From: jim stasheff <jds@math.upenn.edu>
To: Categories@mta.ca
Subject: Re: WHY ARE WE CONCERNED? I
Date: Fri, 31 Mar 2006 09:30:58 -0500 [thread overview]
Message-ID: <E1FPT5p-0005Mu-8Q@mailserv.mta.ca> (raw)
Proofs may be of ultimate importance
but a lot can be accomplished at the penulitmate level
or even sooner
jim
Colin McLarty wrote:
>> There's a saying about Lefschetz that he "never wrote a valid
>> proof, and never made a false conjecture". Now it's not an attitude
>> that want to encourage, but if you have great mathematicians who
>> are like that (and Lefschetz was not just a good mathematician, but
>> a great mathematician, without whom a good deal of modern algebraic
>> geometry would be unimaginable), then this ought to tell us something.
>
>
> This, and much else about Lefschetz has to tell us a lot. As to proof,
> Lefschetz also never published a theorem without a purported proof, and
> he often came to feel very strongly that his proofs were not good
> enough. He wrote two long books on topology in the attempt to repair
> the bad proofs in his influential booklet on cohomology in algebraic
> topology, L'Analysis situs et la Topologie Algebrique. It was so
> important to him that he enlisted many others. Notably for us, he
> asked Eilenberg and Mac Lane to contribute an appendix to his 1942
> TOPOLOGY. This was their first published collaboration "On homology
> groups of infinite complexes and compacta" and pursued the questions
> that quickly led to category theory.
>
> Lefschetz had encouraged work on solving specific problems just over
> the edge of what well-understood foundations for homology could
> handle. Apparently he believed such solutions would lead to
> significantly deeper understanding. He had encouraged Steenrod to work
> on p-adic solenoids because existing methods did not seem adequate to
> it. But whatever his motive, he was determined to see rigorous
> solutions to quite specific problems.
>
> Colin
>
>
next reply other threads:[~2006-03-31 14:30 UTC|newest]
Thread overview: 13+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-03-31 14:30 jim stasheff [this message]
-- strict thread matches above, loose matches on Subject: below --
2006-03-30 23:44 Colin McLarty
2006-03-30 19:28 Marta Bunge
2006-03-30 17:10 Vaughan Pratt
2006-03-30 14:08 Peter Selinger
2006-03-30 10:33 Nikita Danilov
2006-03-30 9:03 Prof. Peter Johnstone
2006-03-30 8:13 Graham White
2006-03-29 15:42 James Stasheff
2006-03-29 13:22 Reinhard Boerger
2006-03-26 21:43 F W Lawvere
2006-03-28 20:51 ` jim stasheff
2006-03-29 20:10 ` Vaughan Pratt
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