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This is a soft question on writing math for research or publication purposes.

When do we number an equation? Or, when should we not number an equation?

Obviously, we number equations when we wish to refer back to them at some later point. But I have observed in textbooks and many publications that the numbering seems to be inconsistent.

For example: Can anyone explain why the top two equations are not numbered, but the bottom ones are? https://arxiv.org/pdf/1201.6656.pdf enter image description here

Is there a stylistic guide as to when a equation should or should not be numbered?

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    $\begingroup$ I only number equations if I need to refer back to them. If you number every equation it can look more cluttered and it's a bit harder to find the ones you refer to. $\endgroup$
    – Jair Taylor
    Jul 18, 2017 at 1:38
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    $\begingroup$ Same here: number them when you refer to them later. If not, no point. $\endgroup$
    – Clement C.
    Jul 18, 2017 at 1:40
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    $\begingroup$ It can also be useful to number any equations that someone else may need to refer to in your paper - i.e.your main result and any possibly any notable steps along the way. That way people can refer to [StrayCat 2017, equation 12] if they need to. $\endgroup$
    – psmears
    Jul 18, 2017 at 12:42
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    $\begingroup$ I love first answer. But as a former (not talented) mathematician, you can name your equations if you are Euler or ramanujan, otherwise you just number them for further references $\endgroup$
    – Regis Portalez
    Jul 18, 2017 at 17:38

7 Answers 7

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The dominant philosophy in most mathematical writing is to only number equations that are referred back to within the paper/article/note/book, or to number particularly important equations.

In general, there are three conflicting trains of thought with respect to numbering of equations in a paper.

  1. Fisher's Rule: Number every equation, every time.
  2. Occam's Rule: Number only those equations which are referred back to.
  3. Fisher-Occam Rule: Number those equations which might be referred back to.

These rules were the subject of the article Writing in the Age of LaTeX appearing in the 1995 Notices of the AMS. But even there, some of the reasons for Fisher's Rule haven't aged particularly well.

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    $\begingroup$ I think Fisher-Occam Rule is the best if you consider it as to number all the equation that might be referred back by you or referred by others $\endgroup$
    – Dac0
    Jul 18, 2017 at 7:15
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    $\begingroup$ I agree with Dac0. And since every equation might be referred to by someone, the Fisher-Occam-Rule is basically the same as the Fisher's Rule. $\endgroup$
    – Marco13
    Jul 18, 2017 at 17:59
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    $\begingroup$ (+1) Document numbering exists to make items easier for the reader to locate. To advocate toward Occam's rule: If an author refers to a specific equation in another paper or book, they do readers a disservice if they do not reproduce that equation in their own work. (In 1995, an external reference meant a trip to the library. Nowadays it may mean only a web search, but that's already annoying if done occasionally, an impediment to reading if done frequently.) This practice of "polite self-containment" at least partly obviates the need to number equations that others might reference. $\endgroup$
    – Andrew D. Hwang
    Jul 19, 2017 at 10:28
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I try to do what the other answerers say to do: only number those equations I refer to. But on looking at the OP's sample page, another reason to number equations occurs to me: other future writers might want to refer to some juicy equation of mine, and it would do them a service to set things up so they could write "According to Kimchilover's equation (17), blah blah".

Added, 18 July: For example, in the body of the paper I say,

This and that. Clearly $$A=B$$ and so the set $S$ is bounded, proving the theorem.

The equation I don't number is $A=B$, which is referred to only by the sentence it occurs in. By the standard rule it gets no equation number. If I had foreknowledge of how important my work will be, I might say something like this in the introduction of the paper, where the problem and methods are described:

Theorem 2 then follows from the application of our Lemma 1, the Krein-Milman theorem, and the simple-looking equation (17).

And then give my faux-humble formula its number (17).

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You should only number equations that you are going to refer back. Most people are not very consistent. But now there are LaTex packages that do exactly that. See this post.

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I think that this was best expressed by physicist David Mermin in his column What's Wrong with These Equations (Physics Today, 1989):

[...]Fisher's rule is for the benefit not of the author, but the reader.

For although you, dear author, may have no need to refer in your text to the equations you therefore left unnumbered, it is presumptuous to assume the same disposition in your readers. And though you may well have acquired the solipsistic habit of writing under the assumption that you will have no readers at all, you are wrong. There is always the referee. The referee may desire to make reference to equations that you did not. Beyond that, should fortune smile upon you and others actually have occasion to mention your analysis in papers of their own, they will not think the better of you for forcing them into such locutions as "the second equation after (3.21)" or "the third unnumbered equation from the top in the left-hand column on p.2485." Even should you solipsistically choose to publish in a journal both unrefereed and unread, you might subsequently desire (just for the record) to publish an erratum, the graceful flow of which could only be ensured if you had adhered to Fisher's rule in your original manuscript.

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The reason I think is because the first two equations serve as "steps" for the third one. And so it is not as important how they got the equation, rather then the equation itself.

It's like: find $z$ such that $z = x + y$ where $x=5, y= 6$.

$$x=5$$

$$y = 6$$

$$z = x + y = 11\text{ (1.2)}$$

$z$ is the most important here, not how we got it, and so in your case, the bound is the most important, rather then the thinking that went behind it. This is my guess. I'm not sure tbh.

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If I am submitting a paper, which will undergo peer-review, I always number all of the equations. This will make the reviewing process much easier.

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From a LaTeX and physics point of view -- and this depends on the style imposed by the journal or other authority:

  • Number (almost) all display maths.
    The "almost" refers to the occasional separate equation often preceding a numbered equation (so you can refer to such steps as "in the derivation of Eq. 1.1").
  • Use display maths for anything you want to refer to, plus anything that needs it for clarity.
  • Use inline maths when display isn't really needed (this is a common journal requirement in physics).

I know there are mathematics fields in which this will work nicely; I know there are others in which it won't.

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