I need to know everything about the [still unproven?] Ferma Theorem -
the story behind it (started 350 years ago), the different approaches
for it's proving during these years, the prizes that have been raised
for that and, eventually, it's latest and complete prove.

The name of a book on this issue (and where to buy it) will be enough.

Mathematics is a hobby for me. Most of the info I know about this
famous mathematical problem is gathered from a popullar-science
magazines and books. The reason I'm interested is that, as a
programmer, I try to understand the principle behind it (the
impossibilities that it states) from a non-mathematician's point of
view.

Any other up-to-date book or site about populat [applied?]
mathematical problems (with less formulas and more diagrams:) will be
very interesting for me.

I assume that you're seeking information on Fermat's Last Theorem, one
of the most famous problems in the history of mathematics. I've
gathered information on several books that I believe you'll find
interesting. Each of these books is available for purchase from
Amazon.com. For a description of the book's contents, ISBN number, and
other details, just click the Amazon link that is under the book's
title.

======================================================================

Fermat's Last Theorem (Paperback)
by Simon Singh 

Amazon.com
http://www.amazon.com/gp/product/1841157910

======================================================================

Fermat's Enigma: The Epic Quest to Solve the World's Greatest
Mathematical Problem (Paperback)
by SIMON SINGH, JOHN LYNCH 

Amazon.com
http://www.amazon.com/gp/product/0385493622

======================================================================

From Fermat to Minkowski : Lectures on the Theory of Numbers and Its
Historical Development (Undergraduate Texts in Mathematics)
(Hardcover)
by W. Scharlau, H. Opolka, W.K. Bühler (Translator), G. Cornell (Translator) 

Amazon.com
http://www.amazon.com/gp/product/0387909427

======================================================================

13 Lectures on Fermat's Last Theorem (Hardcover)
by Paulo Ribenboim 

Amazon.com
http://www.amazon.com/gp/product/0387904328

======================================================================

Notes on Fermat's Last Theorem (Hardcover)
by Alfred J. van der Poorten

Amazon.com 
http://www.amazon.com/gp/product/0471062618

======================================================================

Fermat's Last Theorem : Unlocking the Secret of an Ancient
Mathematical Problem (Paperback)
by Amir D. Aczel

Amazon.com 
http://www.amazon.com/gp/product/0385319460

======================================================================

Algebraic Number Theory and Fermat's Last Theorem (Hardcover)
by Ian Stewart, David Tall 

Amazon.com 
http://www.amazon.com/gp/product/1568811195

======================================================================

Invitation to the Mathematics of Fermat-Wiles (Hardcover)
by Yves Hellegouarch 

Amazon.com 
http://www.amazon.com/gp/product/0123392519

======================================================================

Fermat's Last Theorem for Amateurs (Hardcover)
by Paulo Ribenboim 

Amazon.com 
http://www.amazon.com/gp/product/0387985085

======================================================================

13 Lectures on Fermat's Last Theorem (Hardcover)
by Paulo Ribenboim

Amazon.com 
http://www.amazon.com/gp/product/0387904328

======================================================================

The World's Most Famous Math Problem : The Proof of Fermat's Last
Theorem and Other Mathematical Mysteries (Paperback)
by Marilyn vos Savant 

Amazon.com 
http://www.amazon.com/gp/product/0312106572

======================================================================

Fermat's Last Theorem : A Genetic Introduction to Algebraic Number
Theory (Graduate Texts in Mathematics) (Paperback)
by Harold M. Edwards 

Amazon.com 
http://www.amazon.com/gp/product/0387950028

======================================================================

Modular Forms and Fermat's Last Theorem (Hardcover)
by Gary Cornell (Editor), Joseph H. Silverman (Editor), Glenn Stevens (Editor) 

Amazon.com
http://www.amazon.com/gp/product/0387946098

======================================================================

Number Theory 1: Fermat's Dream (Translations of Mathematical
Monographs) (Paperback)
by Kazuya Kato, Nobushige Kurokawa, Takeshi Saito, Masaeo Kuwata (Translator) 

Amazon.com
http://www.amazon.com/gp/product/082180863X

======================================================================

The Fermat Proof (Paperback)
by C. J. Mozzochi 

Amazon.com
http://www.amazon.com/gp/product/1412022037

======================================================================

Fermat's Last Theorem (Hardcover)
by Ran Van Vo 

Amazon.com
http://www.amazon.com/gp/product/0759654743

======================================================================

Wikipedia's article on Fermat's Last Theorem may be of interest to
you. Be sure to check the links and bibliography at the bottom of the
article:

Wikipedia: Fermat's Last Theorem
http://en.wikipedia.org/wiki/Fermat's_last_theorem

======================================================================

My Google search strategy:

Google Web Search: isbn fermat theorem
://www.google.com/search?hl=en&q=isbn+fermat+theorem

======================================================================

I hope this is helpful! If anything is unclear or incomplete, or if a
link doesn't work for you, please request clarification; I'll gladly
offer further assistance before you rate my answer.

