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韦慰 蟿蔚位蔚蠀蟿伪委慰 胃蔚蠋蟻畏渭伪 蟿慰蠀 桅蔚蟻渭维
蠂(n) + 蠄(n) = z(n) : 魏伪渭委伪 位蠉蟽畏. "螒谓伪魏维位蠀蠄伪 渭喂伪 蟺蟻伪纬渭伪蟿喂魏维 蔚尉伪委蟽喂伪 位蠉蟽畏, 蠈渭蠅蟼 未蔚谓 蟺蟻慰位伪尾伪委谓蠅 谓伪 蟿畏 纬蟻维蠄蠅 纬喂伪蟿委 苇蟻蠂蔚蟿伪喂 蟿慰 蟿蟻伪委谓慰".
螠蟺慰蟻蔚委 谓伪 萎蟿伪谓 蔚位维蠂喂蟽蟿慰喂 慰喂 谓蔚慰蠇蟻魏苇味慰喂 蟺慰蠀 魏伪蟿维位伪尾伪谓 蠈蟿喂 伪蠀蟿蠈 蟿慰 "蠂伪蟻喂蟿蠅渭苇谓伪 位蠈纬喂慰" 纬魏蟻维蠁喂蟿喂 蟽蟿慰 蟽蟿伪胃渭蠈 蟿慰蠀 渭蔚蟿蟻蠈 蟿畏蟼 8畏蟼 慰未慰蠉, 蟽蟿畏 螡苇伪 违蠈蟻魏畏, 蟺伪蟻苇蟺蔚渭蟺蔚 蟽蟿慰谓 蔚未蠋 魏伪喂 蟿蟻喂伪魏蠈蟽喂伪 蠂蟻蠈谓喂伪 维位蠀蟿慰 渭伪胃畏渭伪蟿喂魏蠈 纬蟻委蠁慰, 纬谓蠅蟽蟿蠈 蠅蟼 "蟿慰 蟿蔚位蔚蠀蟿伪委慰 胃蔚蠋蟻畏渭伪 蟿慰蠀 桅蔚蟻渭维" 魏伪喂 蟽蟿畏谓 蟺伪蟻维尉蔚谓畏 喂蟽蟿慰蟻委伪 蟿慰蠀.
韦慰谓 17慰 伪喂蠋谓伪, 渭蔚位蔚蟿蠋谓蟿伪蟼 蟿慰 尾喂尾位委慰 "螒蟻喂胃渭畏蟿喂魏维" 蟿慰蠀 螖喂蠈蠁伪谓蟿慰蠀, 慰 螤喂苇蟻 谓蟿蔚 桅蔚蟻渭维 蟽蟿维胃畏魏蔚 蟽蟿慰 蟺蠀胃伪纬蠈蟻蔚喂慰 胃蔚蠋蟻畏渭伪 (x虏+蠄虏=z虏) 魏伪喂 蟽畏渭蔚委蠅蟽蔚 蟽蟿慰 蟺蔚蟻喂胃蠋蟻喂慰 蟿畏蟼 蟽蔚位委未伪蟼 蟿慰 蟽蠀渭蟺苇蟻伪蟽渭伪 蠈蟿喂 蔚委谓伪喂 伪未蠉谓伪蟿慰谓 谓伪 喂蟽蠂蠉蔚喂 蟿慰 x (n) + 蠄 (n) =z (n). 螘蟺委蟽畏蟼 蟽蠀渭蟺位萎蟻蠅蟽蔚: " 螆蠂蠅 伪谓伪魏伪位蠉蠄蔚喂 渭喂伪 蟺蟻伪纬渭伪蟿喂魏维 胃伪蠀渭维蟽喂伪 伪蟺蠈未蔚喂尉畏, 蠈渭蠅蟼 蟿慰 蟺蔚蟻喂胃蠋蟻喂慰 蟿畏蟼 蟽蔚位委未伪蟼 蔚委谓伪喂 蟺慰位蠉 蟽蟿蔚谓蠈 纬喂伪 谓伪 蟿畏谓 伪谓伪蟺蟿蠉尉蠅". 螕喂伪 蟿伪 蔚蟺蠈渭蔚谓伪 350 蠂蟻蠈谓喂伪, 畏 蠁蟻维蟽畏 伪蠀蟿萎 蟿慰蠀 桅蔚蟻渭维 苇纬喂谓蔚 苇渭渭慰谓畏 喂未苇伪 蟿蠅谓 蟺喂慰 未喂维蟽畏渭蠅谓 渭伪胃畏渭伪蟿喂魏蠋谓 渭蠀伪位蠋谓, 蟺慰蠀 伪蟺蠈 蟿蠈蟿蔚 蟻委蠂谓慰谓蟿伪喂 蟽蝿 苇谓伪谓 蠁慰尾蔚蟻蠈 伪纬蠋谓伪 纬喂伪 蟿畏谓 蔚蟺委位蠀蟽畏 蟿慰蠀 未喂伪蟽畏渭蠈蟿蔚蟻慰蠀 渭伪胃畏渭伪蟿喂魏慰蠉 蟺蟻慰尾位萎渭伪蟿慰蟼.
