Paper A is in the literature, and has been for more than a decade.
An error is discovered in paper A and is substantial in that many
details are affected, although certain fundamental properties
claimed by the theorems are not. (As a poor analogue, it would be
like showing that certain solutions to the Navier-Stokes equations
had different local properties than what were claimed, but that the
global properties were not affected. The error is not of the same
caliber as Russell's correction of Frege's work in logic.)
The author is notified, who kindly acknowledges the error.
Now what?
Should the remaining action lie fully on the author, or should
the discoverer of the error do more, such as contact the journal,
or publish his own correction to paper? How long should one
wait before suitable action is taken? And what would be
suitable action if not done by the author?
Based on remarks from those who previewed this question
on meta.mathoverflow, I propose the following
Taxonomy: There are various kinds of error
that could be considered.
-
typographical – An error where a change of a character or a
word would render the portion of the paper correct. In some
cases, the context will provide enough redundancy that the
error can be easily fixed by the reader. Addressing these
errors by errata lists and other means have their importance,
but handling those properly is meant for another question. -
slip – (This version is slightly different from the
source; cf the discussion on meta for the source
http://mathoverflow.tqft.net/discussion/493/how-do-i-fix-someones-published-error/ )
This is an error in a proof which may be corrected, although
not obviously so. In a slip, the claimed main theorem is either
true or can be rescued with little cost. In my opinion, the degree
of response is proportional to the amount of effort needed to fix it
(and is often minor),
but there may be slips major enough to warrant the questions above. -
miscalculation – Often a sign or quantity error. In some cases
the results are minor, and lead to better or worse results
depending on the calculation. I've included some miscalculations
in some of my work to see if anyone would catch them. I've
also prepared a response which shows the right calculation and
still supports the main claims of the work. (See below on
impact as a factor.) -
oversight or omission – This is stating a fact as true without
sufficient folklore to back up that fact. In some cases the
author doesn't include the backup to ease (the reading of) the
paper and because the author thinks the audience can provide
such backup. More seriously,
the omission occurs because the author thought the fact was
true and that there was an easy proof, when actually the fact
may or may not be a fact and the author actually had a faulty
argument leading him to think it true. -
major blunder – This is claiming a result which is true,
and turns out not to be true in a socially accepted proof
system. Proofs of Euclid's fifth postulate from the other
four fall into this type.
The above taxonomy is suggested to help determine the type
of response to be made by the discoverer. Also, degree of
severity is probably not capable of objective measure, but
that doesn't stop one from trying. However, there are at
least two other considerations:
-
Degree to which other theorems (even from other papers)
depend on the error in the result. I call this impact. -
Degree to which the error is known in the community.
The case that inspired this question falls, in my mind,
into the category of a miscalculation that invalidates a
proposition and several results in paper A following from
the proposition. However, as I alluded to above in the
Navier-Stokes analogy, the corrected results have the same
character as the erroneous results. I would walk on a
bridge that was built using the general characteristics of
the results, and not walk on a bridge that needed the
specific results. In this case, I do not know to what
degree impact the miscalculation has on other papers, nor
how well known this miscalculation is in the community.
If someone thinks they know what area of mathematics my case
lies (and are sufficiently experienced in the area), and they
are willing to keep
information confidential, I am willing to provide more
detail in private. Otherwise, in your responses, I ask that no
confidentiality be broken, and that no names be used
unless to cite instances that are already well-enough
known that revealing the names here will do no harm. Also,
please include some idea of the three factors listed
above (error type, impact on other results, community awareness),
as well as other contributing factors.
This feels like a community-wiki question. Please, one
response/case per answer. And do no harm.
Motivation: Why do I care about fixing someone else's error?
Partly, it adds to my sense of self-worth that I made a
contribution, even if the contribution has no originality.
Partly, I want to make sure that no one suffers from the
mistake. Partly, I want to bring attention to that area
of mathematics and encourage others to contribute. Mostly
though, it just makes an empty feeling when one reaches
the "Now What?" stage mentioned above. Feel free to
include emotional impact, muted sufficiently for civil
discourse.
Gerhard "Ask Me About System Design" Paseman, 2010.07.10
Best Answer
Some advice explicitly directed at less senior people. I would very much advise some who does not yet have tenure to NOT take the nuclear option (e.g. posting a paper on the arXiv accusing someone of being wrong, or writing irate letters to the editors of a journal). In the extremely rare cases in which this has to be done, it is best done by someone who is both pretty senior and very politically skilled. This leads me to my other piece of advice. Namely, talk to other, more senior people in your research area. First, they might be able to convince you that it isn't really as serious an error as you think. Second, they will probably know the personalities involved better, and be more effective at convincing an author to do the right thing if something has to be done.
The two times something like has happened to me, I had ended up proving stronger results than the erroneous papers by pretty different techniques. I buried remarks at the ends of the introductions of my papers mentioning the wrong papers and explaining where they went wrong. On one of those occasions the author had left math and I didn't know how to contact him, so I didn't correspond with him first (after I posted the paper the arXiv, one of his friends contacted him and we exchanged some friendly emails). The other time, I explicitly cleared the language I used with the original author.