From csus.edu!decwrl!decwrl!spool.mu.edu!darwin.sura.net!math.ohio-state.edu!not-for-mail Fri Jun 25 17:16:20 1993
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From: morje@math.ohio-state.edu (Prabhav Morje)
Newsgroups: comp.theory
Subject: Fermat's Last theorem
Date: 24 Jun 1993 08:27:58 -0400
Organization: Department of Mathematics, The Ohio State University
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Status: RO
Somebody asked to confirm the news about Fermat's last theorem:
Here is a local post by Prof.Karl Rubin at Ohio State:
=======================================================================
From K.C.Rubin@newton.cam.ac.uk Thu Jun 24 08:19:22 EDT 1993
Article: 531 of math.announce
Path: math.ohio-state.edu!gateway
From: K.C.Rubin@newton.cam.ac.uk
Newsgroups: math.announce
Subject: Fermat's Last Theorem
Date: 23 Jun 1993 05:56:33 -0400
Organization: The Ohio State University, Department of Mathematics
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In a lecture here at the Newton Institute in Cambridge this
morning, Andrew Wiles announced that he has proved Fermat's
Last Theorem.
He did this by proving a large part of the Taniyama-Weil
conjecture for elliptic curves. He proved that every
semistable elliptic curve over the rational numbers is
attached to a modular form. It has been known for several
years, by work of Frey and Ribet, that this implies Fermat.
-Karl Rubin
============================================================================
From csus.edu!wupost!uunet!munnari.oz.au!cs.mu.OZ.AU!mundoe!lip Mon Jun 28 11:19:29 1993
Newsgroups: sci.math
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From: lip@mundoe.maths.mu.OZ.AU (Lawrence Ip)
Subject: Original Latin for FLT
Message-ID: <9317813.18833@mulga.cs.mu.OZ.AU>
Keywords: Latin, Fermat
Sender: news@cs.mu.OZ.AU
Organization: Computer Science, University of Melbourne, Australia
Date: Sun, 27 Jun 1993 03:29:04 GMT
Lines: 12
Status: RO
Someone asked for the original margin note in Latin. Well here it is :
Cubem autem in duos cubos, aut quadrato-quadratum in duos quadrato-
quadratos, et generaliter nullam in infinitum ultra quadratum potestatem
in duas ejusdem nominis fas est dividere : cujas rei demonstrationem
mirabilem sane detexi. Hanc marginis exiguitas non caparet.
_________________________________________________________________________
Lawrence Ip lip@mundoe.maths.mu.oz.au
c/o Dept of Maths, University of Melbourne, Parkville VIC 3052, Australia
From csus.edu!wupost!uunet!munnari.oz.au!cs.mu.OZ.AU!mundoe!lip Mon Jun 28 11:20:52 1993
Newsgroups: sci.math
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From: lip@mundoe.maths.mu.OZ.AU (Lawrence Ip)
Subject: Original Latin for FLT (with translation)
Message-ID: <9317815.20578@mulga.cs.mu.OZ.AU>
Keywords: Latin, Fermat, FLT
Sender: news@cs.mu.OZ.AU
Organization: Computer Science, University of Melbourne, Australia
Date: Sun, 27 Jun 1993 05:23:47 GMT
Lines: 20
Status: RO
Someone asked for the original margin note in Latin. Well here it is :
Cubem autem in duos cubos, aut quadrato-quadratum in duos quadrato-
quadratos, et generaliter nullam in infinitum ultra quadratum potestatem
in duas ejusdem nominis fas est dividere : cujas rei demonstrationem
mirabilem sane detexi. Hanc marginis exiguitas non caparet.
translated ...
On the other hand, it is impossible to separate a cube into two cubes, or
a biquadrate (fourth power) into two biquadrates, or in general, any power
except a square into two powers with the same exponent. I have discovered
a truely marvellous proof of this, which however the margin is not large
enough to contain.
_________________________________________________________________________
Lawrence Ip lip@mundoe.maths.mu.oz.au
c/o Dept of Maths, University of Melbourne, Parkville VIC 3052, Australia
From csus.edu!decwrl!decwrl!concert!gatech!pitt.edu!dsinc!netnews.upenn.edu!sagi.wistar.upenn.edu Wed Jun 30 13:00:27 1993
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From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Where will Wiles' Proof of FLT be formally published?
