Papers on ArXiv as main references

Question

I am going to prepare a math research paper and one of my main and necessary references is an article on ArXiv. I do not know whether I continue to prepare my article or not. Since I have doubt with ArXivian papers and I think it is not good choice arxiv papers as a main part of a research work.

Answer 1

In my experience, it is common and acceptable for papers in mathematics to rely on arxiv preprints. While there may be something in the idea that if you have a choice, it is better to rely on peer-reviewed publication, if the choice is to use an arxiv preprint or delay the publication of your paper, almost certainly you should use the preprint.

To go a little deeper: the imprimatur carried by a peer reviewed publication is partially real but mostly cultural. Most veteran mathematicians can point to any number of published papers with (sometimes serious) mistakes and also can point to papers of theirs that were accepted by reputable (or strong, or top) journals with so little commentary that they cannot have any confidence that the referee checked the results for correctness in any serious sense. (Note to academics in other fields: I said "referee," not "referees." In pure mathematics the most common number of referees for a paper is one.)

Whenever your work uses others' results, you have to perform some process of evaluating those results. Ideally that would include a careful checking of the proof, but to be honest that is not always practical or possible. (Sometimes you need a result whose proof uses ideas and techniques that would take you months or years of work to understand.) To be honest, the evaluation process is often cultural as well as intellectual, and this is why it can indeed be a little better to rely on a published work: whether someone read the proof carefully or not, at least it is likely that expert eyes evaluated the work for plausibility.

There are ways to evaluate an arxiv preprint for plausibility without reading it line by line:

• Look up the authors. Have they published similar results before? Have their prior results been used by others?
• Does the paper look professional? Is it clearly written?
• Is it reasonable that one could attain the given results with the given techniques?
• Do the results used appear to be a major breakthrough? In that case, you should probably talk to others about the preprint quickly: if it's correct, then likely many other mathematicians are making use of it, possibly the same way you are, and by waiting for publication you could be losing everything. But also it's more likely to to be wrong. (Sorry to say: all other things being equal, the better result is more likely to be wrong.) You don't want to waste your time building on a foundation that evaporates later.

Finally, yes it is possible that if you submit your paper for publication, the referee could say "Well, I don't know about this arxiv preprint, and I don't care to referee it too. You'll have to wait until the preprint is published." Well, referees say the darnedest things. It is still better to have tried.