Path: utzoo!mnetor!uunet!husc6!ncar!ames!ucsd!sdcc6!sdcc13!ln63wgq
From: ln63wgq@sdcc13.ucsd.EDU (Keith Messer)
Newsgroups: sci.crypt
Subject: Re: Fermat's Last Theorem apparently proven
Message-ID: <1014@sdcc13.ucsd.EDU>
Date: 17 Mar 88 09:13:15 GMT
References: <977@thumper.bellcore.com: <7440@brl-smoke.ARPA> <26797@linus.UUCP> <7449@brl-smoke.ARPA> <26822@linus.UUCP> <1009@sdcc13.ucsd.EDU> <7521@boring.cwi.nl> <1010@sdcc13.ucsd.EDU> <27073@linus.UUCP>
Reply-To: ln63wgq@sdcc13.ucsd.edu.UUCP (Keith Messer)
Organization: Univ. of California, San Diego
Lines: 35

In article <27073@linus.UUCP> bs@gauss.UUCP (Robert D. Silverman) writes:
[In my message, I write:]
>:  If a general result of
>:quantificantion theory is that set theory and number theory contain contra-
>:dictions (ie. It's possible to construct a proof for a statement and one for
> 
>Number theory does NOT contain contradictions. CERTAIN set theories can be
>constructed which are formally inconsistent [...]

Ok, remember that I'm >not< claiming to be knowledgable about these things,
but I >am< trying to learn about them, so here is my source, and a quote
from a book I'm reading on the subject:

	"...the sharp question of completeness has led to sharp answers.
	 Godel's famous theorem establishes the conclusion that the usual
	 formal systems for number theory, analysis and set theory are
	 incomplete unless they contain contradictions.  Moreover, given any
	 consistent formal system for one of these theories, a sentence of
	 the system can be constructed which is demonstrably indemonstrable."

		-- Wang Hao, _A_Survey_of_Mathematical_Logic_, Science Press

Now, while I realize that Wang Hao may have been wrong when he wrote that
in his book, you and he >are< in direct contradiction with one another
if number theory is complete.  However, I don't get off on talking about the
completeness and validity of mathematical systems.  Applied cryptology is more
interesting, and I did wrong to post a math question on the crypto board
in the first place, but I had hoped you might have some light to shed on
the subject.. Why do you keep ragging on people?

But, to change the subject, what is your favorite one-way transformation..
I mean the one you feel most secure about being one-way?  And what are your
favorite books in areas of math that are useful in cryptology/cryptoanalysis?

						Keith