螠蟺慰蟻蔚委 谓伪 萎蟿伪谓 蔚位维蠂喂蟽蟿慰喂 慰喂 谓蔚慰蠇蟻魏苇味慰喂 蟺慰蠀 魏伪蟿维位伪尾伪谓 蠈蟿喂 伪蠀蟿蠈 蟿慰 "蠂伪蟻喂蟿蠅渭苇谓伪 位蠈纬喂慰" 纬魏蟻维蠁喂蟿喂 蟽蟿慰 蟽蟿伪胃渭蠈 蟿慰蠀 渭蔚蟿蟻蠈 蟿畏蟼 8畏蟼 慰未慰蠉, 蟽蟿畏 螡苇伪 违蠈蟻魏畏, 蟺伪蟻苇蟺蔚渭蟺蔚 蟽蟿慰谓 蔚未蠋 魏伪喂 蟿蟻喂伪魏蠈蟽喂伪 蠂蟻蠈谓喂伪 维位蠀蟿慰 渭伪胃畏渭伪蟿喂魏蠈 纬蟻委蠁慰, 纬谓蠅蟽蟿蠈 蠅蟼 "蟿慰 蟿蔚位蔚蠀蟿伪委慰 胃蔚蠋蟻畏渭伪 蟿慰蠀 桅蔚蟻渭维" 魏伪喂 蟽蟿畏谓 蟺伪蟻维尉蔚谓畏 喂蟽蟿慰蟻委伪 蟿慰蠀.
韦慰谓 17慰 伪喂蠋谓伪, 渭蔚位蔚蟿蠋谓蟿伪蟼 蟿慰 尾喂尾位委慰 "螒蟻喂胃渭畏蟿喂魏维" 蟿慰蠀 螖喂蠈蠁伪谓蟿慰蠀, 慰 螤喂苇蟻 谓蟿蔚 桅蔚蟻渭维 蟽蟿维胃畏魏蔚 蟽蟿慰 蟺蠀胃伪纬蠈蟻蔚喂慰 胃蔚蠋蟻畏渭伪 (x虏+蠄虏=z虏) 魏伪喂 蟽畏渭蔚委蠅蟽蔚 蟽蟿慰 蟺蔚蟻喂胃蠋蟻喂慰 蟿畏蟼 蟽蔚位委未伪蟼 蟿慰 蟽蠀渭蟺苇蟻伪蟽渭伪 蠈蟿喂 蔚委谓伪喂 伪未蠉谓伪蟿慰谓 谓伪 喂蟽蠂蠉蔚喂 蟿慰 x (n) + 蠄 (n) =z (n). 螘蟺委蟽畏蟼 蟽蠀渭蟺位萎蟻蠅蟽蔚: " 螆蠂蠅 伪谓伪魏伪位蠉蠄蔚喂 渭喂伪 蟺蟻伪纬渭伪蟿喂魏维 胃伪蠀渭维蟽喂伪 伪蟺蠈未蔚喂尉畏, 蠈渭蠅蟼 蟿慰 蟺蔚蟻喂胃蠋蟻喂慰 蟿畏蟼 蟽蔚位委未伪蟼 蔚委谓伪喂 蟺慰位蠉 蟽蟿蔚谓蠈 纬喂伪 谓伪 蟿畏谓 伪谓伪蟺蟿蠉尉蠅". 螕喂伪 蟿伪 蔚蟺蠈渭蔚谓伪 350 蠂蟻蠈谓喂伪, 畏 蠁蟻维蟽畏 伪蠀蟿萎 蟿慰蠀 桅蔚蟻渭维 苇纬喂谓蔚 苇渭渭慰谓畏 喂未苇伪 蟿蠅谓 蟺喂慰 未喂维蟽畏渭蠅谓 渭伪胃畏渭伪蟿喂魏蠋谓 渭蠀伪位蠋谓, 蟺慰蠀 伪蟺蠈 蟿蠈蟿蔚 蟻委蠂谓慰谓蟿伪喂 蟽蝿 苇谓伪谓 蠁慰尾蔚蟻蠈 伪纬蠋谓伪 纬喂伪 蟿畏谓 蔚蟺委位蠀蟽畏 蟿慰蠀 未喂伪蟽畏渭蠈蟿蔚蟻慰蠀 渭伪胃畏渭伪蟿喂魏慰蠉 蟺蟻慰尾位萎渭伪蟿慰蟼.
