Fermat's Last Theorem-alternative proofs?
Paul Bruckman
that an alternative and much shorter proof of FLT had been found by V.K.
Gurtu, professor and head of the Math Department at Laxminarayan
Institute of Technology, Nagpur University, Maharashtra, India, and that
Professor Gurtu was in the process of getting his paper approved, having
sent it to "several renowned international journals". Since then, I
have heard nothing about this. It seems to me as well that a much
shorter and simpler proof of FLT should be available besides the
109-page proof of Andrew Wiles. What can you tell me about this
alternative proof? Has it been published? Was it found to be
erroneous?
Also, about two years ago, I was in contact with a Professor Malvina
Baica at the U.of Wisconsin, Whitewater, who claimed that she had proved
FLT using an extension of continued fractions. I looked at her
development, but I could see no proof there. Admittedly, I am not
sufficiently skilled to give her alleged proof a fair reading, but I
have friends and colleagues that would have the sufficient expertise to
do so. However, when I tried to put them in contact with Dr. Baica, she
stopped communicating with me. I would be interested in hearing if you
or any of your colleagues have heard of either Dr. Gurtu or Dr. Baica
and their efforts at proving FLT.
Sincerely, Paul Bruckman
Robin Chapman
Paul Bruckman <bruc...@silcon.com> wrote:
> I read an article in some newspaper not long ago (within the past
year)
> that an alternative and much shorter proof of FLT had been found by
V.K.
> Gurtu, professor and head of the Math Department at Laxminarayan
> Institute of Technology, Nagpur University, Maharashtra, India, and
that
> Professor Gurtu was in the process of getting his paper approved,
having
> sent it to "several renowned international journals". Since then, I
> have heard nothing about this. It seems to me as well that a much
> shorter and simpler proof of FLT should be available besides the
> 109-page proof of Andrew Wiles.
Surely everybody would like a short and simple proof of FLT.
And most of us would like it to be correct as well.
In January there was some correspondence about Gurtu on sci.math.
See the thread beginning at
http://www.deja.com/=dnc/getdoc.xp?AN=429366514
Apart from the announcement in The Hindu newspaper at
http://www.webpage.com/hindu/daily/990105/02/0205000h.htm
there seemed to be no other information available on Gurtu's argument.
I would certainly appreciate any further information on Gurtu's claim.
> Also, about two years ago, I was in contact with a Professor Malvina
> Baica at the U.of Wisconsin, Whitewater, who claimed that she had
proved
> FLT using an extension of continued fractions. I looked at her
> development, but I could see no proof there. Admittedly, I am not
> sufficiently skilled to give her alleged proof a fair reading, but I
> have friends and colleagues that would have the sufficient expertise
to
> do so. However, when I tried to put them in contact with Dr. Baica,
she
> stopped communicating with me.
For Baica's manuscript see her home page at
http://math.uww.edu/~baicam/
There are many webpages claiming to give proofs of FLT. Several may
be found in Dan Piponi's useful survey of "alternative" mathematics
and physics, "Not the Crackpot Files" at
http://www.tanelorn.demon.co.uk/Physics/pots.html
Perhaps this discussion would be more suitable for the wider
audience of sci.math.
--
Robin Chapman
http://www.maths.ex.ac.uk/~rjc/rjc.html
"They did not have proper palms at home in Exeter."
Peter Carey, _Oscar and Lucinda_
Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.
G. A. Edgar
> I read an article in some newspaper not long ago (within the past year)
Unfortunately, newspapers are often not very reliable when it
comes to mathematical matters.
> that an alternative and much shorter proof of FLT had been found by V.K.
> Gurtu, professor and head of the Math Department at Laxminarayan
> Institute of Technology, Nagpur University, Maharashtra, India, and that
> Professor Gurtu was in the process of getting his paper approved, having
> sent it to "several renowned international journals". Since then, I
> have heard nothing about this. It seems to me as well that a much
> shorter and simpler proof of FLT should be available besides the
> 109-page proof of Andrew Wiles. What can you tell me about this
> alternative proof? Has it been published?
No. At least not in a journal covered by Mathematical Reviews.
> Was it found to be erroneous?
That would be my guess.
> Also, about two years ago, I was in contact with a Professor Malvina
> Baica at the U.of Wisconsin, Whitewater, who claimed that she had proved
> FLT using an extension of continued fractions. I looked at her
> development, but I could see no proof there. Admittedly, I am not
> sufficiently skilled to give her alleged proof a fair reading, but I
> have friends and colleagues that would have the sufficient expertise to
> do so. However, when I tried to put them in contact with Dr. Baica, she
> stopped communicating with me.
Mathematical Reviews does cover Malvina Baica's FLT work.
It seems to have been published in a Bulgarian journal
"Notes on Number Theory and Discrete Mathematics".
The reviewer (Matthew Granville) kindly says that there are not enough
details given for him to judge the correctness of the proof.
--
Gerald A. Edgar ed...@math.ohio-state.edu
Department of Mathematics telephone: 614-292-0395 (Office)
The Ohio State University 614-292-4975 (Math. Dept.)
