TITLE: When should an equation be numbered when writing a paper?
QUESTION [38 upvotes]: 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

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

REPLY [9 votes]: 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.