384 pages, Paperback
First published April 12, 1997
1,247 people are currently reading
37k people want to read
About the author
Simon Singh
17听books1,474听followersSimon Lehna Singh, MBE is a British author who has specialised in writing about mathematical and scientific topics in an accessible manner. He is the maiden winner of the Lilavati Award.
His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem), The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe) and Trick or Treatment? Alternative Medicine on Trial (about complementary and alternative medicine).
He has also produced documentaries and works for television to accompany his books, is a trustee of NESTA, the National Museum of Science and Industry and co-founded the Undergraduate Ambassadors Scheme.
His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem), The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe) and Trick or Treatment? Alternative Medicine on Trial (about complementary and alternative medicine).
He has also produced documentaries and works for television to accompany his books, is a trustee of NESTA, the National Museum of Science and Industry and co-founded the Undergraduate Ambassadors Scheme.
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Displaying 1 - 30 of 1,769 reviews
October 8, 2014
Simon Singh has the ability to present a story about a mathematics problem, and tell it like a detective story. He makes the subject exciting, even though the outcome is well known. Singh intersperses history with discussions about the mathematics, and makes it quite understandable.
Singh starts with the roots of the famous Fermat's Last Theorem, by recounting the stories and mathematics of Pythagoras, Euclid, and Euler. Other, less well-known mathematicians are also given credit, for example Sophie Germain, Daniel Bernoulli, Augustin Cauchy, and Evariste Galois.
Three hundred fifty years ago, Fermat wrote the following theorem in the margin of a mathematics book:
And, Fermat wrote that he had a marvelous proof, but no room in the margin for it. For centuries, mathematicians have attempted to prove the theorem, without success. It had been sort of a "holy grail" of mathematicians to prove the theorem, and many brilliant minds spent years on it. Perhaps in was unprovable, and worst of all, Kurt Godel showed that some theorems are actually undecidable--that is to say, it is impossible even to decide whether or not a theorem is true.
Singh recounts a fascinating story of the gifted mathematician, Paul Wolfskehl. He was very depressed, and decided to commit suicide on a particular night, at midnight. While waiting for that time to arrive, he started to read about the failed attempts to prove Fermat's Last Theorem. He became so engrossed in the subject, that he worked well past midnight. He found a gap in the logic of a predecessor, and was so proud of himself that he gained a new desire for life. And, in his will he established a fund of 100,000 marks to be given to the mathematician who first completes the proof of the theorem!
Much of the book describes how Andrew Wiles developed a growing interest in the theorem. He worked in almost total isolation for seven years, in order not to be distracted. He occasionally published little tidbits unrelated to his real endeavor, in order to dispel suspicions about what his real work entailed.
The central piece of the proof entailed proving the Taniyama-Shimura conjecture, that linked modular forms with elliptic equations. This was a linkage between two far-flung branches of mathematics that seemed to be totally unrelated. To prove the conjecture would allow incredible advances to be made. And then, Ken Ribet showed that a proof of the Taniyama-Shimura conjecture would, in effect, be a direct proof of Fermat's Last Theorem. But many people tried and failed to develop the proof. But that is exactly what Andrew Wiles worked on for so many years.
I had previously read that during Andrew Wiles' famous lecture, he just casually let the unsuspecting audience know, "and that is a proof of Fermat's Last Theorem." Well, this book tells a somewhat different story. Most of the audience had heard rumors that the third of Wiles' lectures would be of historical significance. They came prepared with cameras, and took photographs during the lecture. So, it was a surprise, but not a total surprise.
After Wiles' manuscript of the proof was sent to a publisher, six mathematicians reviewed it, and a crucial gap was found in it. Wiles worked furiously for a nightmarish year, and with the help of Richard Taylor, finally closed the gap. Today, Wiles is recognized as the one who developed the proof. But it is clear, that Wiles "stood on the shoulders of giants"; he used--and developed--mathematical techniques that had not existed just a few decades previously.
Simon Singh writes with a wonderful style. It is clear, not too jargon-heavy but contains enough mathematical "meat" to seem satisfying. The book is followed by ten appendixes that contain more details about some of the mathematics; they are not overly technical, and give the reader a better understanding of some of the issues. I highly recommend this book to everyone interested in math.
Singh starts with the roots of the famous Fermat's Last Theorem, by recounting the stories and mathematics of Pythagoras, Euclid, and Euler. Other, less well-known mathematicians are also given credit, for example Sophie Germain, Daniel Bernoulli, Augustin Cauchy, and Evariste Galois.
