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Fermat's Last Theorem
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2 von 2 Kunden fanden die folgende Rezension hilfreich.
am 30. August 2004
The book has totally fascintated me - from the first word to the last line. The book allows an real inside into the world of mathematicians and their struggle to meet Fermat's challenge. However, while the main theme is Fermat, Simon Singh still mentions other important mathmaticians, starting with the ancient greeks and Pythagoras, working through the centuries and the mathematical genius. However, while outlining some of the big mathematical achievements, Singh still writes plain English and remains understandable. The book is made even better by the proves in the end of it - 'showing the beauty of Maths.
The book is a "must buy" for anyone if an interest in mathematics. You will be fascinated by it for sure!
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1 von 1 Kunden fanden die folgende Rezension hilfreich.
am 15. September 1998
Pierre de Fermat was a state official in seventeenth century France. Forbidden from fraternizing with the locals (whom he might meet in the course of business) he resorted to a solitary hobby -- mathematics. His talent was prodigious, but he was notorious for leaving only sketches of the proofs of his conjectures for others to complete. Over the centuries, all his conjectures were proved correct by others -- except one, that defied all attempts to crack it. Musing on equations in a tome on arithmetic by classical mathematician Diophantus, Fermat looked at the equation x^n + y^n = z^n, and conjectured that there would be no whole-number solutions for x, y or z where n is any whole number greater than 2. He hinted that he had found a proof -- but never delivered. So simply stated, yet so hard to crack, the problem tantalized generations of mathematicians and would-be-mathematicians. Simon Singh tells the story of how a British-born mathematician working in the US, Andrew Wiles, worked in secret for 7 years, throwing every 20th-century technique at Fermat's puzzle, and eventually solving it. But did he? An error was found in his huge proof, hundreds of pages long, that took "a year of hell" to solve. Writing engagingly about maths is very hard, but Singh cuts through the technicalities to deliver a page-turner worthy of every airport lounge. I cried real tears at the part where Wiles descends from his attic den to announce to his (presumably long-suffering) wife that he had solved the 350-year-old riddle. I did have one or two puzzles of my own: first, I think Singh skates a little too much over certain mathematical technicalities that it would have done no harm to delve into a little, such as the critical field of modular forms. Ian Stewart does not shy from these in his (admittedly terser) 'From here To Infinity'. Second, the puzzle still lingers -- Wiles solved the problem with modern maths that would have been unavailable to Fermat. So did Fermat really have a proof in mind -- or didn't he?
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2 von 2 Kunden fanden die folgende Rezension hilfreich.
am 14. Dezember 2001
Obwohl der eigentliche Beweis für Fermats letztes Problem natürlich für einen Nicht-Mathematiker unverständlich bleiben muss, gelingt es Singh die Suche nach dem Beweis auch dem Laien nachvollziehbar zu machen. Außerdem macht dieses Buch Lust auf Mathe, denn es zeigt einem die Menschen und Leidenschaften hinter den Formeln.
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1 von 1 Kunden fanden die folgende Rezension hilfreich.
am 13. Mai 2013
Ich hatte das Buch aufgrund der guten Bewertung im Vergleich zum hervorragenden 'The Poincare Conjecture' gekauft und bin schwer enttäuscht. Z.B. wird gleich zu Beginn die Absolutheit des mathematischen Beweises gepriesen, der Beweis des Pythagoras aber in den Anhang verbannt, man hätte ihn aber besser ganz weggelassen denn er ist sehr unvollständig und
so wie dort abgedruckt geradezu ein Musterbeispiel dafür wie Fehlschlüsse entstehen können wenn man sich eben nicht an
die Methodik des guten alten Euklid (alles NUR ausgehend von Axiomen und Definitionen logisch zu erschliessen) hält: Solange man nicht weiss ob das Viereck mit Kantenlängen z auch ein Quadrat ist (rechte Winkel) ist seine Fläche eben unbekannt und damit der Beweis nicht erbracht. Das ist einfach schlecht woanders abgeschrieben (was man schon am Wechsel der 'Terminologie' von a,b,c nach x,y,z merkt). In ähnlicher Qualität geht es dann weiter. Das Buch mag sich für Laien gut lesen, führt gerade diese aber eher aufs Glatteis und zu Pseudowissen. Ich kann das Buch daher nicht empfehlen.
