Date: Thu, 16 Oct 2003 11:00:53 -0400 (EDT)
From: Dan Hoey <Hoey@aic.nrl.navy.mil>
To: math-fun@mailman.xmission.com
Subject: [math-fun] Re: Poincare Conjecture

"Jon Perry" <perry@globalnet.co.uk> writes:

> Thanks - I can see the weaknesses in my argument.

Very good, if true.

> However, is there anything wrong with this;

> PC is true because from the 3-sphere, a compact, simply connected
> manifold, through only operations which preserve homeomorphicity, we
> can attain every other compact, simply-connected 3-manifold.

Yes, there's something wrong with that.  Any statement of the form "PC
is true because <sentence>" is hogwash.  If you were going to prove
PC, you would need more than a sentence to express a convincing proof.

It might be accurate to say "If I could prove <sentence>, that would
imply PC".  That depends on the sentence, of course.

If you ever convinced someone that you might have a proof of PC, then
it might be appropriate to say something of the form, "I have proved
<sentence>, and that implies PC."

But you made the statement in the hogwash form.  Moreover, you made
that statement in reply to a message that shows that you not only did
not present a realistic approach to a proof of PC, but were apparently
unclear on the concept of what a proof of PC would be, and that you
were beginning to sound like a crank.

I hope your statement is not a proof, because it certainly isn't a
proof of the Poincare conjecture.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil