Fred wrote: << Anyone who has attempted seriously to program mathematical algorithms for computer [an activity almost co-extensive with theorem- proving] will be aware of the pleasurable momentary surge of astonishment when a progam of --- say --- ten lines or so apparently works at the first attempt; not to mention the familiar incredulous frustration when closer investigation establishes that it in practice still fails to do after the tenth. It follows that any proof published at the research level is almost certainly technically incorrect --- even discounting failures at the "typographical" level, which might be dismissed as amenable to an informed reader's error-correction facility. A less obvious consequence involves the observable inherent reluctance on the part of most readers to accept that a purported proof is fallacious, particularly once it has been digested and (unconsciously) accepted.
Very interesting hypothesis! But I can't agree. Most published math papers I've seen are flawless (proofwise, not exposition-wise). There still remain a significant number of errors, but having done a lot of both theorem-proving and computer programming, I feel it's far easier for a programming error to hang around a long time than a math error. The math error will introduce a contradiction somewhere (even if it leads to a flawed proof of a true theorem), so is ultimately untenable. The programming error may be what I call Type 3: (it compiles, it runs, but it doesn't do what you wanted). Such a program actually exists in the real world, so no contradiction is involved. There may be no way to learn anytime soon whether its output is right or not. There are a few famous cases of math errors hanging around for many years (e.g., Kempe's attack on the 4-color theorem was believed for 11 years; part of Hilbert's 16th Problem problem (Dulac claimed to prove that any planar polynomial vector field has only finitely many limit cycles; a flaw was found 58 years later. (In 1988 it was finally proved.) But the reason these are famous is that they are extremely rare. A published math error, in a field within the mainstream, will usually be spotted fairly soon by experts in the field, especially now that dissemination of papers via the arXiv works so well. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele