41. Marginal Revolution: Andrew Wiles And Fermat's Last Theorem Aug 29, 2010 Here is one of my all time favorite documentaries, the 45 minute Fermat s Last Theorem made by Simon Singh and John Lynch for the BBC in http://www.marginalrevolution.com/marginalrevolution/2010/08/andrew-wiles-and-fe

42. Fermat's Last Theorem Poetry Challenge The proof of Fermat s last theorem by Andrew Wiles and Richard Taylor was presented to an audience of over 300 people during a tenday conference at Boston http://www.math.uic.edu/~jeremy/poetry.html

Fermat's Last Theorem Poetry Challenge While you're here, you can check out my home page, or visit the UIC math department. The proof of Fermat's last theorem by Andrew Wiles and Richard Taylor was presented to an audience of over 300 people during a tenday conference at Boston University in August, 1995. At that conference, I issued a poetry challenge asking for occasional verse to celebrate the proof. While the authors' anonymity was preserved at the meeting, all things are revealed in time. If you would like to contribute to this poetry competition, please send your masterpiece to Jeremy Teitelbaum . The editor's decisions regarding suitability for publication in this forum are arbitrary, personal, and final. With thanks to all of the participants, here are the entries (in no particular order). Author: John Fitzgerald Fermat's last theorem Is a puzzling queer one: Squares of a plane Wholely squared, aren't arcane; Cubic volumes and more, though Have no solutions, I'm sure; so All postulates otherwise Will prove other than wise.

43. Timeline Of Fermat's Last Theorem Fermat s Last Theorem (FLT) states that nth power of a positive integer cannot be expressed as the sum of nth powers of two smaller positive integers, http://www.public.iastate.edu/~kchoi/time.htm

Drink to Me (Carolan, sequenced by Barry Taylor) Timeline of Fermat's Last Theorem when who what 1900 BC Babylonians A clay tablet, now in the museum of Columbia University, called Plimpton 322, contains 15 triples of numbers. They show that a square can be written as the sum of two smaller squares, e.g., 5 circa 530 Pythagoras Pythagoras was born in Samos. Later he spent 13 years in Babylon, and probably learned the Babylonian's results, now known as the Pythagorean triples. Pythagoras was also the founder of a secret society that studied among others "perfect" numbers. A perfect number is one that is the sum of its multiplicative factors. For instance, 6 is a perfect number (6 = 1 + 2 + 3). Pythagoreans also recognized that 2 is an irrational number. circa 300 BC Euclid of Alexandria Euclid is best known for his treatise Elements circa 400 BC Eudoxus Eudoxus was born in Cnidos, and became a colleague of Plato. He contributed to the theory of proportions, and invented the "method of exhaustion." This is the same method employed in integral calculus. circa 250 AD Diophantus of Alexandria Diophantus wrote Arithmetica , a collection of 130 problems giving numerical solutions, which included the Diophantine equations , equations which allow only integer solutions (e.g, ax + by = c, x

44. ZPEnergy.com New Energy Revolution There are currently, 131 guest(s) and 9 member(s) that are online. You are Anonymous user. http://www.zpenergy.com/modules.php?name=News&file=article&sid=1609

45. Proof Of The Fermat S Last Theorem File Format PDF/Adobe Acrobat Quick View http://files.asme.org/MEMagazine/Articles/Web/15299.pdf

46. Re: MATH : Fermat's Last Theorem: Did Fermat Have Proof Or Did He Guess? Re MATH Fermat's Last Theorem did Fermat have proof or did he guess? Date Mon Feb 16 142642 1998 Posted By William A. Wheaton, Staff Scientist, IPAC, Infrared http://www.madsci.org/posts/archives/1998-02/887691432.Ph.r.html