Three hundred fifty years ago, Fermat wrote the following theorem in the margin of a mathematics book:
And, Fermat wrote that he had a marvelous proof, but no room in the margin for it. For centuries, mathematicians have attempted to prove the theorem, without success. It had been sort of a "holy grail" of mathematicians to prove the theorem, and many brilliant minds spent years on it. Perhaps in was unprovable, and worst of all, Kurt Godel showed that some theorems are actually undecidable--that is to say, it is impossible even to decide whether or not a theorem is true.Singh recounts a fascinating story of the gifted mathematician, Paul Wolfskehl. He was very depressed, and decided to commit suicide on a particular night, at midnight. While waiting for that time to arrive, he started to read about the failed attempts to prove Fermat's Last Theorem. He became so engrossed in the subject, that he worked well past midnight. He found a gap in the logic of a predecessor, and was so proud of himself that he gained a new desire for life. And, in his will he established a fund of 100,000 marks to be given to the mathematician who first completes the proof of the theorem!
Much of the book describes how Andrew Wiles developed a growing interest in the theorem. He worked in almost total isolation for seven years, in order not to be distracted. He occasionally published little tidbits unrelated to his real endeavor, in order to dispel suspicions about what his real work entailed.
The central piece of the proof entailed proving the Taniyama-Shimura conjecture, that linked modular forms with elliptic equations. This was a linkage between two far-flung branches of mathematics that seemed to be totally unrelated. To prove the conjecture would allow incredible advances to be made. And then, Ken Ribet showed that a proof of the Taniyama-Shimura conjecture would, in effect, be a direct proof of Fermat's Last Theorem. But many people tried and failed to develop the proof. But that is exactly what Andrew Wiles worked on for so many years.
I had previously read that during Andrew Wiles' famous lecture, he just casually let the unsuspecting audience know, "and that is a proof of Fermat's Last Theorem." Well, this book tells a somewhat different story. Most of the audience had heard rumors that the third of Wiles' lectures would be of historical significance. They came prepared with cameras, and took photographs during the lecture. So, it was a surprise, but not a total surprise.
After Wiles' manuscript of the proof was sent to a publisher, six mathematicians reviewed it, and a crucial gap was found in it. Wiles worked furiously for a nightmarish year, and with the help of Richard Taylor, finally closed the gap. Today, Wiles is recognized as the one who developed the proof. But it is clear, that Wiles "stood on the shoulders of giants"; he used--and developed--mathematical techniques that had not existed just a few decades previously.
Simon Singh writes with a wonderful style. It is clear, not too jargon-heavy but contains enough mathematical "meat" to seem satisfying. The book is followed by ten appendixes that contain more details about some of the mathematics; they are not overly technical, and give the reader a better understanding of some of the issues. I highly recommend this book to everyone interested in math.
January 3, 2018
Before delving into the book itself, I thought I鈥檇 start things off by introducing the problem it鈥檚 concerned with, just in case you aren鈥檛 already familiar with it.
So, what exactly is Fermat鈥檚 Last Theorem?
Well, basically, this is it:
As you can see, the conjecture is quite easy to understand, and yet, believe it or not, it was so remarkably difficult to prove that it took over 350 years to accomplish! The fact that Fermat (teasingly?) scribbled this rather infuriating note in the margin only added to the frustration felt by the scores of mathematicians who did battle with it over the centuries: 鈥淚 have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.鈥�
No doubt the cheeky bastard would鈥檝e enjoyed Twitter:
Okay, now that that鈥檚 been taken care of, it鈥檚 time to look at the actual book.
What Kind of Book is Fermat鈥檚 Enigma?
Simply put, Fermat鈥檚 Enigma is a history book. It is most definitely NOT a math book, so don鈥檛 expect to find any degree of mathematical rigor or complexity here. There are a handful of fairly simple proofs included in the appendices, but overall, the concepts under discussion are glossed over in a superficial manner, never examined in any kind of detail. If you want something that fleshes out how the proof actually works, I鈥檓 afraid you鈥檒l have to look elsewhere. (Singh was kind enough to include quite a few 鈥渇urther reading suggestions鈥� at the end of this book. While I鈥檝e not looked into any of the titles he recommended, I assume many of those might prove more to your liking if you prefer a 鈥渕ath book鈥� on the subject.)
In any case, while Singh did not pursue the actual mathematics in any real sense, he did positively excel at telling the story of an utterly fascinating struggle, one which spanned hundreds of years and ensnared countless brilliant, talented minds. Readers make the acquaintance of such notable mathematicians as Pythagoras (whose work paved the way for Fermat), Leonhard Euler, Paul Wolfskehl, Sophie Germain, Daniel Bernoulli, Augustin-Louis Cauchy, Evariste Galois, Yutaka Taniyama, Goro Shimura, and of course Andrew Wiles, the man, the myth, the legend who finally proved the damn thing.