Best regards,
pinkfreud

---

Request for Answer Clarification by shashko-ga on 22 Mar 2006 14:54 PST

Yeah, it turns out it's an easy question :) I didn't know that (had to
google first!:)

Ok, but what about the second part of my question - the online
resources on such and similar issues?

I hate paper books (although I prefer them) because they tend to form
piles and stay half-read, especially when they are not well written :)
I.e., I can't buy all these books just to browse them and choose the
best to read it. I would preffer an online source of info even if it's
not about this particular problem.

I.e, some more links, please? I have a search-a-phobia :))

---

Request for Answer Clarification by shashko-ga on 22 Mar 2006 15:21 PST

Also: As far as I know, there is (was) a huge premium, about a million
$$, for the one who proves it a 100%. I read this 15 years ago, I
don't know what is it's current status (proven or still not), who or
which association has organized this prize but I'm shure that there
is, if not a site, at least an official page devoted to this issue.

---

Clarification of Answer by pinkfreud-ga on 22 Mar 2006 15:54 PST

I'll do some additional research and get back to you tomorrow, if that
is acceptable. In the meantime, please check the Wikipedia links.
There are several fascinating sites there.

http://en.wikipedia.org/wiki/Fermat%27s_last_theorem#External_links_and_references

One of my favorites:

http://www.fermatslasttheorem.blogspot.com/

Best regards,
pinkfreud

---

Clarification of Answer by pinkfreud-ga on 22 Mar 2006 15:58 PST

You'll also find lots of good references here:

http://mathworld.wolfram.com/FermatsLastTheorem.html

~pinkfreud

---

Clarification of Answer by pinkfreud-ga on 23 Mar 2006 11:27 PST

For your browsing pleasure, I've put together a collection of links to
sites that I think you'll like. Some of these are specifically on the
subject of Fermat's Last Theorem, and some are about mathematics in
general.

Some links to pages that discuss Fermat's Last Theorem:

Fermat Corner
http://www.simonsingh.net/Fermat_Corner.html

MacTutor History of Fermat's Last Theorem
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html

The Mathematics of Fermat's Last Theorem
http://cgd.best.vwh.net/home/flt/fltmain.htm

Timeline of Fermat's Last Theorem
http://www.public.iastate.edu/~kchoi/time.htm

Fermat's Last Theorem - The story, the history and the mystery
http://www.geocities.com/fermatnow/flt/index.htm

Info about the Wolfskehl Prize:

Fermat?s Last Theorem and the Wolfskehl Prize
http://www.simonsingh.net/Wolfskehl_Prize.html

General mathematics sites that I recommend:

MathWorld (to which I linked above, and which ansel001 has cited in a
comment below) is a treasure-trove of material related to mathematics.
In addition to the Fermat article already mentioned, you'll find
articles and links on many mathematical topics. Just examine the index
on the homepage and click on a subject that interests you.

MathWorld
http://mathworld.wolfram.com/

MathWorld is a creation of Wolfram Research. Wolfram also offers a
very useful site called Wolfram Functions, a collection of thousands
of formulas:

The Wolfram Functions Site
http://functions.wolfram.com/

Other Wolfram sites are linked here:

Wolfram Web Resources
http://www.wolfram.com/webresources.html

PlanetMath is another useful resource for the math buff. In addition
to providing a user-created encyclopedia, PlanetMath offers discussion
forums and research-caliber papers, some of which have not been
published elsewhere.

