the same concept,

Not sure if this is the place to ask about this. But for lack of knowledge of a better resource, I turn here.

When citing papers which use the different notation for the same model, is it better to leave the notation as is when citing each source, or, to retain consistency conform to one notation?

If I were to conform to one notation, does the more recent source take priority when choosing notation or the earlier source? Additionally how would it be formatted when quoting the source with the altered notation?

• It is hard to answer in a vacuum. Most professional researchers in math and related areas are used to dealing with inter-paper notational inconsistencies. Drawing attention to it might be distracting. On the other hand, if there is something about the case that makes misunderstanding likely, by all means point it out. Commented Mar 13, 2018 at 13:02

This probably varies between fields, but in my field, mathematics, what I"d do is to explain the notation that I want to use and then express other people's results in that notation. I'd probably say something like "XXX proved [citation] a theorem that, in the notation explained above, says YYY."

• A phrase that is appealing to me is "In the language of X, the result of Y can be stated as follows:..." Commented Mar 13, 2018 at 13:02
• Here are some various choices of wording I've used in the past: "In 1968, Littlewood wrote that '[direct quote]' (but note that his n is our n+1)." "A 1986 conjecture of Boyd, translated into our notation, speculates that mu grows like the square root of n." Commented Mar 13, 2018 at 14:53

When citing papers which use the different notation for the same model, is it better to leave the notation as is when citing each source, or, to retain consistency conform to one notation?

It is extremely important to maintain notational consistency within your own paper; never double-up on notation or give inconsistent notation within your paper. As to where your notation should come from, as a general principle, you should use whatever notation is easiest for the reader, whether this is taken from another paper, or your own adaptation or invention.

Bear in mind that established fields tend to have notational conventions that people are used to, so if there are symbols commonly used for particular objects, it is generally best to use these unless there is a good reason to the contrary. When notational conventions from multiple fields conflict (e.g., you are doing a paper on random matrices, and the capitalisation conventions for probability conflict with the capitalisation conventions for linear algebra) you will need to make judgments as to what is easiest for the reader.

If I were to conform to one notation, does the more recent source take priority when choosing notation or the earlier source? Additionally how would it be formatted when quoting the source with the altered notation?

There is no temporal priority rule for notation, but bear in mind that if a new notation is sufficiently well-established, it may constitute the current notational convention (check multiple papers for this, not just one newer one). When quoting a result from another paper, in your own altered notation, you should add some parenthetic remark to make the reader aware of the change:

Example: Wilbur (2009) notes that "...if A and B are engaged in exclusive contractual negotiations, and C interferes with this process, causing economic harm to B, then C could be liable for tortious interference" (p. 85, notation altered).

• This is a great answer and it works quite well for algorithms as well. In my MSc thesis I had to cite a paper proposing a very efficient (but cumbersome) C code. "Decompiling" it into pseudo-code made it a lot clearer. Commented Mar 13, 2018 at 23:09

is it better to leave the notation as is... or to conform to one notation?

1. Mention both notations once (one in a clearly-marked definition, the other right next to it/after it).
2. Choose one, and explicitly state which one you've chosen (and perhaps even why you've chosen it, if it matters).
3. Use your chosen notation consistently throughout the paper.

That's what I would like best as a reader.

Try to cite the paper with the notation you want to use first and introduce the use of the notation like "following the notation of X, we define ...".

If the papers are very different, you may point the reader to the differences: "In contrast to X, Y defined `A_k` using the Foo operator. Following theorem Z the equivalence can be proven". It is up to the reader to see how the equivalency follows of if he just believes you and reads on. For smaller differences you may mention them (note that Y is using Einstein notation in theorem Z).

When citing formulas make sure to use the same notation. If they look too different you may include them in the other notation and mention "Theorem Z from Y restated in the notation of X", but in the end the reader should be able to follow your notation and you only follow other notations yourself to keep it similar to what the reader already knows.