[ALGTOP-L] the value of MR AND Zentralblatt

Ronnie Brown ronnie.profbrown at btinternet.com
Tue Sep 29 13:54:04 EDT 2009


Dear All,

I entirely agree with Max.

It could reasonably be said that in mathematics there is an urgency to 
meet schedules (i.e. to get published) and also a weak system of 
communication of dangers. These were two factors in a famous shipping 
disaster - the Titanic. (The enquiry also insisted on other 
recommendations, such as internal watertight bulkheads: I'll leave you 
all to suggest mathematical analogues!)

In physics, there is a creative synergy of opposites between theory and 
experiment.

Perhaps in mathematics there is an analogous symmetry between 
imagination and logic (any other suggestions?). What is the difference 
between a `result' with a lousy proof, possibly incorrect, and a 
`speculation'? See also
www.bangor.ac.uk/r.brown/Grothendieck-speculation.html

Years ago a postdoc from New York visited Bangor. He told me that as a 
student he was asked to give a seminar on a paper. He found he could not 
understand it. His supervisor, initially sceptical, finally could not 
understand it either. Eventually the student asked the author who 
responded: "I knew the result was true, so I just wrote something down. "

In Edinburgh in 1958 as a callow research student I overheard Bott say: 
"Grothendieck is prepared to work very hard to make something 
tautological!"  Three cheers for Grothendieck!!

Grothendieck was also very interested in foundations, and his perception 
of our interest in that was a spur  to our relationship. (see his 
`letter to Quillen', the introduction to `Pursuing Stacks'. )  But 
foundations has only a weak interest in algebraic topology, I perceive. 
What is of interest is `results', particularly for Editors of `top 
journals'.

The reputation of our subject could well get damaged if it is found out 
that or thought that we have no adequate safety organisation! i.e. 
procedures for discovering and dealing with errors, and are against, or 
give no sustenance to,  `whistleblowers'. (When the railways were 
privatised in the UK in the 1990s there were warnings that the 
structural  organisation proposed would prejudice safety but these were 
ignored .....Guess what happened? )

Ronnie Brown




Max Karoubi wrote:
> Dear all,
>
> I agree with many that it is important to spot the errors before they 
> become a calamity for working mathematicians.
>
> One of my students lost one year of research because the proof of his 
> main theorem was relying on somebody else work and we discovered there 
> was a serious gap in the proofs.
> I can also list 2 or 3 bad experiences in my own research which force 
> me now to publish a paper only if I can be sure of the proofs of the 
> theorems I am using!
>
> However, as we can see in this intense discussion on the Web, there is 
> no obvious mathematical and ethical consensus for a solution to this 
> problem.
>
> I have a modest suggestion which might contribute to a partial 
> solution. If we spot an important mistake in a paper, why we don't 
> send a message to the reviewer in the Math Reviews (or Zentralblatt) 
> in charge of this paper ? This reviewer may act as a moderator. If he 
> is honest, he will change his review according to the remarks he is 
> receiving (anonymously if he is asking to act this way). Sometimes 
> also (more often than one thinks), the author of a paper would like to 
> mention serious mistakes or incomplete proofs for the benefit of the 
> communauty. This would keep track of various errata one is not always 
> aware of.
>
> Of course, this suggestion will work only if the Math Reviews and the 
> reviewer accept to work in a "dynamical" way, by correcting their 
> reviews electronically, each time it is really necessary (following 
> the model of the ArXiv system for instance).
>
> Best regards,
>
> Max Karoubi
>
>
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