Mathematics - The history of the solution of Fermat's theorem.

<b>Mathematics</b> - The history of the solution of Fermat's theorem.


              Pierre de Fermat

                 1601-65


 Nizhegorodskaya Pravda, August 22. 1998

      Category "History of Discoveries"

        Gennady Ivanov (Sarov)


          Great Theorem had fallen,

    but it took three hundred years



   Lawyer Pierre Fermat, who is also an outstanding
scientist, not published in his life nor
 one job

   Ed.: "One mathematical essay written
by him was published in his lifetime. "
(Http://www.geocities.com/fermatnow/flt/
flt1.htm)

   engaged in mathematics, as it is now
said, in his spare time, on
fields, one of the books recorded the theorem for
which found amazing evidence
for which supposedly did not have enough space.

   ... Many mathematicians ever since, and among
are the largest: Euler, Lagrange, Gauss,
Dirichlet, Kummer, Sophie Germain and others,
lost rest, chewing this theorem. She was named
"Great" or "last."

   Pierre Fermat's easy to prove the equation for
n = 4, passed the torch to the next. Only
through 140 years of the great Euler was able to overcome
"Great" to the third degree, after 195 years
found evidence for a 5-degree (not
Metz, Dirichlet and Legendre, a Frenchman), and only through
209 years - to 7-th degree (French Lame).

   Mysterious three letters, like three cards
teased and fascinated. Great Gauss
Kummer, a Frenchwoman Sophie Germain broke th
traps, but in vain - the complete solution of any
XVIII, nor in the XIX century and did not get QS
gly.

   To encourage efforts to resolve the
"Great" and the search for new mathematical
FIR methods, the French Academy of Sciences in
In 1850 established a prize in the 3000 francs
(Our - 57 million rubles per 0.9 kg of gold
coin). Nobody could not get it, though
Many tried.

   To raise the prestige of mathematical
Works German lover of mathematics one
P. Volfskel established in 1908 award
his name for ... finding a general proof
proof of "Fermat's Last Theorem." Size
Awards 100 thousand marks (or 36 kg gold
 coin).

   Ed.: By Encarta'96, this award now
awarded to the University of Gottingen
for proof (not denial) of this
theorem, proven to September 13, 2007
year.

   Immediately start a real boom in
Academy of certain countries flooded the proof
ments. From mathematicians, amateurs and pro
everything that got the nickname "fermatistov.
Many of them found themselves in a mental hospital - not
kept nerves. The outbreak of the First World
curve after the war and the subsequent destruction
German inflation turned Volfskelev
skuyu award to nothing.

   By 1941, the efforts of outstanding works
Mathematicians "Great Theorem" was proved
 on to higher degrees (n = 6 billion)

   Ed.: This is incorrect; Shay (see below) pi
Sheth, using methods that Kummer'a (1857)
"In 1937 the theorem was verified for all
powers till 617, in 1955 it was verified
for all powers till 4,001, in 1976 - till
125,000, and in 1992 FLT was verified for
each power till 4,000,000 ".

   but the evidence "in general terms, then
is an arbitrary n, we did not succeed
valos anyone.

   The rapid development of mechanized mathematics
made it possible to move forward. But the "Great"
in general remained unproven,
despite the use of the most sophisticated
mathematical methods. Peace Academy of
continues to receive its "evidence" which
rye invariably fall into the basket for th ...
Sor.

   Author of the article are interested in a topic has
in the early 80's by chance on
circumstance. And when, in the early 90's
there have been reports that some angliys
cue mathematician found the general solution of it is
considering themselves prepared for the issue of
thought: perhaps, in some English
madhouse, just in case the place for neschas
tnogo "fermatista" cooked. However, with
life did not go according to this scheme.

   At held in 1992 the first story
cally conference on nuclear weapons in
our Sarov (then Arzamas-16) case
Tea asked who was present at her
Academician Vladimir Vladimirov (then director
The Institute of Mathematics of them. Steklov - ca
ICDO competent in Russia mathematical
of institution): as there are cases in part
"Closure" another attempt to "fermatista"
and soon to be expected scandalous op
roverzheniya?

   Vasily Sergeyevich kindly informed that
Our experts have discovered in the system transformation
dstavlennyh evidence set Ogre
Hove. In other words, the evidence is not obvious
visible, may crumble ...

   At the meeting, 1994 (anniversary of Julia Hare
tone), the conversation went back to the farm and
his "Great." In this case, Vladimirov races
said that many people doubt the proof
wah Englishman persists, but koechto still left. It is worth 
recalling: 40's - early 50-ies in Sarov was

concentrated perhaps the most powerful in that
time math brains. Enumeration
giants such as acad. Bogolyubov (he
of Nizhny Novgorod), Lavrent'ev, V. Vladimirov
ditch, M. Keldysh, speaks for itself. Later
Active members of many different academic
missions, then they were forced to engage in
complex mathematical problems in foreign
'interest of nuclear weapons.

   Renowned physicist W. Adamski in one of
interviews noted: our physical ideas podtol
knuli development of many mathematical methods
transitions and, more importantly, we found the main Zach
zchikami and consumers of powerful computers. Occupy
malsya if any of these mathematicians
at least out of curiosity, "Great Theorem"
while in Sarov, failed to learn.

   But recently, VNIIEF was the second study
toric conference on the history of
development of Soviet nuclear oruzhiya.Se
halis many veterans, including and Academician
Vladimirov, speaking with the memories.
Asking him to clean the duty question, what is for
ended the history from English "FERMATIS
Tom, I heard:

   - And after all our experts in this area
Tee RECOGNIZED PROOF OF THEOREM TO ASSURE
Telnov, all your questions FOUND AGAIN
REShENIE.Dokazatelstva very difficult, almost
in a hundred pages. These cases in our Institute
tute worked Shafarevich group, and,
their opinion, Fermat's Theorem Prove.

