1

Given this question of mine I wondered: If one wants to publish a new result which

  • one couldn't find any information where the result could have possibly been covered (and neither could one's friends and colleagues) and
  • is part of a topic that is so rich on literature that it is absolutely impossible to read it all,

how can one write about this result without assuming that it never has been covered and without expressing one's own inability to find the literature in question?

Example: I think that both formulations

This result wasn't explicitly stated before.

and

The authors couldn't find any material covering the result.

sound unprofessional.

  • Isn't this a good reason for peer review? Maybe this a good question for Academia.SE – Carlo Mar 17 '18 at 22:23
  • @bumpy I decided for writing instead because I was looking for a formulation. – SK19 Mar 18 '18 at 3:04
  • Do you really need to state it at all? Doesn't the very fact that you want to publish the result already imply it? – celtschk Mar 18 '18 at 21:36
3

I don't know much about mathematics, but in the natural sciences you perform an in-depth research in the publication databases of your field. Just looking at textbooks is not sufficient for a peer-reviewed publication. (Apparently I don't know what a "MIZAR article" is, so your requirements may differ.)

If you find any publications that are in any way related to your own research, you report it (if there is much you summarize key publications). Even if what you study hasn't been studied before (and you therefore find "nothing" on that topic), probably some areas related to it have been studied, so you report those related publications both as an introduction for why you study what you study and in an attempt to deduce plausible hypotheses for your own research. The natural sciences commonly attempt to falsify hypotheses, and post-hoc "data dredging" is strongly discouraged, so natural scientists always begin by reporting the current status quo in their field before they derive their research questions and experimental design from this.

Similarly, I guess you would put the question you attempt to answer with your publication in the context of the existing mathematical theories. You wouldn't just begin your text with: "Any graph drawable by hand (i.e. with finitely many vertices and edges) actually exists mathematically", and then write out your proof. You will begin with explaining why this problem is relevant and needs to be addressed at all, and where you got the idea for your solution to the problem.

In the natural sciences, there is a type of article called a "meta analysis". This type of study does not report the outcome of an experiment by its authors, but rather collects, analyses, and summarily reports all (available) studies on a specific topic. Since it is usually impossible for anyone to find everything every written on a topic, the authors of a meta analysis report what kind of literature search they performed. Usually they will state which databases they queried, which terms they used, how many results were returned, and how many of those were relevant and how many were excluded and for what reasons.

Similarly, if you really find nothing of relevance, you could briefly (i.e. in a few sentences) describe where you searched and how. That way, any reader can perform the same search – or know where you failed to search.

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