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am 16. November 1999
Dieses Buch von Simon Singh beschreibt die Geschichte und Loesung des wichtigsten mathematischen Raetsels: Fermats Theorem. Der Satz von Pythagoras ist vermutlich den meisten aus ihrer Schulzeit bekannt, was aber passiert, wenn man nicht das Quadrat der Zahlen nimmt, sondern ganze Zahlen groesser zwei? Das diese Gleichungen keine Loesungen haben koennen, hat Fermat vor dreihundert Jahren festgestellt, allerdings ohne Beweis. Diesen Beweis zu finden war dreihundert Jahre lang das Ziel vieler hochintelligenter und begabter MathematikerInnen. Erst 1996 wurde dieser Beweis von Wiles gefuehrt und als richtig anerkannt. Mr. Singh beschreibt den Wettkampf um die Beweisfuehrung dieses Theorems, indem er die Geschichte der Mathematik und mathematischer Raetsel erlautert, um dann in einem spannenden Countdown von der endgueltigen Entdeckung der Loesung zu berichten. Das Buch ist einfach und sehr gut verstaendlich geschrieben, es vermittelt ein Bild von mathematischen Gedankengaengen ohne mathematische Hochleistungen vom Publikum zu verlangen. Singh versteht es, Faszination fuer Mathematik zu wecken, die man in sich selber vielleicht nicht vermutet hat. Dieses Buch beherbergt zum Beispiel eine Vielzahl mathematischer Geschichten und Anekdoten, die ich jedem (zukunftigen) Mathelehrer ans Herz legen mochte, der seine Schueler fuer Mathematik begeistern mochte. Haetten meine Mathelehrer das selbe erzaehlerische und motivierende Talent Mathematik zu vermitteln gehabt wie Mr. Singh, haette ich mit Sicherheit mehr Spass an diesem Fach gehabt, als ich es hatte. (wuerde vielleicht heute Mathe studieren, wer weiss...) Dieses Buch ist allen zu empfehlen, die nur ein wenig Spass an logischen Gedanken und Raetseln haben, auch wenn sie nie Lust auf Mathematik hatten oder nichts davon verstanden haben. Es ist auch in Englisch sehr angenehm zu lesen, da es wirklich nicht kompliziert ist. Eint tolles Weihnachtsgeschenk! (Dies ist eine Amazon.de an der Uni-Studentenrezension.)
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am 15. Juni 1998
Great read.I was highly impressed by the fluency of the book. The author has tackled the insides of a very difficult and incomprehendable field not only in a manner that it come to grips with the lay persons but also in a way that he has happened to show the adventures and the joy of doing mathematics! Which is a feat in itself. Every now and then he takes us to the history of Mathematics and it's fore-bearers in such a way that it comes entwined with the history of mankind. I loved it the way he has successfully showed in the end that how the story of Fermat's Theorem has it's roots from the time of Pythagora's and how eventually Andrew Wiles takes the route of the mathematics from that of Greeks to Euler,to Euclid to Gauss and all the way to Shamura and Tanyaman to this day in the 90's; he makes one full circle, in solving this most difficult problem of mathematics.Bravo! However I did find one peice of historical narration out of place in the book which I'd like to point out over here, because if I don't, this review would not be of justice. The author while describing the granduer of the famous library of Alexandria has quoted that the library was brought down to it's demise first by the christians and then later by the Muslim conquerer Hazrath Umer Farooq in the 7th century AD. However the American Historian Hitti in his famous book "The Arabs:A short History" has dealt with this myth in his words:"The story that by Caliph's order Amr for six long months fed the numerous bath furnaces of the city with the volumes of the Alexandrian library incidentally, makes a good fiction but bad history.The great library was burned as early as 48 BC by Julius Ceaser. A later one reffered to as the Daughter Library,was destroyed about AD 389 by the Roman Emporer Theodosius.At the time of the Arab conquest, no library of importance existed in Alexandria and no contemporary writer ever brought the charge against Amr or Umer.(Pg70). So I really don't know where the author got his source of inform! ation on this matter, and I think I'd be justified to ask him that in the name of History the author should correct himself in the later editions of this book.
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am 29. April 2000
Singh provided a touching degree of warmth to the otherwise perceived cool if not cold affectations often associated with mathmaticians and their mystique or oftimes obsessions with numbers in his enticing work "Fermat's Enigma," a story woven and embellished by his thoroughly researched history of numbers as seen through the eyes of ambitious mathematician's and viewed in context of the true story of contemporary mathematician Andrew Wiles whose passion propelled him to solve a cryptic theorem made by Pierre de Fermat in 1637 and which posed a tempting and baffling riddle for some 350 years.