Overall, I was surprised and delighted by just how compelling the story actually was. For me, this book quickly became a veritable page-turner, one I was loathe to put aside. Some may argue that in order to accomplish this, he omitted too much relevant information, that he sacrificed depth for readability. Perhaps this is true to an extent, but in my opinion, while it was admittedly easy to read and follow, it still managed to include a fair amount of pertinent, interesting material. More importantly, it never got bogged down with unnecessary details or lost in minutiae, and never meandered down exasperating tangents, as many otherwise outstanding history books are wont to do.
And ultimately, what made this book so very stimulating was that the manner in which the story was told really made it come alive. Singh bestowed a truly suspenseful, exciting quest upon the reader, one full of twists and turns, and even *gasp* its fair share of drama. He enthusiastically demonstrated just how action-packed and exhilarating the life of the mind can be. And for accomplishing this tremendous feat, I heartily recommend the book, warts and all.
And Now, For a Few Words on the Star of the Show
Andrew Wiles is an extraordinary human being. Fascinated by Fermat鈥檚 Last Theorem since he was ten years old, he vowed to conquer that most impossible of proofs. This was at the age of ten, mind you. I seriously can鈥檛 get past that. And then, true to his word, the little rascal grew up to become an eminent mathematician, one who finally went into seclusion for seven years in order to hack away at this tremendous proof. While a not insignificant error marred the first release of said proof, he didn鈥檛 let that deter him, but persevered and managed to rectify the error, and, within a couple of years, came out with THE proof. Holy goddamn shit.
To me, Wiles鈥� story was completely and utterly inspiring. I was frankly amazed by what the human mind can achieve; I think I will always be in awe of Wiles鈥� fierce determination and incredible tenacity. Mad respect.
Anyway, as you can probably tell, Andrew Wiles is a personal hero of mine. He is an undeniable, ultimate badass. Wayne and Garth said it best:
So, what exactly is Fermat鈥檚 Last Theorem?
Well, basically, this is it:
As you can see, the conjecture is quite easy to understand, and yet, believe it or not, it was so remarkably difficult to prove that it took over 350 years to accomplish! The fact that Fermat (teasingly?) scribbled this rather infuriating note in the margin only added to the frustration felt by the scores of mathematicians who did battle with it over the centuries: 鈥淚 have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.鈥�
No doubt the cheeky bastard would鈥檝e enjoyed Twitter:
Okay, now that that鈥檚 been taken care of, it鈥檚 time to look at the actual book.
What Kind of Book is Fermat鈥檚 Enigma?
Simply put, Fermat鈥檚 Enigma is a history book. It is most definitely NOT a math book, so don鈥檛 expect to find any degree of mathematical rigor or complexity here. There are a handful of fairly simple proofs included in the appendices, but overall, the concepts under discussion are glossed over in a superficial manner, never examined in any kind of detail. If you want something that fleshes out how the proof actually works, I鈥檓 afraid you鈥檒l have to look elsewhere. (Singh was kind enough to include quite a few 鈥渇urther reading suggestions鈥� at the end of this book. While I鈥檝e not looked into any of the titles he recommended, I assume many of those might prove more to your liking if you prefer a 鈥渕ath book鈥� on the subject.)
In any case, while Singh did not pursue the actual mathematics in any real sense, he did positively excel at telling the story of an utterly fascinating struggle, one which spanned hundreds of years and ensnared countless brilliant, talented minds. Readers make the acquaintance of such notable mathematicians as Pythagoras (whose work paved the way for Fermat), Leonhard Euler, Paul Wolfskehl, Sophie Germain, Daniel Bernoulli, Augustin-Louis Cauchy, Evariste Galois, Yutaka Taniyama, Goro Shimura, and of course Andrew Wiles, the man, the myth, the legend who finally proved the damn thing.
Overall, I was surprised and delighted by just how compelling the story actually was. For me, this book quickly became a veritable page-turner, one I was loathe to put aside. Some may argue that in order to accomplish this, he omitted too much relevant information, that he sacrificed depth for readability. Perhaps this is true to an extent, but in my opinion, while it was admittedly easy to read and follow, it still managed to include a fair amount of pertinent, interesting material. More importantly, it never got bogged down with unnecessary details or lost in minutiae, and never meandered down exasperating tangents, as many otherwise outstanding history books are wont to do.
And ultimately, what made this book so very stimulating was that the manner in which the story was told really made it come alive. Singh bestowed a truly suspenseful, exciting quest upon the reader, one full of twists and turns, and even *gasp* its fair share of drama. He enthusiastically demonstrated just how action-packed and exhilarating the life of the mind can be. And for accomplishing this tremendous feat, I heartily recommend the book, warts and all.