Message-ID: <133941@netnews.upenn.edu>
Date: 29 Jun 93 21:59:31 GMT
References: <20q52m$imt@usenet.INS.CWRU.Edu>
Sender: news@netnews.upenn.edu
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
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In-reply-to: rfd@po.CWRU.Edu (Richard F. Drushel)
Status: RO
In article <20q52m$imt@usenet.INS.CWRU.Edu>, rfd@po (Richard F. Drushel) writes:
> I hope it's a monograph, because then I can buy my own copy.
>If it's printed in a journal, then poor Wiles will be deluged with
>reprint requests; also, that particular issue will disappear from
>all the libraries (or be put immediately into non-circulating special
>collections)--just try to find any of Einstein's original papers in
>the journal stacks, for example.
Hmmm. That's a good point. I've got an idea. Notice that Ribet's
proof of FLT **ASSUMING** Taniyama-Weil did _not_ suffer this fate.
Go ahead, see for yourself if volume 100 of INVENTIONES MATHEMATICAE
is still on your library's shelf, with pages 431-476 intact. (And
check next week, in case this article gave anyone some ideas.)
So, what Wiles must do is write his proof in the proper manner,
emphasizing that he is **ASSUMING** the Axiom of Choice all along,
and that all he has done, and which the media overlooked in their
hysteria for a good story, was to prove FLT **ASSUMING** AC.
The logically challenged reader will have no idea of what's going on,
and with luck will feel that he's missing out on the real proof for
all posterity. This will also keep the cranks employed.
------------------------------------------------------------------------
By the way, since no one seems to have mentioned it: this being Tuesday,
check out the NYT Science Times. Page C1 has a story on Wiles, and the
effect of the announcement. Princeton's math department is currently
being deluged with congratulations. According to the story, Wiles worked
for 7 years non-stop on this with Nick Katz as his sworn-to-secrecy
sounding board. He expressed some sadness at finishing the problem
off.
The article mentioned that one of his last steps was a technique he
picked up from some random Mazur paper, a technique that apparently
dates back to last century, but that Wiles had somehow never heard of
until late in the game. Does anyone know what this is in reference to?
--
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From csus.edu!decwrl!ames!agate!howland.reston.ans.net!ux1.cso.uiuc.edu!mp.cs.niu.edu!rusin Thu Jul 1 11:04:55 1993
Newsgroups: sci.math
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From: rusin@mp.cs.niu.edu (David Rusin)
Subject: FLT and math thugs...
Message-ID: <1993Jun30.195849.32450@mp.cs.niu.edu>
Organization: Northern Illinois University
Date: Wed, 30 Jun 1993 19:58:49 GMT
Lines: 117
Status: RO
The following column appeared in the Chicago Tribune / DuPage County edition
Tuesday June 29 1993 page 2-1.
MATH RIOTS PROVE FUN INCALCULABLE
/by/ Eric Zorn
/begin italics/
News Item (June 23) -- Mathematicians worldwide were excited and
pleased today by the announcement that Princeton University professor
Andrew Wiles had finally proved Fermat's Last Theorem, a 365-year-old
problem said to be the most famous in the field.
/end italics/
Yes, admittedly, there was rioting and vandalism last week during the
celebration. A few bookstores had windows smashed and shelves stripped,
and vacant lots glowed with burning piles of old dissertations. But
overall we can feel relief that it was nothing -- nothing -- compared
to the outbreak of exuberant thuggery that occurred in 1984 after
Louis DeBranges finally proved the Bieberbach Conjecture.
"Math hooligans are the worst," said a Chicago Police Department
spokesman. "But the city learned from the Bieberbach riots. We were
ready for them this time."
When word hit Wednesday that Fermat's Last Theorem had fallen, a
massive show of force from law enforcement at universities all around
the country headed off a repeat of the festive looting sprees that have
become the traditional accompaniment to triumphant breakthroughs in
higher mathematics.