   How is this? Committed such an event,
and we, as the saying goes, no one eye.

   Came the idea: why not learn from ca
ICDO academician Shafarevich recognized specialists
specialists on the theory of numbers, his assessment of by
latter proof of Fermat's theorem, pop
rosiv to emphasize a few words. In response,
academic letter confirmed: "Indeed,
proof of the "last" (or "the Great")
Fermat's theorem is obtained by the British mathematician
Teak Wiles, and from what I know now
No one has no doubts. "

   So, we've witnessed the fall of
Lika mathematical mysteries ... Joker and
great scientist Farm - "get it"! But in
it took ... 330 years and more than a hundred
pages of complex evidence.


                  *


            P.S. From the Editor



   Naturally, the statement Shafarevich - not
ultimate truth (especially
when you consider the nonsense that he wrote out
mathematics). For example, JJ O'Connor
and E F Robertson (http://www-groups.dcs.
st-and.ac.uk / ~ history / HistTopics /
Fermat's_last_theorem. Html) not as a category
gorichny: "No proof of the complexity of
this can easily be guaranteed to be
correct, so a very small doubt will remain
for some time ".



   http://cgd.best.vwh.net/home/flt/
fltmain.htm said that the proof
 Wiles is based on two theorems:

   Theorem A (Gerhard Frey, 1982, proved
Ken Ribet with Jean-Pierre Serre,
 1986):

   If there is a solution (x, y, z, n) to the
Fermat equation, then the elliptic curve
defined by the equation is semistable but
 not modular.

    (So-called epsilon conjecture)

   Theorem B (for the first time expressed Yutaka
Taniyama, 1955, in a general form given by Goro
Shimura and Andre Weil, Andrew proved
 Wiles with the help of Richard Taylor, 1993-95):

   All semistable elliptic curves with
 rational coefficients are modular.

   (So-called Taniyama-Shimura con
jecture)

   Wikipedia explains that, under the name
elliptic curve is hidden diophantine equation
equation y ¤ = x · (xa ^ n) · (x + b ^ n), where a and b -
parameters of the equation Fermat's Last Theorem
a ^ n + b ^ n = c ^ n.



   http://www.geocities.com/fermatnow/flt/
flt9.htm argues that the evidence
Wiles (129 pages) is here:
http://math.stanford.edu/ ~ lekheng / flt /
index.html (Andrew Wiles, Modular elliptic
curves and Fermat's Last Theorem, Annals
one hundred and forty-one of Mathematics (1 995), 443-551; 
Andrew Wiles and Richard Taylor, Ring-theoretic

properties of certain Hecke algebras,
Annals of Mathematics 141 (1995), 553-572)



   I'm not going to sign any
for or against Wiles. I only know
that the 100 pages without a single mistake to write
virtually impossible. Same number of components
competence of the auditors nastolno small,
ensure that no errors nel
SC. We will wait for checks not we take
metsya computer. However, is not yet known
on a system of axioms based dokazate
lstvo, and the first thing that will need to
 compilation of test programs.

   One way or another (http://www.princeton.
edu/pr/news/98/q3/0827-wiles.htm), A. Wiles
already received a special medal (18 August
1998), and its proof has been shown
documentary (8 September 1998).
Moreover, Ruth Stevens wrote that Wiles
September 2, 2005 receives the "2005 Shaw Prize
in Mathematical Sciences ", a major award
administered by the Shaw Foundation of
Hong Kong, the sum of $ 1 million.
But he decided to Göttingen University,
so far failed to learn.



   Sample survey "fermatistov" may
serve the proposed James Constant, 2003
(Http://www.coolissues.com/mathematics/
Fermat / fermat.htm) is very short, "the proof
proof of "Fermat's Last Theorem by bi
nomial series. Already in the 2 nd formula author
allowing gross lapse - the first member
a number of what he gets is not 1, but something has
yuschee minus one factor in the numerator;
even the second term he has a zero factor
carriers in the numerator. A number 6 in the formula and
subsequent explanation (based on the use
Roll The author believes that the remainder
member, not tending to zero, should be
irrational), he essentially "refuted" perturbation
zhnost solutions in positive integers the equation
equation x ¤ + y ¤ = z ¤, which is not going to
 do.

   Recently in this field has decided to mark
Xia and our countryman:


   Mathematician from Omsk, Alexander Ilyin UP
Seemed "Great" Fermat's theorem. "The proof
The proof need 15 minut.Dokazatelstvo as
one would expect, lies within the medium
 days of school. "

   The proof will be found in 2
year for which mathematics should be verified
We say the calculations. The theorem does not matter
 in practice, however, this event ...

   

               (Recorded SWW)


   Then, I remember, was a close-up of
proved board with sinuses.



   I suppose there is hardly necessary to describe
the role of each of the scientists who have had relevance to
proofs of the theorem for the special case
ev. This can be (and quite easily, having
access to the internet) to write a book.
Therefore, instead recommend an article vysheupo
myanutogo David Shay (http://www.geocities.
 com / fermatnow / flt / index.htm)

   In conclusion, we must mention funny
fact: Shay at http://www.geocities.com/
fermatnow/flt/flt4.htm wrote that the theorem
four-color, too, proved (Wolfgang
Haken and Karl Appel, 1976), however, it is up to
The proof is still bigger than uaylzovskoe
the proof of Fermat's Last Theorem.