Comments on: Errors in math papers not a big deal? http://www.johndcook.com/blog/2008/11/11/errors-in-math-papers-not-a-big-deal/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Daniel Lemire http://www.johndcook.com/blog/2008/11/11/errors-in-math-papers-not-a-big-deal/comment-page-1/#comment-9323 Daniel Lemire Fri, 14 Nov 2008 01:15:01 +0000 http://www.johndcook.com/blog/?p=843#comment-9323 Excellent post. If I might add something: software can help debug math, and vice versa. 1) Sometimes, you can determine mathematical some expectations software must meet. Are you using up n^3 time to merge sort an array? Something is wrong. 2) [More interesting] Do you claim that a given quantity grows as "1.4 * x^2"? Then let me see a plot generated from a computer simulation. You can't simulate it? Really? Excellent post.

If I might add something: software can help debug math, and vice versa.

1) Sometimes, you can determine mathematical some expectations software must meet. Are you using up n^3 time to merge sort an array? Something is wrong.

2) [More interesting] Do you claim that a given quantity grows as “1.4 * x^2″? Then let me see a plot generated from a computer simulation. You can’t simulate it? Really?

]]> By: John Venier http://www.johndcook.com/blog/2008/11/11/errors-in-math-papers-not-a-big-deal/comment-page-1/#comment-9243 John Venier Tue, 11 Nov 2008 17:19:51 +0000 http://www.johndcook.com/blog/?p=843#comment-9243 I'd add the qualification that for well-used software to have fewer bugs the users must recognize the bugs and they must be fixed when recognized. Neither of those are certain, and in the case of close-source software the latter depends on users reporting the bugs and the source owners' fixing them. I suspect a lot of the bugs in published math are rarely recognized and when recognized are not necessarily reported to the author. For cases where the bugs are obvious but no one bothers to report them, think about popular literature -- extremely well read, but often full of unintentional spelling and grammar errors. Actually, spelling and grammar errors are extremely common in the electronic realm, even in situations where they are read extensively. Even news reporting agencies frequently have such errors, but I doubt they are often reported -- most readers ignore them if they even catch them. You might argue that this is not so important since these reports are ephemeral, but archiving is nearly universal. I’d add the qualification that for well-used software to have fewer bugs the users must recognize the bugs and they must be fixed when recognized. Neither of those are certain, and in the case of close-source software the latter depends on users reporting the bugs and the source owners’ fixing them.

I suspect a lot of the bugs in published math are rarely recognized and when recognized are not necessarily reported to the author.

For cases where the bugs are obvious but no one bothers to report them, think about popular literature — extremely well read, but often full of unintentional spelling and grammar errors.

Actually, spelling and grammar errors are extremely common in the electronic realm, even in situations where they are read extensively. Even news reporting agencies frequently have such errors, but I doubt they are often reported — most readers ignore them if they even catch them. You might argue that this is not so important since these reports are ephemeral, but archiving is nearly universal.

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