MadSci Network : Physics Query: Re: MATH : Fermat's Last Theorem: did Fermat have proof or did he guess? Date: Mon Feb 16 14:26:42 1998 Posted By: William A. Wheaton, Staff Scientist, IPAC, Infrared Processing Center Area of science: Physics ID: 887560977.Ph Message: Fermat Theorem This is definitely not my field of expertise, but I am pretty sure that it is the consensus of the experts that Fermat was probably mistaken. First, the problem has received an enormous amount of attention over the centuries from the very best mathematicians. The fact that none of them found a short proof (supposing Fermat's proof was not much longer than the margin would hold this is suggested by Fermat's description of it as "truly wonderful"), nor indeed any proof at all, makes one wonder. Second, it seems clear that if Fermat had a proof, it must have been quite different than the one we have today. For the prerequisites, the mathematical concepts used in the proof, on which Wiles was able to build, had not even been developed in Fermat's time. Third, there are some shorter partial proofs, and I think even some short, seductive, but mistaken ones, that have been discovered over the years, some by good mathematicians. Possibly Fermat's proof was one of these. Mathematicians do often guess, but of course a guess is never a proof! The inspired guess leads the way, motivates and guides the hard struggle to construct a rigorous proof, but no honest mathematician would ever knowingly say he had proved something that he had only guessed. But a strong hunch can lead you to believe a conjecture is true, and then it is not too uncommon to overlook subtle logical flaws in the proof constructed to establish the guess beyond all doubt. Wiles himself at first fell victim to such an error, which, fortunately, he was able to repair.

47. Modular Arithmetic, Fermat Theorem, Carmichael Numbers - Numericana Modular arithmetic. The generalized theorem of Fermat and its converse versions, including Carmichael numbers and stochastic primality testing. http://www.numericana.com/answer/modular.htm

home index units counting ... physics Final Answers , Ph.D. Modular Arithmetic Mathematics is the Queen of sciences, and arithmetic the Queen of mathematics. Carl Friedrich Gauss (1777-1855) Chinese remainder theorem : Remainders define an integer, within limits. Modular arithmetic : The formal algebra of congruences, due to Gauss. Fermat's little theorem : For any prime p not dividing a a p is 1 modulo p. Euler's totient function f (n) counts the integers coprime to n, from 1 to n. Fermat-Euler theorem : If a is coprime to n, a to the f (n) is 1 modulo n. Carmichael's reduced totient function l ) : A special divisor of the totient. 91 is a pseudoprime to half of the bases coprime to itself. Carmichael Numbers : An absolute pseudoprime n divides a n a for any a Chernik's Carmichael numbers : 3 prime factors (6k+1)(12k+1)(18k+1). Large Carmichael numbers may be obtained in various ways. Conjecture : Any odd integer coprime to its totient has Carmichael multiples. Articles previously on this page: Pseudoprimes to base a The above articles have moved...

48. 1993: Fermat's Theorem Solved A proof of Fermat s last theorem would at best provide a logical demonstration of why no other numbers fit into the equation without actually checking every http://www.capitalcentury.com/1993.html

Andrew Wiles flashes a huge grin after publicly showing off his proof for the first time in 1993. A shy and secretive Princeton University mathematics professor in 1993 unraveled a mystery that had frustrated and intrigued mathematicians for 350 years. Andrew Wiles, fascinated by math problems since age 10, figured out the last theorem of 17th century mathematician Pierre De Fermat, achieving what the most obsessed numbers crunchers of three centuries could not. The Scottish-born Wiles, in a rare interview, said the draw to solve the theorem, which stemmed from Fermat's studies of the ancient Greek text "Arithmetic," was so strong because the theorem was so simple-sounding. It says that while the square of a whole number can be broken into two other squares of whole numbers, the same cannot be done with cubes or higher powers. The theorem is based on the ancient equation developed by sixth century mathematician Pythagoreas, "X squared plus Y squared equals Z squared." The equation guided Pythagoreas' famous theory for calculating the hypotenuse of a triangle. Although Fermat himself claimed to have already proved the theorem, his notes were lost, and mathematicians, none of whom were able to solve it until Wiles, had often doubted the existence of a formal proof.

49. Compiler Theory, Quantum Physics And Fermat's Theorem « Otaku, Cedric's Blog May 2, 2010 Compiler theory, quantum physics and Fermat s theorem. It s not very often I come across a post that talks about math and programming that http://beust.com/weblog/2010/05/02/compiler-theory-quantum-physics-and-fermats-t

50. Little Fermat Theorem X (p1) - Y (p-1) = m X and Y not equal to p, a prime X (p-1) (-1) - Y (p-1) (+1) =m Subtract and Add a 1 (X (p-1)-1) - (Y (p-1)-1) = m Associate and factor a (-1) http://home.earthlink.net/~usondermann/little2.html

