Re: JSH: Fraud question is pertinent
- From: "Proginoskes" <CCHeckman@xxxxxxxxx>
- Date: 19 May 2006 23:31:20 -0700
Gene Ward Smith wrote:
jstevh@xxxxxxx wrote:
[...]
The best explanation is that it doesn't work very well.
My own research leads me to conclude that errors dominate the modern
math field in areas of "pure math" where you have to take people's word
for it that mathematical arguments are correct.
What the hell is this supposed to mean?
His results disagree with standard mathematics. Therefore, at least one
of the following statements is true:
(1) His results are false.
(2) Standard math is false.
He can't imagine (1) being true, so he concludes that (2) must be.
It looks like errors came in over a hundred years ago, and have
dominated pure math ever since.
Not that you actually can point to one, of course...
Ideal theory is wrong; he can't point any more precisely than that.
(Actually, when JSH posted a result, someone else pointed out that that
result contradicted ideal theory. JSH responded by saying he'd found an
error in ideal theory. No further word or details, of course.)
You haven't been reading much of JSH.
One odd clue that mathematicians are at least on some level aware that
much of the field is full of errors--the weird inability to get
widespread computer checking of mathematical arguments claimed to be
proofs.
In fact, quite a lot has been done with computer-verifying mathematics,
so this is baloney.
Computers help medical doctors, expert systems are dominate in all
sorts of areas, but in mathematics, for some reason, supposedly,
computers are not up to the challenge.
You don't know what the hell you are talking about.
Indeed. OTOH, I can speak out of personal experience. (The people who
know about my minor role in the new 4CT proof can skip the next
paragraph. JSH should read it but probably won't.)
When I started graduate school, I was a GRA for Robin Thomas, who would
eventually become one of the four co-authors of a new proof of the Four
Color Theorem. The idea was to use the Appel-Haken ideas --- which no
one had any fundamental disagreements with --- and to try to get a
better proof, because of the extra knowledge, faster computers, and
better algorithms discovered since 1976. I was one of two of RT's
doctoral students who took the C programs, debugged them, and rewrote
them in Pascal. (What is not generally revealed is that I found several
bugs in the C program for discharging.) Another task was given to
several of RT's students, to basically find a minimum-sized transversal
for a sequence of sets. (That is, given sets A(1), A(2), ..., A(n),
find a set B of minimum size such that A(i) intersected B is nonempty,
for all i.) For doing these things, my name was mentioned in the
acknowledgments section of the proof when it appeared in print.
This was basically a brute-force check, with a proof-like guideline
("branch and bound"), which is well-suited for computers to check.
I also found out recently that the new 4CT proof had been checked (in
2003?) by a computer-based logic system and found to be valid.
--- Christopher Heckman
.
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