And Now, For a Few Words on the Star of the Show
Andrew Wiles is an extraordinary human being. Fascinated by Fermat鈥檚 Last Theorem since he was ten years old, he vowed to conquer that most impossible of proofs. This was at the age of ten, mind you. I seriously can鈥檛 get past that. And then, true to his word, the little rascal grew up to become an eminent mathematician, one who finally went into seclusion for seven years in order to hack away at this tremendous proof. While a not insignificant error marred the first release of said proof, he didn鈥檛 let that deter him, but persevered and managed to rectify the error, and, within a couple of years, came out with THE proof. Holy goddamn shit.
To me, Wiles鈥� story was completely and utterly inspiring. I was frankly amazed by what the human mind can achieve; I think I will always be in awe of Wiles鈥� fierce determination and incredible tenacity. Mad respect.
Anyway, as you can probably tell, Andrew Wiles is a personal hero of mine. He is an undeniable, ultimate badass. Wayne and Garth said it best:
September 2, 2021
This book is endowed with all elements of a perfect story, which are curiosity, surprising events, tragedy, ambition, alternating defeat / triumph and finally an astonishing success.
The 鈥淔ermat鈥檚 enigma鈥� is a tremendously inspiring narrative of one of the most important and most difficult conundrums of mathematics. It was devised by the reverend Pierre de Fermat who was called 鈥淭he prince of amateurs鈥� because he had neither had any formal education in mathematics nor he had any known tutor. He learned maths by some copies of ancient books written by Euclid鈥檚 disciple named Diophantus.
When mathematicians scrutinized margins of his books they saw a short note which baffled the brightest minds for more than 350 years. Fermat claimed a groundbreaking conjecture in the margin of Diophantus book without any proof, but the line next to the proof made the case much worse for other mathematicians. he wrote beside the conjecture:
鈥淚 have a truly marvelous demonstration of this proposition which this margin is too narrow to contain鈥� .This showed the fact that the formula had indeed a proof but it was lost. If you want to know what that theory is you can search on google because it can鈥檛 be properly explained in this review.
Since the last 350 years the formula had been attacked by the most eminent mathematicians including Leonhard Euler but none of them could prove it thoroughly.
After so many years of fruitless endeavor Andrew wiles managed to prove it. For Andrew the Fermat鈥檚 last theorem was personally and emotionally significant because he had been in love with the theorem since he first encountered it when he was just ten years old. After thirty years he used so many new mathematical techniques and finally he put more than 8 years on proving this conjecture in order to firmly prove it and finally he did.
This book is only recommended for those who appreciate the true value of mathematics.
The 鈥淔ermat鈥檚 enigma鈥� is a tremendously inspiring narrative of one of the most important and most difficult conundrums of mathematics. It was devised by the reverend Pierre de Fermat who was called 鈥淭he prince of amateurs鈥� because he had neither had any formal education in mathematics nor he had any known tutor. He learned maths by some copies of ancient books written by Euclid鈥檚 disciple named Diophantus.
When mathematicians scrutinized margins of his books they saw a short note which baffled the brightest minds for more than 350 years. Fermat claimed a groundbreaking conjecture in the margin of Diophantus book without any proof, but the line next to the proof made the case much worse for other mathematicians. he wrote beside the conjecture:
鈥淚 have a truly marvelous demonstration of this proposition which this margin is too narrow to contain鈥� .This showed the fact that the formula had indeed a proof but it was lost. If you want to know what that theory is you can search on google because it can鈥檛 be properly explained in this review.
Since the last 350 years the formula had been attacked by the most eminent mathematicians including Leonhard Euler but none of them could prove it thoroughly.
After so many years of fruitless endeavor Andrew wiles managed to prove it. For Andrew the Fermat鈥檚 last theorem was personally and emotionally significant because he had been in love with the theorem since he first encountered it when he was just ten years old. After thirty years he used so many new mathematical techniques and finally he put more than 8 years on proving this conjecture in order to firmly prove it and finally he did.
This book is only recommended for those who appreciate the true value of mathematics.
February 15, 2023
That's an excellent history of mathematics from antiquity to the present day. The author skillfully captures the pedagogical trick of the Last Theorem. This "mathematical siren, ..., which attracted geniuses to destroy their hopes" better is a common thread that compellingly guides us through anecdotes, concepts very well explained in the maze of mathematics. The author gives both a technical and societal dimension to his story, thereby maintaining the reader's attention from start to finish.
Very successful. Good reading.
Very successful. Good reading.
July 23, 2017
Being a scientist of long standing and loving all aspects of science and maths, Fermat's Last Theorem in itself was a wonderful mystery, what I would give to see Fermat's note book with a note in the margin about cubic numbers as opposed to squares. A very trite remark, too lengthy to write in the margin so it is elsewhere, and no one has ever found it or managed to prove his statement, until - - - this book is a brilliant read, you would think it would be as dry as dust, but no! It is a superb account of the proof of the last theorem from Fermat's notebook to be proven. The only thing that still niggles at me, although the mathematical proof is fabulous, it uses modern techniques not available to Fermat, so it is proven but how the hell did Fermat do it??????
