121
votes
Accepted
Extent of “unscientific”, and of wrong, papers in research mathematics
"Are most areas safe, or contaminated?"
Most areas are fine. Probably all important areas are fine. Mathematics is fine. The important stuff is 99.99999% likely to be fine because it has been ...
93
votes
Accepted
Math papers where the only issue is that someone else could've done it but didn't
As Sam Hopkins comments, the short answer to the stated question is "yes, all the time." You'd be hard-pressed to find a professional mathematician who hasn't received a referee report that ...
79
votes
Endless controversy about the correctness of significant papers
(Also mentioned in Oliver Nash's comment)
From a February 2017 article in Quanta Magazine called "A fight to fix geometry's foundations" (the original has relevant links in the text):
...in 2012, ...
63
votes
Obsessive editing/revising of math papers
My quick thoughts on the topic:
Most of the papers are not written carefully. Here are my major complains that apply to many (if not to most) of the papers that I have seen:
Proofs are too sketchy ...
63
votes
What about a mathematics journal for 'negative' results?
I don't really know what an answer is for a question like "what about ...?" but I have some thoughts.
In fact, way back around 2006-2007 (according to the dates on the ArXiv, see Multiplying ...
62
votes
Endless controversy about the correctness of significant papers
The Jordan curve theorem asserts that a simple continuous closed curve separates the plane into two distinct connected open sets.
Whether Camille Jordan's original proof is correct or not seems to be ...
59
votes
Accepted
The editor wrote the paper for me
[Comments combined into a community wiki answer.]
Copyright is the wrong word in this context; the correct word is authorship. A reasonable course of action is to propose to the editor that you and ...
55
votes
Accepted
Is it the referee's responsibility to verify results from arXiv preprints used in the refereed paper?
I'm going to use the word "I" in this answer since there is no universally agreed-upon standard for what a referee should do.
I feel that the referee's only job is to make an informed ...
51
votes
Accepted
Frequency of papers showing academic misconduct among the articles indexed by MathSciNet and Zentralblatt MATH
On behalf of zbMATH (which is certainly also the case for MathSciNet), we would very much appreciate a notification of such cases, if they have not yet been detected at the level of editors or ...
50
votes
Accepted
Rejection for a seemingly odd reason
When you submit to an elite journal, expect a rejection most of the time. Then submit to a less-prestigious journal. It is a waste of your time to attempt an analysis of the reasons given for ...
49
votes
What are some very important papers published in non-top journals?
The proof of the Gaussian correlation inequality by Thomas Royen was published in Far East Journal of Theoretical Statistics. This resolved a major conjecture at the interface of probability and ...
49
votes
Accepted
What to do if you notice a substantial improvement to a result in a paper whilst refereeing it?
Option (1) is definitely the professional course of action in this case. As pointed out in the remarks, it is likely to lead to an offer of co-authorship from the original author, but that is purely ...
48
votes
Publishing mathematical coincidences
There is actually the possibility for publishable research on this topic, in the context of computational complexity: How many formulas should one try for a relative accuracy of $10^{-p}$? The answer ...
48
votes
Extent of “unscientific”, and of wrong, papers in research mathematics
As Kevin Buzzard himself admits in his answer, he somewhat exaggerated his point for effect.
However, I'd submit that if you were unsettled by his talk, then that's a good thing. I don't think that ...
47
votes
On what basis does a paper get accepted into a top journal?
Here is a starting point, backed up with some data from mathscinet. My intended audience is a young mathematician who knows very little about the "top" journals.
There are five journals that ...
45
votes
Endless controversy about the correctness of significant papers
Edit: a (methodo-)logical proposal to make this thread more transparent
It can be argued that, broadly, there are three quite distinct 'types' of such controversies (and I propose that each answer in ...
45
votes
Endless controversy about the correctness of significant papers
Stanley Yao Xiao's comment has been upvoted so highly that it seems worth posting as an answer.
There is a currently unresolved controversy over Shinichi Mochizuki's claimed proof of the abc ...
43
votes
Publishing conjectures
If you have numerical evidence in support of the conjecture, the journal of Experimental Mathematics seems to fit the bill:
Experimental Mathematics publishes original papers featuring formal
...
43
votes
What percentage of published mathematics papers are correct?
This graph from Errors and Corrections in Mathematics Literature indicates about 1.4% of published mathematics papers were followed by a correction.
Corrections as percent of journal documents for ...
- 188k
41
votes
Accepted
Conjectures or Results?
The standard way is to leave the conjectures as they are, and add a remark, or a footnote, saying that "after this paper was written (or after it was submitted for publication) this conjecture ...
40
votes
Accepted
Requesting a referee's report on my paper from a math journal
No, you do not have this right. When this first happened to me (more precisely, to my student), I also was outraged and demanded a report. They replied that this is a journal policy: they decide when ...
40
votes
Publishing papers that became classics before they were submitted
Such things frequently happened to papers of William Thurston.
His opus magnum "Geometry and topology of 3-manifolds" existed as a preprint
for several decades, until a part of it was ...
39
votes
Frequency of papers showing academic misconduct among the articles indexed by MathSciNet and Zentralblatt MATH
On behalf of MathSciNet / Mathematical Reviews, I concur with Olaf Teschke that we appreciate notification of such cases. We too sense that the number of cases has increased. The majority of the ...
39
votes
Access to journals during pandemic
Some are just too shy to actually give the concrete answer, so here it is:
Sci-Hub: https://sci-hub.st
Pro-tip: Go to the WikipediA page of Sci-Hub to keep up with the new domains of Sci-Hub (since ...
38
votes
Accepted
How can I seek help in preparing a very long research article for publication?
First of all, I would consider it against the ethics of scientific publishing to accept an offer as a co-author when you were not involved in the research. So I don't think that is viable route.
What ...
37
votes
Accepted
Evaluation of the quality of research articles submitted in mathematical journals: how do they do that?
Assume we are talking about a good journal with a large editorial board representing a wide scope of mathematical interests. I will describe both the role of the editors and the role of the referees. ...
37
votes
Do empirical studies have a place in contemporary mathematics research?
You can browse the journal Experimental mathematics, which publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting ...
36
votes
Accepted
Dealing with unwanted co-authorship requests
Well, of course the young mathematician should simply discuss the
matter with the senior mathematician and perhaps the student until
they can come to an agreeable arrangement. My advice is that they
...
36
votes
Accepted
How reliable is arXiv to use as a reference in a paper?
In general it is poor scholarly practice to make a final decision about how trustworthy something is solely on the basis of where it appears, whether it's the arXiv or a published journal. As ...
36
votes
Misspelling my name on my mathematical publications
People change their names for various reasons and manage to maintain the attribution of their work. Should you decide to go with the correct spelling of your name (as I would do if it were me) then ...
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