[Philnet] The Poincare Conjecture

[Prof S.R.L. Clark]

An interesting story from Peter Suber's FOS Newsletter 4/29/02

---------- Forwarded message ----------
Date: Mon, 29 Apr 2002 13:21:00 -0400
From: Peter Suber <peters@earlham.edu>

The Poincar=E9 conjecture

The Poincar=E9 conjecture is unusual in several respects.  First, it's on
every shortlist of the most famous and difficult unsolved problems in
mathematics.  Second, the Clay Mathematics Institute has offered a $1
million prize for a proof of the conjecture.  Third, a serious assault on
the problem is now taking place in a free online preprint archive.

Martin Dunwoody, a mathematician at Southampton University, posted a
tentative proof of the conjecture to the Southampton Pure Mathematics Group
Preprint Archive.  Dunwoody has revised his text several times as readers
found flaws in his proof and as he found solutions.  When I last visited,
he was up to version 8, and wrestling with a difficulty pointed out by
Warwick mathematician Colin Rourke.

Despite the setbacks and fixes, the evolving proof is generating
excitement.  Arthur Jaffe, president of the Clay Institute, called
Dunwoody's work "the first serious effort" on any of the institute's seven
prize-winning problems.  Mathematician Ian Stewart calls Dunwoody's proof
"the first good shot at this problem in years."

 From an FOS point of view, this is an experiment in putting unfinished
work on an open-access preprint server, updating the work in response to
criticism, harnessing informal peer review to improve a result before
submitting it to formal peer review, and letting the world watch every step
free of charge.

If Dunwoody never quite fixes the leaks in his proof, he will still have
proved the utility of free online preprint archives in gathering relevant
expertise and focusing it on an important scientific problem.  If his proof
succeeds, then it will count not only as the world's first proof of the
Poincar=E9 conjecture, but as an elegant new proof of the FOS Quality
Theorem, which asserts that first-rate science and scholarship do not
depend on the medium (print or electronic) or cost (priced or free) of the
channel of distribution.

Martin Dunwoody, "A Proof of the Poincar=E9 Conjecture?"
http://www.maths.soton.ac.uk/~mjd/Poin.pdf

Southampton Pure Mathematics Group Preprint Archive
http://www.maths.soton.ac.uk/pure/preprints.phtml

The Clay Mathematics Institute
http://www.claymath.org/index.htm
(The CMI list of seven "Millennium Problems" was announced in 2000 as a
deliberate echo of Hilbert's famous list of 23 in 1900.)

Background on the Poincar=E9 conjecture
http://www.claymath.org/prizeproblems/poincare.htm
http://www.math.unl.edu/~mbritten/ldt/poincare.html

AP story on Dunwoody's proof
http://www.cnn.com/2002/TECH/science/04/26/britain.math.mystery.ap/

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Peter Suber
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Copyright (c) 2002, Peter Suber
http://www.earlham.edu/~peters/copyrite.htm

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