Sunday, July 18, 2004
JSH: Mistakes happen
Now a poster has found a minor series of mistakes in my APF paper, and I admit some chagrin. But mistakes happen. As an author you can write something and for a lot of psychological reasons (and just plain carelessness) miss mistakes.
I don't know why I wasn't notified of that mistake by Ioannis Argyros, but given what I've seen from editors at Southwest Journal of Mathematics, I'm not surprised.
There are now questions for all the papers published by that journal, and it might be time for me to notify the other authors given this latest issue.
Now, even if the mistake had been noticed—as it should have been—and someone informed me, the fix is easy, so it wouldn't have been a big deal, but there's an important point here: even in a VERY short paper, apparently mathematicians can overlook mistakes.
Yet, there are people with supposed proofs that are hundreds of pages long.
How many people looked over my VERY SHORT paper and failed to notice the minor error? Sure it doesn't change the conclusion of the paper, but it does give pause.
The reality is that human beings make mistakes.
As long as mathematicians rely on human eyes to look over "proofs" then it's possible that errors remain, and they may not be minor.
Now I'm a supposed "crank" with a lot of people hostile to me, who have a strong motivation to find errors in my work, and make a big stink about it, and you can see that with the poster currently making a big stink about this error that he found. I say kudos to him for finding the mistakes.
I've acknowledged what are basically typos and given the fix.
But Andrew Wiles is apparently a beloved member of a community that wants to believe, and does believe, in him.
What makes any of you believe that a paper that's hundreds of pages long could really be just checked by human eyes and definitely not have a critical error?
I say, groupthink. You want to believe.
Computers need to check long math "proofs". There's just no objective way around that conclusion.
Mistakes happen. And people can overlook them, for many reasons.
I don't know why I wasn't notified of that mistake by Ioannis Argyros, but given what I've seen from editors at Southwest Journal of Mathematics, I'm not surprised.
There are now questions for all the papers published by that journal, and it might be time for me to notify the other authors given this latest issue.
Now, even if the mistake had been noticed—as it should have been—and someone informed me, the fix is easy, so it wouldn't have been a big deal, but there's an important point here: even in a VERY short paper, apparently mathematicians can overlook mistakes.
Yet, there are people with supposed proofs that are hundreds of pages long.
How many people looked over my VERY SHORT paper and failed to notice the minor error? Sure it doesn't change the conclusion of the paper, but it does give pause.
The reality is that human beings make mistakes.
As long as mathematicians rely on human eyes to look over "proofs" then it's possible that errors remain, and they may not be minor.
Now I'm a supposed "crank" with a lot of people hostile to me, who have a strong motivation to find errors in my work, and make a big stink about it, and you can see that with the poster currently making a big stink about this error that he found. I say kudos to him for finding the mistakes.
I've acknowledged what are basically typos and given the fix.
But Andrew Wiles is apparently a beloved member of a community that wants to believe, and does believe, in him.
What makes any of you believe that a paper that's hundreds of pages long could really be just checked by human eyes and definitely not have a critical error?
I say, groupthink. You want to believe.
Computers need to check long math "proofs". There's just no objective way around that conclusion.
Mistakes happen. And people can overlook them, for many reasons.
# posted by James Harris @ 12:06 