Mounted police throughout Hyde Park kept crowds of delirious wizards at
the University of Chicago from tipping over cars on the midway as they
first did in 1976 when Wolfgang Haken and Kenneth Appel cracked the
long-vexing Four-Color Problem. Incidents of textbook-throwing and
citizens being pulled from their cars and humiliated with difficult
story problems last week were described by the university's math
department chairman Bob Zimmer as "isolated."
Zimmer said, "Most of the celebrations were orderly and peaceful. But
there will always be a few -- usually graduate students -- who use any
excuse to cause trouble and steal. These are not true fans of Andrew
Wiles."
Wiles himself pleaded for calm even as he offered up the proof that
there is no solution to the equation x^n + y^n = z^n when n is a
whole number greater than two, as Pierre de Fermat first proposed in
the 17th Century. "Party hard but party safe," he said, echoing the
phrase he had repeated often in interviews with scholarly journals as
he came closer and closer to completing his proof.
Some authorities tried to blame the disorder on the provocative
taunting of Japanese mathematician Yoichi Miyaoka. Miyaoka thought he
had proved Fermat's Last Theorem in 1988, but his claims did not bear
up under the scrutiny of professional referees, leading some to
suspect that the fix was in. And ever since, as Wiles chipped away
steadily at the Fermat problem, Miyaoka scoffed that there would be no
reason to board up windows near universities any time soon; that God
wanted Miyaoka to prove it.
In a peculiar sidelight, Miyaoka recently took the trouble to secure a
U.S. trademark on the equation "x^n + y^n = z^n " as well as the
now-ubiquitous expression "Take that, Fermat!" Ironically, in defeat,
he stands to make a good deal of money on cap and T-shirt sales.
This was no walk-in-the-park proof for Wiles. He was dogged, in the
early going, by sniping publicity that claimed he was seen puttering
late one night doing set theory in a New Jersey library when he either
should have been sleeping, critics said, or focusing on arithmetic
algebraic geometry for the proving work ahead.
"Set theory is my hobby, it helps me relax," was his angry explanation.
The next night, he channeled his fury and came up with five critical
steps in his proof. Not a record, but close.
There was talk that he thought he could do it all by himself,
especially when he candidly referred to University of California
mathematician Kenneth Ribet as part of his "supporting cast," when most
people in the field knew that without Ribet's 1986 proof definitively
linking the Taniyama Conjecture to Fermat's Last Theorem, Wiles would
be just another frustrated guy in a tweed jacket teaching calculus to
freshmen.
His travails made the ultimate victory that much more explosive for
math buffs. When the news arrived, many were already wired from
caffeine consumed at daily colloquial teas, and the took to the streets
en masse shouting, "Obvious! Yessss! It was obvious!"
The law cannot hope to stop such enthusiasm, only to control it. Still, one has
to wonder what the connection is between wanton pillaging and a mathematical
proof, no matter how long-awaited and subtle.
The Victory Over Fermat rally, held on a cloudless day in front of a
crowd of 30,000 (police estimate: 150,000) was pleasantly peaceful.
Signs unfurled in the audience proclaimed Wiles the greatest
mathematician of all time, though partisans of Euclid, Descartes,
Newton, and C.F. Gauss and others argued the point vehemently.
A warmup act, The Supertheorists, delighted the crowd with a ragged
song, "It Was Never Less Than Probable, My Friend," which included such
gloating, barbed verses as --- "I had a proof all ready / But then I
did a choke-a / Made liberal assumptions / Hi! I'm Yoichi Miyaoka."
In the speeches from the stage, there was talk of a dynasty,
specifically that next year Wiles will crack the great unproven Riemann
Hypothesis ("Rie-peat! Rie-peat!" the crowd cried), and that after the
Prime-Pair Problem, the Goldbach Conjecture ("Minimum Goldbach," said
one T-shirt) and so on.
They couldn't just let him enjoy his proof. Not even for one day. Math
people. Go figure 'em.
/end of article/
[Comments: I believe the author is grandson of Max Zorn.
Out-of-towners may need to know that Chicago's professional basketball
team just won the national championship; most of these jokes parody
events of the championship series.]