'Rashomon' - A Mathematical Parody
And everyone has different story to tell - the wife, the bandit,... and the dead Samurai's spirit...
The core facts: Some time back, an article presenting a conjecture and a proposing a partial resolution thereof was submitted to a popular Mathematical journal. That set in motion a 'process' which has lasted several months ....
A somewhat old version of the article may be seen here:
Here I record what people had to say - A Reviewer for the Journal, the Spirit of the Article (aka the Authors), and three Witnesses, all with substantial academic standing and who are up-to-date with everything that has happened to the article.
1. The authors prove only N=2 of the conjecture. The rest of this long paper has only false starts and incomplete investigations - more than 20 pages worth!
2. The authors write in a choppy style, breaking up the flow with multiple 'observations'; the writing is verbose and uses phrases like 'thought construction', 'proposed proof' etc.. which indicate they are not sure about what they are talking about!
3. There are far too many numerical investigations rather than tight and elegant writing.
Summing up: The article is not suitable at all for publication.
The Spirit (responding to above comments in order):
1. The reviewer has got even basic facts wrong - apart from the obvious N=2 case, the article contains a complete proof for N=4 with indications of how to generalize it even further. There are a couple of other complete results as well. Yes, we also show how and why some 'standard' approaches to the problem won't work. These are not 'false starts' or whatever but examples which describe the *context* of the problem and show how difficult it is.
2. The numbered 'observations' are not breaks in the flow of some liquid but *steps* building towards the proof. It does not take an Einstein to recognize this, if one has read it with a minimum of sense that is. And if non-standard terminology is so irritating, there are but 2-3 instances and five minutes worth of editing would have cleaned them up.
3. The numerical investigations are there not for the heck of it but to show concrete examples. If they really got his goat for whatever reason, the reviewer could have asked for them to be compressed or deleted. And some seriously analytical thinking will still remain.
Summing up: The reviewer has not bothered to evaluate the main proof we presented (N=4) - indeed the very core of the article has been just ignored - and has gone strictly by peripheral stylistic considerations. His main concerns could have been taken care of with a 2 day rewrite/editing but he has projected these irritants as sufficient grounds to summarily reject our work - without appeal. The fellow has not only made snide remarks on our work but made factually incorrect (indeed we would say, untruthful) observations about the article.
It was unfortunate that the article got rejected. The numerical examples seem to have been a major irritant. And maybe the length. I was worried about these factors myself but also quite hopeful that the article would be still accepted, for it really had some serious substance. The reviewer certainly did not do his job properly.
But that said, I would suggest that the authors write the article afresh, get rid of all those numbers and leave out some side-investigations and maybe tighten up the presentation of the N=4 proof... Then it should stand a better chance with some other journal.
A general point: The article appears to use a lot of intuitive, visual arguments. Some rigorous tightening on that front could help.
I did not think the article was bad at all. Yes, it was on the longer side, and had a rambling, notes-to-myself feel; but to me, these are not fatal defects. Yes, things were not presented strictly canonically but the journal in question too had said they accept and encourage unconventional/speculative stuff. The reviewer could have commented, rather should have commented on the logical content but he probably had other ideas...
Anyways, I would suggest that the authors take the reviewer's suggestions seriously, tighten up the terminology. And yes, cut the length at least by 60 percent, perhaps by leaving out those numerical examples and submit somewhere else. The full article could of course be kept online as a further reference to those who want the details.
I was sure the article would be rejected; and I am not surprised there has been no further review - indeed I think it was an easy decision for the reviewer, in terms of the style as well as the content. Unless one writes Mathematics rigorously, it won't be read. Reviewers do their work as some sort of voluntary service to the community - they are not even paid for it. And the reviewer won't read the article fully unless the writing is rigorous. And it is the writers job to impress him and to keep him interested, else the logic or whatever simply won't be evaluated.
As for the content, an article has to have at least a couple of solid results; just a conjecture is not really good enough, since there are hundreds of conjectures all over the place. And even using the word 'conjecture' is shaky here; what has been presented is more of an interesting problem than a proper conjecture - indeed, there does not appear to be enough intuition in the work to really float a serious conjecture.
Anyways, I shall try to read the article and give some specific inputs as to how the writing could be improved....
(continuing after a week)
The article is absolutely unreadable; no mathematician will read it and no serious journal publish it. This may sound harsh but that is the fact of the matter.
And here is what another Witness had to say the other day:
"I saw the article about 2 months back and read the initial few pages, maybe 2 or 3 pages.... yes, I had an impression then ... rather, I remember forming a general impression then, that the article was a piece of bad writing. I can't recollect anything more!"
And I sign off with a quote, the source of which I won't reveal: "The pressure for conformity is enormous. I have experienced it in editors’ rejection of submitted papers, based on venomous criticism of anonymous referees. The replacement of impartial reviewing by idiotic censorship will be the death of science."