X (p-1) - Y (p-1) = mod(p) X (p-1) - Y (p-1) = m X and Y not equal to p, a prime X (p-1) (-1) - Y (p-1) (+1) =m Subtract and Add a 1 (X (p-1) -1) - (Y (p-1) -1) = m Associate and factor a (-1) p(t) - p(u) = m Factor p via Little Fermat Theorem p(t-u) = pk Substituting m=pk and Factoring p X (p-1) - Y (p-1) = mod(p) Substituting and applying mod

51. Bluffer's Guide To Fermat's Last Theorem Allan Adler, Lecture notes on Fermat s last theorem, University of Rhode Island, June 7–August 12, 1993 (original files available here) http://math.stanford.edu/~lekheng/flt/

Bluff your way in Fermat's Last Theorem The proof Annals of Mathematics , 2nd Series, Front Matter Andrew Wiles, " Modular elliptic curves and Fermat's last theorem Andrew Wiles and Richard Taylor, " Ring-theoretic properties of certain Hecke algebras Back Matter Alternative version of the Wiles paper and the Wiles-Taylor paper (courtesy of Derek Buchanan). A review Kenneth A. Ribet Also of interest: the proof of Shimura-Taniyama-Weil conjecture Fred Diamond, " On deformation rings and Hecke rings Annals of Mathematics , 2nd Series, Brian Conrad, Fred Diamond and Richard Taylor, " Modularity of certain potentially Barsotti-Tate Galois representations Journal of the American Mathematical Society Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor, " On the modularity of elliptic curves over Q : wild 3-adic exercises Journal of the American Mathematical Society The bluffer's guide to Fermat's Last Theorem The papers above are provided for the benefit of those without access to JSTOR or JAMS but would nevertheless like to know what the proof of the most celebrated theorem in Mathematics looks like.

52. Generalization Of Euler Fermat Theorem Article on Generalization Of Euler Fermat Theorem where and depend on and , also is one more than the number of steps in the algorithm, while is a divisor of , and they are http://myyn.org/m/article/generalization-of-euler-fermat-theorem/

53. Fermat's Last Theorem - The Theorem And Its Proof: An Exploration Of Issues And Speaker Robert Osserman, Lenore Blum, Ken Ribet, John Conway, Lee Dembart. http://www.archive.org/details/fermats_last_theorem

Web Moving Images Texts Audio ... UChannel Search: All Media Types Wayback Machine Moving Images Community Video Ephemeral Films Movies Sports Videos Videogame Videos Vlogs Youth Media Texts American Libraries Canadian Libraries Universal Library Community Texts Project Gutenberg Biodiversity Heritage Library Children's Library Additional Collections Audio Community Audio Grateful Dead Live Music Archive Netlabels Non-English Audio Radio Programs Software CLASP Tucows Software Library CD Bulletin Board Software archive Education Math Lectures from MSRI Chinese University Lectures AP Courses from MITE MIT OpenCourseWare UChannel Forums FAQs Advanced Search Anonymous User login or join us Upload Open Educational Resources Math Lectures from MSRI Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas Related Subjects Mathematics lecture View educational material Run time: 1:38:10 Video Files Fermat's Last Theorm- The Theorm and it's Proof: An Exploration of Issues and Ideas Other Files All Files: HTTP Resources Bookmark Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas (July 28, 1993)

54. Fermat's Last Theorem: Report From A Conference On The Proof By Andrew J. Wiles A description of the underlying ideas of Wiles proof of Fermat s Last Theorem. An explaination of the proof for the mathematicallyminded non-mathematician http://rendezvous.com/tangledweb/conferences/fermat/index.html

Back to The Tangled Web FERMAT'S LAST THEOREM Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caparet. By contrast it is impossible to separate a cube into two cubes, a fourth power into two fourth powers, or in general any power above the second into two powers of the same degree. I have found a truly marvelous proof of this theorem but this margin is too narrow to contain it. A Conference on the proof of Andrew J. Wiles Boston University August 9-18th, 1995 Interim Reports by Roy Lisker Exclusive to The Tangled Web The Romance of Fermat's Last Theorem Extensive background information about the theorem as well as an analysis of prior "proofs" and excerpts of letters from individuals who claim to have solved Fermat's Last Theorem using only elementary arithmetic. August 11, 1995 The field proves to be a hybrid of number theory and algebraic geometry, with surprisingly little number theory. August 12, 1995

55. Re: Wiles Proof Of Fermat Theorem be able to refer to them in formulae of a formal system. definitions of ordinals. amateur comes up with, and is, in the end, nothing but excited fluff. http://sci.tech-archive.net/Archive/sci.math/2008-11/msg02049.html