Knowledge of numbers or higher mathematics is not essential to the reader as Singh introduces these judiciously, just adequately to whet our appetites and tease us about the novelty and also delightful simplicity of numbers - so we can better try to appreciate the challenge to Wile, his preparation (ostensibly from childhood) and eventual generally conceded victory re: A^n + B^n = C^n where (n >2), the Pythagorean to a power cubed or greater.
Chapters "A Mathematical Disgrace" and "A Slight Problem" are especially well-written. The author appears to have been a bit heavy in the re-stating of Andrew's quest but this is his main focus. Singh's intriguing review of historical data and selection of subject matter covering numbers may have also set the stage for a notable documentary, "The Code Book," which discusses the Scherbius's Enigma machine and a few notables also appearing in Fermat's Enigma. We are wont to wonder if Fermat had, afterall, a solution himself. Once begun, the book is hard to put down until read.
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am 21. Februar 2000
The author does an admirable review and explanation of Fermat's Last Problem, but only up to a certain point. He should have tried to get Andrew Wiles to be more explicit about about the details of his proof and if Wiles lacked the capacity to provide a sequence of simple unambiguous steps of explanation, there are certainly others who could have helped both Wiles and Singh.
For example, there is nothing that should have been difficult in explaining what constitutes an "algebra" or a "ring" like the Hecke Ring Wiles used, let alone the Selmer "group" also used. This is because algebras, rings, and groups are all well defined structures. A simple explanation of how the operators critically worked together would have worked. This is especially so when Wiles found that even though both his research of Kolyvagin-Flach and that of the Isawa Theory were individually inadequate but their overlaping results with each other ended up completing the chain, and thereby completing the solution to the long sought after Taniyama-Shimura conjecture. Just how this last conjecture actually causes the famous Fermat Conjecture to be true, is a terrific story itself.
All this could have been done so simply and would have made "the hunt" really exciting acements s well as far more enjoyable to the averagely intelligent reader. Just too much was left out because of a rush to publish?
I hope when Simon Singh writes another edition, he will be just a little more thorough. It's worth hiring an algebraist to help him
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am 1. April 2000
Pierre de Fermat, a seventeenth century French mathematician, challenged his colleagues and perhaps future generations of mathematicians to prove the following formula: a^n + b^n = c^n will be false for n > 2. Fermat wrote in the margins of his notebook that he had proven the assertion, but he did not outline it.
Singh's book chronicles the development of mathematics from ancient Greece to the 1990s.
Singh begins with a discussion of Pythagoras and his famous theorem for calculating right triangles. It is the Pythagorean formula that is the basis for Fermat's equation.
Singh then discusses the many famous mathematicians that had attempted to reproduce Fermat's proof. Although they were able to prove the formula's validity for specific values of n, no one had succeeded in proving it for infinite values of n. Without this proof of universality, there had existed the possibility that some value will disprove Fermat's assertion.
Singh then focuses his attention on Andrew Wiles, the man who would succeed where others had failed. After studying the futile attempts of his predecessors, Wiles decides to employ twentieth century mathematics. With developments from other colleagues in other areas of mathematics, Wiles embarks on a personal and secretive mission to resolve this enduring problem and a contemporary mathematical challenge.
Fermat's Enigma is a nontechnical exploration of the mathematics and mathematicians from ancient Greece to the twentieth century. It requires knowledge of only high school mathematics.
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am 18. September 2009
The book is about the history of one of the most outstanding problems in the history of mathematics namely; Fermat's last theorem. Fermat's famous theorem can be understood by middle school pupils but it's proof has persistently eluded history's most powerful minds for over 350 years. Singh's master piece follows Fermat's theorem from its very roots some 2000 years before the birth of Fermat to its final proof by Andrew Wills in 1993. Singh literally transport's the reader from ancient Greece, to third century Alexandria, to seventeenth century France, to second world war Europe, to the boots of Andrew Wills in pursuit of this unique theorem. Three centuries of rich history are beautifully woven into a thrilling tale. The book covers a wide assortment of very interesting topics including; Pythagoras and his secret society, Euclid and his elements, Fermat and his legacy, Euler and his attempts, women in mathematics, Hilbert and his problems, Turing and his machines, Wills and his determined struggle and much more all in clear and vivid narration readily accessible to the general reader. The book establishes a tender balance between daunting detail and frustrating superficialism; an impressive task considering the highly complicated mathematics included. The author gives readers a new perspective to the world of mathematics. All said, this is one of the best popular science books I ever read. It gripped my attention from the moment I flipped its front cover to the moment I put it down a couple of days later. Simply magnificent!
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