PlanetMath
http://planetmath.org/

Felynx Cougati discusses several concepts in mathematics, with the use
of many graphics and illustrations:

Felynx Cougati: Selected Topics in Mathematics
http://www.cougati.net/

The Mathematical Atlas is a good collection of articles on a wide
variety of mathematical subjects:

The Mathematical Atlas: a gateway to Mathematics
http://www.math.niu.edu/~rusin/known-math/

In closing, I'd like to put in a good word for the works of Douglas
Hofstadter. You may be familiar with Hofstader as one of the former
authors of the "Mathematical Games" column in "Scientific American"
(with typical quirky wit, Hofstadter renamed the column "Metamagical
Themas" - an anagram of "Mathematical Games"). Douglas Hofstadter is,
in my view, one of the truly great minds of our times. Seldom is
erudition so beautifully mixed with humor. Anyone who enjoys
mathematics as a hobby is likely to find Hofstadter to be a rare
treat. He combines concepts from mathematics, logic, philosophy, and
other intellectual disciplines in a remarkable way that is both
educational and entertaining.

These two books by Hofstader are likely to be of particular interest
to the mathematically-minded reader:

Metamagical Themas
http://www.amazon.com/gp/product/0465045669

Gödel, Escher, Bach
http://www.amazon.com/gp/product/0465026567

The Google Directory's listing for Hofstader:

Google Directory: Hofstadter, Douglas R.
://www.google.com/Top/Computers/Artificial_Intelligence/Creativity/Hofstadter,_Douglas_R./

I hope this provides lots of food for thought! Happy dining!

Best regards,
pinkfreud

---

Clarification of Answer by pinkfreud-ga on 23 Mar 2006 11:32 PST

Much to my embarrassment, I see that I have misspelled 'Hofstadter' a
couple of times in my remarks above. I apologize to Professor
Hofstadter and to the reader. Sometimes the fingers on the keyboard
are more fleet than the mind of the typist. ;-)

~pinkfreud

You guys are GREAT! :-)
Thank you, and thanks to ansel001 too!
When I have time I'll read all this mountain of info... :)

Fermat's Last Theorem, has in fact been proved.

Here is a link to Wolfram Research's MathWorld which discusses it.

http://mathworld.wolfram.com/FermatsLastTheorem.html

Excerpts from the link are below.

Fermat's last theorem is a theorem first proposed by Fermat in the
form of a note scribbled in the margin of his copy of the ancient
Greek text Arithmetica by Diophantus . The scribbled note was
discovered posthumously, and the original is now lost. However, a copy
was preserved in a book published by Fermat's son. In the note, Fermat
claimed to have discovered a proof that the Diophantine equation

x^n + y^n = z^n

has no integer solutions for n>2 and x, y, z not equal to zero.

As a result of Fermat's marginal note, the proposition that the
Diophantine equation

x^n + y^n = z^n

where x,y,z, and n are integers, has no nonzero solutions for n>2 has
come to be known as Fermat's Last Theorem. It was called a "theorem"
on the strength of Fermat's statement, despite the fact that no other
mathematician was able to prove it for hundreds of years.

In 1993, a bombshell was dropped. In that year, the general theorem
was partially proven by Andrew Wiles (Cipra 1993, Stewart 1993) by
proving the semistable case of the Taniyama-Shimura conjecture.
Unfortunately, several holes were discovered in the proof shortly
thereafter when Wiles' approach via the Taniyama-Shimura conjecture
became hung up on properties of the Selmer group using a tool called
an Euler system. However, the difficulty was circumvented by Wiles and
R. Taylor in late 1994 (Cipra 1994, 1995ab) and published in Taylor
and Wiles (1995) and Wiles (1995). Wiles' proof succeeds by (1)
replacing elliptic curves with Galois representations, (2) reducing
the problem to a class number formula, (3) proving that formula, and
(4) tying up loose ends that arise because the formalisms fail in the
simplest degenerate cases (Cipra 1995a).

The proof of Fermat's Last Theorem marks the end of a mathematical
era. Since virtually all of the tools which were eventually brought to
bear on the problem had yet to be invented in the time of Fermat, it
is interesting to speculate about whether he actually was in
possession of an elementary proof of the theorem. Judging by the
tenacity with which the problem resisted attack for so long, Fermat's
alleged proof seems likely to have been illusionary. This conclusion
is further supported by the fact that Fermat searched for proofs for
the cases n=4 and n=5, which would have been superfluous had he
actually been in possession of a general proof.

I don't claim to understand the proof.

Pink,

I didn't see your link to the same sight when I added my comment.  We
must have overlapped.

...to the same site

Mathworld is one of the best sites to look up things pertaining to mathematics.