There is an interesting discussion taking place at MO over the suitability of this question: Complex structure on $S^6$ gets published in Journ. Math. Phys. The question is about the correctness of a paper that has recently appeared in a peer-reviewed journal, purporting to settle a long-standing open problem regarding existence of a complex structure on the 6-dimensional sphere $S^6$.
The basic question here is whether the community thinks this type of question could be suitable for MO, but a subsidiary consideration is how to edit this particular question to remove at least some of the features that some commenters found objectionable. Namely, they found the question brusque and somewhat confrontational or less than respectful to the paper's author. Let me then take a crack at rewording the question:
A paper purporting to solve a major open problem has recently appeared:
- Gabor Etesi, Complex structure on the six dimensional sphere from a spontaneous symmetry breaking, Journ. Math. Phys. 56, 043508-1-043508-21 (2015). Link: http://arxiv.org/abs/math/0505634
An earlier preprint by this author on this topic, http://arxiv.org/abs/math/0505634 (now 10 years old), had some problems [insert specific criticisms here]. My question is whether these difficulties have been satisfactorily addressed in the current paper, and if so, whether this paper has indeed answered this outstanding question (whether a complex structure on $S^6$ exists).
This rewording could perhaps be improved, but the idea would be to try and pinpoint the specific mathematical considerations within the body of the question, and do so in a more or less polite and decorous way.
Onto the more general question: personally, I'm somewhat torn. We've generally declared to would-be solvers of the Riemann Hypothesis (etc.) that MathOverflow is not to be used as a vetting service, and that certainly seems like wise policy to me. Some users (I'll quote Joseph O'Rourke in his comment) take it a little further and say "It is inappropriate to discuss the flaws in a paper in a public forum." Other commenters seem perplexed by this stance.
I'd like to hear more discussion on this. I can definitely see that we do not want to be in the business of raking people over the coals, whether they be cranks or serious researchers. But if we manage to take the personal element out of it and get straight down to the business of pinpointing really specific mathematical difficulties encountered in peer-reviewed published papers, it's hard for me to think of really convincing counterarguments. Anyway, what do you think about this?
Last I checked there are three votes to reopen, so maybe it's good to discuss this openly here.
Oh, by the way: what about Community Wiki? There's another closely related question Is there a complex structure on the 6-sphere? which mentions the same paper that is CW. (I think one could argue that a suitably reworded question with specific mathematical content would not be a duplicate.)