Columbus, OH 43210 614-292-1479 (Dept. Fax)
Boudewijn Moonen
>
> I read an article in some newspaper not long ago (within the past year)
> Gurtu, professor and head of the Math Department at Laxminarayan
> Institute of Technology, Nagpur University, Maharashtra, India, and that
> Professor Gurtu was in the process of getting his paper approved, having
> sent it to "several renowned international journals". Since then, I
> have heard nothing about this. It seems to me as well that a much
> shorter and simpler proof of FLT should be available besides the
> 109-page proof of Andrew Wiles. What can you tell me about this
> erroneous?
>
> Baica at the U.of Wisconsin, Whitewater, who claimed that she had proved
> FLT using an extension of continued fractions. I looked at her
> development, but I could see no proof there. Admittedly, I am not
> sufficiently skilled to give her alleged proof a fair reading, but I
> have friends and colleagues that would have the sufficient expertise to
> do so. However, when I tried to put them in contact with Dr. Baica, she
> or any of your colleagues have heard of either Dr. Gurtu or Dr. Baica
> and their efforts at proving FLT.
>
> Sincerely, Paul Bruckman
A link to Malvina Baica can be found at Dan Piponi's page
http://www.tanelorn.demon.co.uk/Physics/pots.html
It works out as
http://math.uww.edu/~baicam/b4-gifs.html
and was active as I tried it out. The material there looks cranky at
first sight.
Regards
--
Boudewijn Moonen
Institut fuer Photogrammetrie der Universitaet Bonn
Nussallee 15
D-53115 Bonn
GERMANY
e-mail: Boudewij...@ipb.uni-bonn.de
Tel.: GERMANY +49-228-732910
Fax.: GERMANY +49-228-732712
William C Waterhouse
_Algebras, Groups, and Geometries_ was once (partially) respectable,
so I was sad to find that Volume 15, no 3 (1998) contains three
(yes, count 'em: three!) supposed elementary proofs of FLT:
Athanasopoulos, S. N. An algebraic proof of Fermat's last theorem.
247--288.
Obi, C. Fermat's last theorem. 289--298.
Trell, E. Isotopic proof and re-proof of Fermat's last theorem
verifying Beal's conjecture. 299--318.
There is an editorial statement that some of the editors opposed their
publication, but they were being printed anyway, and comments would
be printed later if any were submitted. The third proof refers
to the "hadronic mathematics" of Santilli, who is the publisher
and chief editor, so we can probably guess how the decision was
reached. For all I know, a fourth paper there also claims to contain
a proof; it is
Jiang, C. X. On the Fermat-Santilli isotheorem. 319--349.
William C. Waterhouse
Penn State
Tapio Hurme
first proof based on the elliptic curves is very old. I wish somebody, who
can read German and French, would revisit and comment the original papers
and especially who disproved Von Maillet's (and Bachmann's) proof.
Prof. Dr. Paul Bachmann :" Das Fermatproblemen in seiner bischerigen
Entwicklung"
Berlin und Leipzig 1919, (Walter de Gruyter & Co) pp156 - 157. (Felix Klein
zum funfzigjahrigen Doktorjubileum)
On the page 156 (51) Bauchmann writes that von Maillet has proofed
Equation 1: x^p+y^p=C*z^p has no solution p>2, because C does not equal to
1.
Bachmann refers also Kummer.
He gives also two references:
1) Acta Math 24 s 247 (written as it appears in the footnote)
and
2) Annali di Math (3) 12 s 145 (written as it appears in the footnote)
Finally Bachmann writes (my translation from Germany): Those who are
interested in the original work should refer:
3) "Association Francaise pour avancement des Sciences, St. Etienne, see,
26, 1897, 2me partie p. 156" (written as it appears in the footnote)
1) I do not have the original paper that Bauchmann refers. Thus no comments.
2) According to Bachmann the proof of Von Maillet (partially based on
Kummer's work ?) looks like a modular elliptic curves (see equation 1
above).
Because my German is more bad than my poor English, I would be pleased, if
somebody, who is able to read the original papers, would comment the
validity and the proof of FLT by Von Maillet & Bachmann (possible Kummer -
too). Actually - what is really proofed ?
Additionally - if possible - I'm interested in who has pointed that this
"old proof" is not valid - with references.
Thank you very much for your help.
Tapio
Boudewijn Moonen wrote in message <37C2602B...@ipb.uni-bonn.de>...
|Paul Bruckman wrote:
|>
|> I read an article in some newspaper not long ago (within the past year)
|> that an alternative and much shorter proof of FLT had been found by V.K.
|> Gurtu, professor and head of the Math Department at Laxminarayan
|> Institute of Technology, Nagpur University, Maharashtra, India, and that
|> Professor Gurtu was in the process of getting his paper approved, having
|> sent it to "several renowned international journals". Since then, I
|> have heard nothing about this. It seems to me as well that a much
|> shorter and simpler proof of FLT should be available besides the
|> 109-page proof of Andrew Wiles. What can you tell me about this
|> alternative proof? Has it been published? Was it found to be
|> erroneous?
(snip)
|> Sincerely, Paul Bruckman