[FRIAM] A question for tomorrow
lrudolph at meganet.net
lrudolph at meganet.net
Sat Apr 27 21:53:06 EDT 2019
> Thanks, Marcus.
>
> How often are proofs with errors published in refereed articles or
> textbooks?
Some years ago, when you guys in Santa Fe were reading Ruben Hersh's "18
Unconventional Essays on the Nature of Mathematics", I took the
opportunity to download a copy for myself. Assuming you(-all) still have
your copies too, I recommend that you read (or reread) the
philosopher-of-mathematics Jody Azzouni's chapter, "How and why
mathematics is unique as a social practice", where he elaborates an idea
he calls "the benign fixation of mathematical practice". Here's a brief
passage from that chapter (asterisks indicate italicized matter):
===begin===
Lets turn to the second (*unnoticed*) way that mathematics
*shockingly* differs from other group practices. *Mistakes are ubiquitous
in mathematics.* [...] What makes mathematics difficult is (1) that its
*so easy* to blunder in; and (2) that its *so easy* for others (or
oneself) to see
when theyre pointed outthat blunders have been made. (pp. 204 and 205
of Hersh's book)
===end===
If the claims in that passage are true (and they ring true to me), then
even the informal refereeing (from colleagues, friends, or students) to
which a proposed proof is subjected at the blackboard or in pre-print form
is likely to turn up mistakes, and even less-than-diligent formal
refereeing to which a proof submitted for publication is subjected most of
the time, are likely to lead to corrections before eventual publication;
and if errors persist (as they often do), then unless the publication goes
unread (as many do...) they too will likely be corrected, eventually.
None of this quantifies the "how often" question, but it is consistent
with the general consensus "not often (but sometimes), and eventually
corrected (unless no one gives a good goddamn about the result)".
For more on this, read the chapter by me at the following link (I may have
sent the list, or some subset of it, this chapter once before; sorry about
that), which (incidentally relevant to an earlier subthread) has a
footnote mentioning computations with unreliable oracles.
https://clarkuedu-my.sharepoint.com/personal/lrudolph_clarku_edu/_layouts/15/onedrive.aspx?id=%2Fpersonal%2Flrudolph%5Fclarku%5Fedu%2FDocuments%2Flogics%5Ffor%5Farxiv%2Epdf&parent=%2Fpersonal%2Flrudolph%5Fclarku%5Fedu%2FDocuments&cid=2d17a63c-3b2f-4b08-ada5-7f384570ef5a
More information about the Friam
mailing list