[FOM] What's going on with the Poincare conjecture?

joeshipman@aol.com joeshipman at aol.com
Sat Jun 17 03:10:19 EDT 2006

Grigori Perelman of the Steklov Institute announced in 2003 that he had 
proved Thurston's Geometrization Conjecture (and, as an easier subcase, 
the Poincare Conjecture), and circulated some preprints which have been 
scrutinized carefully in seminars over the last several years, with 
consensus growing that Perelman had actually done it, but no formal 
announcement that the proof had been fully validated.

This month, there has been a flurry of news stories that two Chinese 
mathematicians, Cao and Zhu, have provided the "final brick" in the 
proof, and that the Poincare conjecture is now proved. However, there 
are two disturbing things about this:

1) Although I have found a large number of articles about this, none of 
them state explicitly what "gap" in Perelman's proof they are supposed 
to have filled in. The earlier stories I had read about Perelman's work 
had said that on every occasion where Perelman was asked for more 
details by the mathematicians examining his work, he had satisfactorily 
supplied them, and that all errors that had been discovered were minor 
and easily patched.

2) In the two weeks since the initial announcement from the Chinese 
news agency Xinhua, I have seen no statement by any person who was not 
Chinese that Cao and Zhu had either provided a complete and validated 
proof, or filled in a clear lacuna in Perelman's work.

Perelman is notoriously uninterested in publishing or in claiming the 
$1,000,000 Clay Institute Prize for a proof of the Poincare conjecture, 
and China seems to be heavily hyping the achievement of Cao and Zhu.

Can anyone on this list find out what's really going on from someone in 
the know?

-- Joe Shipman
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