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| fermat's last theorem solution: Modular Forms and Fermat’s Last Theorem Gary Cornell, Joseph H. Silverman, Glenn Stevens, 2013-12-01 This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource. |
| fermat's last theorem solution: Fermat's Last Theorem Simon Singh, 2022-05-26 Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience - classics which will endure for generations to come. |
| fermat's last theorem solution: 13 Lectures on Fermat's Last Theorem Paulo Ribenboim, 2012-12-06 Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co. |
| fermat's last theorem solution: The Girl who Played with Fire Stieg Larsson, 2010 When the reporters to a sex-trafficking exposé are murdered and computer hacker Lisbeth Salander is targeted as the killer, Mikael Blomkvist, the publisher of the exposé, investigates to clear Lisbeth's name. |
| fermat's last theorem solution: The Last Theorem Arthur C. Clarke, Frederik Pohl, 2008-12-07 The final work from the brightest star in science fiction’s galaxy. Arthur C Clarke, who predicted the advent of communication satellites and author of 2001: A Space Odyssey completes a lifetime career in science fiction with a masterwork. |
| fermat's last theorem solution: Fermat's Last Theorem Harold M. Edwards, 2000-01-14 This introduction to algebraic number theory via the famous problem of Fermats Last Theorem follows its historical development, beginning with the work of Fermat and ending with Kummers theory of ideal factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book. |
| fermat's last theorem solution: Fermat’s Last Theorem Simon Singh, 2012-11-22 ‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’ |
| fermat's last theorem solution: Fermat’s Last Theorem for Amateurs Paulo Ribenboim, 2008-01-21 In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results. |
| fermat's last theorem solution: Abelian l-Adic Representations and Elliptic Curves Jean-Pierre Serre, 1997-11-15 This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one |
| fermat's last theorem solution: Algebraic Number Theory and Fermat's Last Theorem Ian Stewart, David Tall, 2001-12-12 First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it |
| fermat's last theorem solution: Mathematics Keith J. Devlin, 1999 A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms. |
| fermat's last theorem solution: The Simpsons and Their Mathematical Secrets Simon Singh, 2013-01-01 From bestselling author of Fermat's Last Theorem, a must-have for number lovers and Simpsons fans |
| fermat's last theorem solution: Fearless Symmetry Avner Ash, Robert Gross, 2008-08-24 Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory. |
| fermat's last theorem solution: Invitation to the Mathematics of Fermat-Wiles Yves Hellegouarch, 2001-09-24 Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem |
| fermat's last theorem solution: Fermat's Enigma Simon Singh, 2017-03-01 xn + yn = zn, where n represents 3, 4, 5, ...no solution I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain. With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's Nova--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics. |
| fermat's last theorem solution: Learning Modern Algebra Albert Cuoco, Joseph Rotman, 2013 A guide to modern algebra for mathematics teachers. It makes explicit connections between abstract algebra and high-school mathematics. |
| fermat's last theorem solution: Fermat's Last Theorem Amir D. Azcel, Amir D. Aczel, 2007-10-12 Simple, elegant, and utterly impossible to prove, Fermat's last theorem captured the imaginations of mathematicians for more than three centuries. For some, it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Amir D. Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised from the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, Fermat's Last Theorem brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down. |
| fermat's last theorem solution: Local Fields Jean-Pierre Serre, 2013-06-29 The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of local (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of localisation. The chapters are grouped in parts. There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their globalisation) and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the norm map is studied; I have expressed the results in terms of additive polynomials and of multiplicative polynomials, since using the language of algebraic geometry would have led me too far astray. |
| fermat's last theorem solution: Math with Bad Drawings Ben Orlin, 2018-09-18 A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark bad drawings, which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike. |
| fermat's last theorem solution: From Fermat to Minkowski W. Scharlau, H. Opolka, 1985 Translated from the German by Bühler, W.K.; Cornell, G. |
| fermat's last theorem solution: Prime Obsession John Derbyshire, 2003-04-15 In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: On the Number of Prime Numbers Less Than a Given Quantity. In the middle of that paper, Riemann made an incidental remark †a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic †defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark †the Riemann Hypothesis †that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows †subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many †the veritable great white whale of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof †and those who have been consumed by it. |
| fermat's last theorem solution: The Last Problem Eric Temple 1883-1960 Bell, 2021-09-09 This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| fermat's last theorem solution: The Mathematical Career of Pierre de Fermat, 1601-1665 Michael Sean Mahoney, 2018-06-05 Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his truly marvelous demonstration. Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics. |
| fermat's last theorem solution: An Invitation to Arithmetic Geometry Dino Lorenzini, 2021-12-23 Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject. |
| fermat's last theorem solution: The Arithmetic of Elliptic Curves Joseph H. Silverman, 2013-03-09 The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics. |
| fermat's last theorem solution: My Search for Ramanujan Ken Ono, Amir D. Aczel, 2016-04-20 The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity. |
| fermat's last theorem solution: A First Course in Modular Forms Fred Diamond, Jerry Shurman, 2006-03-30 This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included. |
| fermat's last theorem solution: Lie Algebras and Lie Groups Jean-Pierre Serre, 2009-02-07 The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0 A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x). |
| fermat's last theorem solution: Elliptic Curves Lawrence C. Washington, 2008-04-03 Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application |
| fermat's last theorem solution: Algebraic Number Theory Richard A. Mollin, 2011-01-05 Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications. |
