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[Henry Gould]

I recall such a paper. The author published a paper giving a new 
definition  for the dimension of a topological space. He built up a 
chain of lemmas, ending up with a grand and glorious theorem based on 
the properties of a sequence of sets. The paper got bu the referees and 
the editors of a leading American research journal. When the 
Mathematical Reviews came out the very intelligent reviewer reported all 
the things in the paper and then ended with an incisive comment that 
unfortunately the author had failed to notice that every set in his 
sequence happened to be EMPTY. That was such a remarkable review.

A friend and colleague  of mine made up a new definition of a pseudo 
inverse of  a matrix and was about to publuish it when it suddenly 
downed on him that none of the matrices he had invented existed.

So, yes, this kind of thing can happen.

Henry Gould

= = = = = = =

franktaw at netscape.net wrote:
> I'd like to put my plug in for more application in math.
>
> I heard of a case some years ago where a paper was published about 
> some kind of mathematical object (I think it was a kind of topological 
> space, but it really doesn't matter).  Three or four more papers were 
> published, establishing more and more properties for this type of 
> object - until finally it was proved that they don't exist!  This 
> wouldn't have happened if somebody had asked for an example at an 
> early stage.
>
> There is a strong tendency in mathematics to start at the end.  The 
> researcher pursues a line of thought, which eventually leads to a 
> spiffy proof.  The proof is then published, with no hint of the 
> process by which it was reached.  This is a disservice to anybody who 
> might use a similar approach to solve some other problem.  It is 
> especially a disservice when presented to students.
>
> On a more personal level, I find when looking a math paper, I want to 
> know how this relates to problems that I am already interested in or 
> at least familiar with.  If I can't get an answer to that, I have a 
> hard time maintaining any interest.
>
> Franklin T. Adams-Watters
>
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