Abstract
Generally, a referee has to make one of the following recommendations:
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Publish essentially as is; the only changes necessary are very simple typographical matters which can be changed by the editor.
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Publish after author’s minor revision; the referee suggests points which must be changed before the paper meets the standards for publication.
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Publish only if the author makes major revisions. (Perhaps the paper is much too long or is badly written. The revised paper will be refereed again.)
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Reject. (There is nothing salvageable.)
These ‘Hints for Referees’ [1, p.36] are all very well, but one might wonder just how to distinguish. So Don Knuth reminds referees that to be publishable:
a. The paper should contribute to the state of the art and/or should be a good expository paper. If it is purely expository it should be clearly designated as such.
b. All technical material must be accurate. A referee should check this carefully.
c. The article must be understandable, readable, and written in good English style.
d. The bibliography should be adequate.
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References
Knuth, D.E., Larrabee, T., Roberts, P.M.: Mathematical Writing. MAA Notes Number. Mathematical Association of America 14 (1989)
Kuperberg, G.: Scholarly mathematical communications at a crossroads. Nieuw Arch. Wisk. 3(5), 262–264 (2002); arXiv:math.HO/0210144
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van der Poorten, A.J. (2003). Peer Refereeing ...Will It Be Missed?. In: Bai, F., Wegner, B. (eds) Electronic Information and Communication in Mathematics. ICM 2002. Lecture Notes in Computer Science, vol 2730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45155-6_14
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