Re: Wiles proof of Fermat theorem From aatu.koskensilta@xxxxxx Date : 18 Nov 2008 13:36:54 +0200 Aatu Koskensilta wrote: Yes, in many ways an expert in some branch of mathematics may well resemble an amateur when it comes to another. Some even go for outright crankhood! Would you dare to mention names for the latter case? N.J. Wildberger comes to mind. Alas, I'm too timid to name any other names. It could ruin my academic career. Well, probably not, so I'll name John Nash who has perhaps not opted for full crankhood but whose musings on logic are well nigh incomprehensible, and not at all in the good sense of being highly advanced. In a talk available at his home page Nash for example reports the following remarkable discovery In my own thinking, after a long period of study and after encountering the problem that although one could talk about "ideal" (or mathematical) ordinals one would need names for them in order to be able to refer to them in formulae of a formal system. Ultimately I came to the idea that instead of associating the levels of a system with ordinal numbers they could instead be associated with definitions of ordinals.

56. Chike Obi And Fermat S Last Theorem By far, the best known of Fermat s many theorems, it states that the equation xn +yn=zn; where x,y,z, and n are positive integers, has no solution if n is http://www.math.buffalo.edu/mad/PEEPS/obi-chike-fermat.html

57. Mbox: Wiles' Proof Of The Fermat Theorem Wiles' proof of the Fermat Theorem Zdzislaw Meglicki (Zdzislaw.Meglicki@cisr.anu.edu.au) Mon, 14 Nov 1994 160644 +1100 (EST) Messages sorted by Next message Andrzej http://mizar.org/qed/mail-archive/volume-2/0077.html

Wiles' proof of the Fermat Theorem Zdzislaw Meglicki Zdzislaw.Meglicki@cisr.anu.edu.au Mon, 14 Nov 1994 16:06:44 +1100 (EST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Andrzej Trybulec: "Rusty Lusks question" Previous message: Lyle Burkhead: "Platonism" In the last issue of the New Scientist, I've found a brief note that Andrew Wiles has fixed the problem in his proof of the last Fermat Theorem, which should really be renamed to "Fermat-Wiles" theorem, if the proof is correct. Chatting about it with John Slaney, we came to the conclusion that the verification of that proof would be an ideal Holy Grail for QED. In other words, if you could use the QED system in order to verify a proof as complex and convoluted as Wiles' proof, you'd demonstrate to all mathematicians enormous usefulness of such a system. Greetings to all, Zdzislaw Meglicki, Zdzislaw.Meglicki@cisr.anu.edu.au The Australian National University, Canberra, A.C.T., 0200, Australia, fax: +61-6-249-0747, tel: +61-6-249-0158 Next message: Andrzej Trybulec: "Rusty Lusks question" Previous message: Lyle Burkhead: "Platonism"

58. The Fermat–Euler Theorem V.10 Fermat S Last Theorem File Format PDF/Adobe Acrobat Quick View http://press.princeton.edu/chapters/gowers/gowers_V_10.pdf

59. Euler-Fermat Theorem Definition Of Euler-Fermat Theorem In The Free Online Encyc Euler's theorem ′ȯi lərz ‚thir əm (mathematics) For any polyhedron, VE + F = 2, where V, E, F represent the number of vertices, edges, and faces respectively. http://encyclopedia2.thefreedictionary.com/Euler-Fermat theorem

60. Fermat's Last Theorem Feb 20, 1998 Theorem 1 Fermat s Last Theorem There are no positive integers x, y, z, and n 2 such that x^n + y^n = z^n. http://www.cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node9.html

Next: Prime Numbers Up: Number Theory Previous: Number Theory Fermat's Last Theorem History of Fermat's Last Theorem Pierre de Fermat (1601-1665) was a lawyer and amateur mathematician. In about 1637, he annotated his copy (now lost) of Bachet's translation of Diophantus' Arithmetika with the following statement: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. In English, and using modern terminology, the paragraph above reads as: There are no positive integers such that x^n + y^n = z^n for . I've found a remarkable proof of this fact, but there is not enough space in the margin [of the book] to write it. Fermat never published a proof of this statement. It became to be known as Fermat's Last Theorem (FLT) not because it was his last piece of work, but because it is the last remaining statement in the post-humous list of Fermat's works that needed to be proven or independently verified. All others have either been shown to be true or disproven long ago. What is the current status of FLT?

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