[ALGTOP-L] the value of MR AND Zentralblatt

Martin C. Tangora tangora at uic.edu
Sun Sep 27 13:49:28 EDT 2009

It is my opinion that the field of academic mathematics
would suffer terribly if the general public began to understand
that we publish lots of mistakes.

Algebraic topology is, according to my experience,
one of the worst offenders.

The reason that errors are accepted is that,
contrary to public impression of mathematicians
as people who are absolutely rigorous and always correct,
in the academic discipline the mathematicians 
who earn the greatest prestige and renown 
are those who have the deepest ideas, 
not those whose work is absolutely reliable.

The fact that government-supported researchers
with small teaching loads frequently publish papers
in which not only some details are wrong
but sometimes the main result is wrong --
if that reached the ears of one influential person,
such as a certain senator -- whom I will not name,
out of fear that someone on his staff, googling idly,
will find this posting -- it would be a disaster.

The point is not whether ordinary people would start
browsing the wikis to see what we are saying
about each other's work.  The point is that
one pithy article would appear which could be summed up
by the statement that mathematicians don't care
whether their results are correct or not,
as long as they are deep.

The rest of this note will be personal, but I have
two relevant Frank Adams anecdotes that may be of interest.

My research was mostly long and difficult calculations.
I always wanted it to be 100% correct, and maybe
you would all say that about your own work, but ...
I have seen papers that had dozens of small errors,
and papers in which the main result was wrong,
not just a gap in the proof, but the wrong result.

When I first met Frank Adams (Manchester 1966),
he took me to his office and gave me his current reprints.
One of them was a paper with co-authors, and as
Frank red-penciled the paper with numerous corrections,
you could see that he was almost boiling over.
I gathered that his co-authors had made errors
and that Frank had not thought it necessary to check their work
until it was too late.

A few years later, a year that I spent at Oxford, 
I was having lunch with Frank at the BMC, and I told him that I had
collected enough material to publish a good-sized paper
consisting only of corrections to results published by others.  
I said that I wasn't sure that such a paper would be of interest.

Frank did not say that it would be wrong to publish
such an article (point 2, "socially unacceptable").
Nor did he suggest that it would be bad publicity
for our field (point 1).

He just joked, "No, Marty, such a paper would be
of great interest; but you must be sure that it isn't
just the first in an iterative sequence."

At 11:00 AM 9/26/2009, you wrote:
>Date: Sat, 26 Sep 2009 10:57:33 +0200
>From: Tilman Bauer <bauer.tilman at googlemail.com>
>Subject: Re: [ALGTOP-L] the value of MR AND Zentralblatt
>To: algtop <algtop-l at lists.lehigh.edu>
>Dear list,
>re John Klein's objection 1 (that pointing out errors publicly damages  
>our subject's reputation): I actually think the opposite is true.  
>Everybody makes mistakes. Making mistakes does not damage our  
>reputation nearly as much as trying to cover up, deny, hide. I think  
>we can set a positive example by being open about our errors -- also  
>to other disciplines, and to our students. (Chiming in with Pablo  
>Angulo here.) It's also what we try to teach them: if you don't  
>understand something, if you get something wrong, don't hide it, it  
>will come out eventually anyway. We need to show humility to our  
>subject and not let pride get in the way. I think we need not be  
>ashamed to send the message "We don't get it right every time, but we  
>always get it right eventually, together."
>I don't think a wiki-based refereeing, commenting, and error-reporting  
>system would have significant impact on our subject's reputation with  
>the general public *except* for its mere existence, which would be a  
>positive impact. I don't think ordinary people will start browsing the  
>comments about our papers, which they won't understand anyway, and  
>extract that most of mathematics seems to be wrong or shaky.
>Our non-mathematician colleagues, on the other hand, know that there  
>are mistakes in a lot of the math literature anyway, so there's no  
>point in hiding that. Dealing with it in a professional way, however,  
>will impress them and further our subject's reputation.
>re objection 2 (it's socially unacceptable to point out our  
>colleagues' mistakes in print): agreed, but there's always a way of  
>doing this that allows them to save their face. For example, you can  
>just pose it as a question: "why is this true?" which allows them to  
>correct themselves (or for you to find out it was right after all!) If  
>an author stubbornly refuses to address such problems, we need to put  
>the finger on the mistake explicitly, but we've done that in the past  
>as well, haven't we?  
> ( ... )

Martin C. Tangora
University of Illinois at Chicago
tangora at uic.edu

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