> 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 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