| fermat's last theorem solution: Emmy Noether 1882–1935 DICK, 2012-12-06 N 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at tractive and informative mural, about 13 feet long, sponsored by one of the largest com puter manufacturing companies and present ing a brief survey of the history of mathemat ics. Entitled, Men of Modern Mathematics, it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom panied by the following text: Emmy Noether, daughter of the mathemati cian Max, was often called Der Noether, as if she were a man. |
| fermat's last theorem solution: Math Girls 3 Hiroshi Yuki, 2016-05-15 In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilbert's program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Godel stunned the world by proving that Hilbert's goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Godel's incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Godel's famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Godel's Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators. |
| fermat's last theorem solution: LMSST: 24 Lectures on Elliptic Curves John William Scott Cassels, 1991-11-21 A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters. |
| fermat's last theorem solution: How Euler Did Even More C. Edward Sandifer, 2014-11-19 Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context. |
| fermat's last theorem solution: The Devil and Simon Flagg and Other Fantastic Tales Arthur Porges, 2009-05-30 A superb collection of weird fantasy tales by Arthur Porges (1915-2006). Includes four previously unpublished stories. |
| fermat's last theorem solution: A Mathematician's Apology G. H. Hardy, 1992-01-31 G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. |
| fermat's last theorem solution: Diophantus of Alexandria Thomas L. Heath, 1910 |
| fermat's last theorem solution: Fermat's Last Theorem Takeshi Saitō, 2013-11-01 This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics. |
| fermat's last theorem solution: Random Curves Neal Koblitz, 2009-05-03 Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume. Besides his own personal career in mathematics and cryptography, Koblitz details his travels to the Soviet Union, Latin America, Vietnam and elsewhere; political activism; and academic controversies relating to math education, the C. P. Snow two-culture problem, and mistreatment of women in academia. These engaging stories fully capture the experiences of a student and later a scientist caught up in the tumultuous events of his generation. |
| fermat's last theorem solution: Elliptic Curves S. Lang, 2013-06-29 It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points. |
Pierre de Fermat - Wikipedia
Pierre de Fermat (/ fɜːrˈmɑː /; [2] French: [pjɛʁ də fɛʁma]; 17 August 1601 [a] – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal …
FERMAT - AI made for you
Fermat is the Generative AI toolbox used by the best global Fashion & Luxury brands. Design from moodboards, create realistic renders, apply materials and fit garments on virtual models. Get …
FERMÀT: Tailor Every Touchpoint
FERMÀT is the AI native commerce platform that optimizes shopping experiences, leading to best-in-class shopper engagement and conversion. Instantly generate, test, and refine shopping …
Pierre de Fermat | Biography & Facts | Britannica
Pierre de Fermat (born August 17, 1601, Beaumont-de-Lomagne, France—died January 12, 1665, Castres) was a French mathematician who is often called the founder of the modern theory of …
PIERRE DE FERMAT MATHEMATICIAN - The Story of Mathematics
Pierre de Fermat, effectively invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician.
Pierre de Fermat - National MagLab
Pierre de Fermat was a lawyer by occupation, but possessed one of the greatest mathematical minds of the seventeenth century. He made major contributions to geometric optics, modern …
Pierre de Fermat - Rutgers University
Pierre de Fermat was one of the most brilliant and productive mathematicians of his time, making many contributions to the differential and integral calculus, number theory, optics, and analytic …
Pierre de Fermat - Biography, Facts and Pictures - Famous Scientists
Pierre de Fermat was one of the greatest mathematicians in history, making highly significant contributions to a wide range of mathematical topics. He was a guiding light in the invention of …
Pierre de Fermat Facts & Biography | Famous Mathematicians
Pierre de Fermat, one of the prominent mathematicians of the 17th century, is better known for his contribution towards development of infinitesimal calculus. He was also a lawyer in terms of …
Pierre de Fermat - History of Math and Technology
Pierre de Fermat (1607–1665) was a French mathematician, lawyer, and polymath whose profound contributions transformed the landscape of mathematics. Often regarded as one of the founders …
Pierre de Fermat - Wikipedia
Pierre de Fermat (/ fɜːrˈmɑː /; [2] French: [pjɛʁ də fɛʁma]; 17 August 1601 [a] – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal …
FERMAT - AI made for you
Fermat is the Generative AI toolbox used by the best global Fashion & Luxury brands. Design from moodboards, create realistic renders, apply materials and fit garments on virtual models. …
FERMÀT: Tailor Every Touchpoint
FERMÀT is the AI native commerce platform that optimizes shopping experiences, leading to best-in-class shopper engagement and conversion. Instantly generate, test, and refine …
Pierre de Fermat | Biography & Facts | Britannica
Pierre de Fermat (born August 17, 1601, Beaumont-de-Lomagne, France—died January 12, 1665, Castres) was a French mathematician who is often called the founder of the modern …
PIERRE DE FERMAT MATHEMATICIAN - The Story of Mathematics
Pierre de Fermat, effectively invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician.
Pierre de Fermat - National MagLab
Pierre de Fermat was a lawyer by occupation, but possessed one of the greatest mathematical minds of the seventeenth century. He made major contributions to geometric optics, modern …
Pierre de Fermat - Rutgers University
Pierre de Fermat was one of the most brilliant and productive mathematicians of his time, making many contributions to the differential and integral calculus, number theory, optics, and analytic …
Pierre de Fermat - Biography, Facts and Pictures - Famous Scientists
Pierre de Fermat was one of the greatest mathematicians in history, making highly significant contributions to a wide range of mathematical topics. He was a guiding light in the invention of …
Pierre de Fermat Facts & Biography | Famous Mathematicians
Pierre de Fermat, one of the prominent mathematicians of the 17th century, is better known for his contribution towards development of infinitesimal calculus. He was also a lawyer in terms of …
Pierre de Fermat - History of Math and Technology
Pierre de Fermat (1607–1665) was a French mathematician, lawyer, and polymath whose profound contributions transformed the landscape of mathematics. Often regarded as one of …