A brilliant book, beautifully written a tremendous historical question answered in a very modern way, fabulous, well done for readability.
A brilliant book, beautifully written a tremendous historical question answered in a very modern way, fabulous, well done for readability.
February 28, 2016
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唳椸Γ唳苦Δ唰� x^3 鈥� x^2 = y^2 + y 唳� 唳оΠ唳｀唳� 唳膏Ξ唰€唳曕Π唳｀唰� 唳Σ唳� 唳灌Ο唳� 唳忇Σ唳苦Κ唰嵿唳苦唰� 唳囙唰佮Ο唳监唳多Θ啷� 唳忇唳熰 唳膏Ξ唰€唳曕Π唳｀唳� 唳呧Ω唰€唳� 唳膏唳栢唳 唳膏Ξ唳距Η唳距Θ 唳ム唳曕Δ唰� 唳唳班, 唳唳班Δ唰嵿Ο唰囙唳熰 唳ㄠ唳唰� 唳嗋Σ唳距Ζ唳� 唳唳 唳曕唳� 唳曕Π唳む 唳唳撪Ο唳监唳熰 唳ㄠ唳む唳ㄠ唳� 唳唳曕唳啷� 唳膏Ξ唰€唳曕Π唳｀唳� 唳膏Ξ唰嵿Ν唳距Μ唰嵿Ο 唳膏唳� 唳膏Ξ唳距Η唳距Θ唳曕 唳膏Ω唰€唳� 唳忇唳熰 唳涏唳熰唳� 唳膏唳唳膏 唳唳班唳距Χ 唳曕Π唳む 唳唳班Σ唰� 唳曕唳溹唳� 唳忇唰嵿唰囙Μ唳距Π唰囙 唳膏唳� 唳灌Ο唳监 唳Α唳监啷� 唳唳ㄠ唳� 唳樴Α唳监 唳嗋Μ唳苦Ψ唰嵿唳距Π 唳曕Π唰囙唰� 唳膏Ξ唳唳曕 唳忇唳熰 唳涏唰� 唳唳侧 唳曕唳� 唳膏唳� 唳曕Π唰� 唳唳侧Μ唳距Π 唳溹Θ唰嵿Ο啷� 唳樴Α唳监 唳ㄠ 唳ム唳曕Σ唰� 唳唳多唳� 唳唳膏唳む唳� 唳膏Ξ唳唰囙Π 唳曕唳� 唳唳ㄠ唳︵唳む 唳嗋Ξ唳班 唳嗋唳� 唳む 唳曕唳ㄠ 唳唳澿Δ唰囙 唳唳班Δ唳距Ξ 唳ㄠ (唳忇唳ㄠ 唳 唳栢唳� 唳唳班 唳む唳� 唳ㄠΟ唳�, 唳むΜ唰� 唳忇唳熰 唳о唳班Γ唳� 唳呧Θ唰嵿Δ唳� 唳曕Π唳む 唳唳班)啷� 唳呧Ξ唰佮 唳曕唳溹唳� 唳班唳む 唳曕Π唰� 唳︵唳 唳Σ唳侧 唳む 唳栢唳� 唳唳唳班唳ㄠ唳む唳曕Π 唳多唳ㄠ唳, 唳曕唳班Γ 唳班唳� 唳呧Θ唰囙唳椸唳侧 唳呧Θ唰嵿Η唳曕唳� 唳膏Ξ唳唰囙Π 唳唳椸Λ唳�; 唳班唳む 唳曕唳� 唳曕唳溹唳� 唳灌Μ唰� 唳む 唳ㄠ唳多唳氞唳� 唳灌唳唳� 唳唳唳ㄠ啷� 唳班唳� 唳ㄢ€權唳距Ο唳� 唳曕Π唰� 唳︵唳 唳Σ唳侧 唳唳ム唳熰 唳Π唳苦Ψ唰嵿唳距Π 唳灌Ο唳监 唳唳啷� 唳膏Ξ唳唰囙Π 唳忇 唳膏唳苦 唳Π唳苦Ξ唳距Κ唰囙Π 唳溹Θ唰嵿Ο唳� 唳唳ㄠ唳� 唳樴Α唳监唳む 唳膏Ξ唳唳曕 唰оЖ 唳熰 唳唳椸 唳唳� 唳曕Π唰� 唳ㄠ唳唰囙唰囙イ 唳膏Ξ唰€唳曕Π唳� 唳膏Ξ唳距Η唳距Θ唰囙Π 唳曕唳粪唳む唳班唳� 唳忇 唳唳︵唳о 唳栢唳熰唳ㄠ 唳唳啷�
唳氞唳む唳班唳� 唳樴Α唳监唳熰 唳唳囙Ν-唳曕唳侧 唳呧唳唳班唳ムΞ唰囙唳苦 唳膏唳膏唳熰唳イ 唰� 唳ム唳曕 唰� 唳樴Π 唳膏唳Θ唰� 唳嗋唳距Σ唰� 唳嗋Ξ唳班 唰� 唳� 唳唳佮唳距, 唳呧Π唰嵿Ε唳距, 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唳唳栢唳ㄠ 唰� + 唰� = 唰�, 唳唳囙Ν-唳曕唳侧 唳呧唳唳班唳ムΞ唰囙唳苦 唳膏唳膏唳熰唳 唰� + 唰� = 唰︵イ 唰� 唳ム唳曕 唰� 唳樴Π 唳膏唳Θ唰� 唳嗋唳距Σ唰� 唳唳佮唳距 唰� 唳忇イ 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唰� + 唰� = 唰�, 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唰� + 唰� = 唰р€︵唳む唳唳︵啷�
唳撪Κ唳班 唳夃Σ唰嵿Σ唰囙唳苦Δ x^3 鈥� x^2 = y^2 + y 唳膏Ξ唰€唳曕Π唳｀唳苦Π 唳膏Ξ唳距Η唳距Θ 唰唳苦
唳多唳� 唳膏Ξ唳距Η唳距Θ唳熰 (x = 1, y = 4) 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唳犩唳� 唳椸唳班唳｀Ο唰嬥唰嵿Ο 唳ㄠ 唳灌Σ唰囙 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唳唳 唳唳 唳唳侧 唳唳唳�
x^3 鈥� x^2 = y^2 + y
1^3 -1^2 = 4^2 + 4
1-1 = 16 + 4
0 = 20
唳唳灌唳む 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唰� = 唰�, 唰� 唳忇Π 唳膏唳� 唳椸唳｀唳む唳� (唰�, 唰оЕ, 唰оЙ, 唰ㄠЕ鈥︹€�) 唳む唳� 唰� 唳� 唳灌Μ唰囙イ 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唳膏唳栢唳 唳涏唳侧 唰唳� (唰�,唰�,唰�,唰�,唰�), 唳嗋Π 唳膏Ξ唳距Η唳距Θ 唳涏唳侧 唰唳�, 唳む唳� 唳忇唰� E5 = 4 唳侧唳栢 唳灌Ο唳监イ 唳Ζ唳� 唰� 唳樴Α唳监 唳Ζ唰嵿Η唳む 唳唳Μ唳灌唳� 唳曕Π唳� 唳灌Δ唰� (唳呧Π唰嵿Ε唳距 唳樴Α唳监唳む 唳︵唳唳� 唳膏唳栢唳唳椸唳侧 唳灌Δ唰� 唰�,唰�,唰�,唰�,唰�,唰�,唰�) 唳む唳灌Σ唰� 唳膏Ξ唳距Η唳距Θ 唳灌Δ唰� 唰唳苦イ 唳忇唳距唰� 唳忇唳� 唳忇唳熰 唳膏唳班唳� 唳嗋唳距Π唰� 唳侧唳栢 唳唳侧 唳唳む 唳唳班唳� (E 唳膏唳班唳�)
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唰唰� + 唰猑唰� = 唰玘唰�
唳, 唰� + 唰оК = 唰ㄠЙ
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唳椸Γ唳苦Δ唰� x^3 鈥� x^2 = y^2 + y 唳� 唳оΠ唳｀唳� 唳膏Ξ唰€唳曕Π唳｀唰� 唳Σ唳� 唳灌Ο唳� 唳忇Σ唳苦Κ唰嵿唳苦唰� 唳囙唰佮Ο唳监唳多Θ啷� 唳忇唳熰 唳膏Ξ唰€唳曕Π唳｀唳� 唳呧Ω唰€唳� 唳膏唳栢唳 唳膏Ξ唳距Η唳距Θ 唳ム唳曕Δ唰� 唳唳班, 唳唳班Δ唰嵿Ο唰囙唳熰 唳ㄠ唳唰� 唳嗋Σ唳距Ζ唳� 唳唳 唳曕唳� 唳曕Π唳む 唳唳撪Ο唳监唳熰 唳ㄠ唳む唳ㄠ唳� 唳唳曕唳啷� 唳膏Ξ唰€唳曕Π唳｀唳� 唳膏Ξ唰嵿Ν唳距Μ唰嵿Ο 唳膏唳� 唳膏Ξ唳距Η唳距Θ唳曕 唳膏Ω唰€唳� 唳忇唳熰 唳涏唳熰唳� 唳膏唳唳膏 唳唳班唳距Χ 唳曕Π唳む 唳唳班Σ唰� 唳曕唳溹唳� 唳忇唰嵿唰囙Μ唳距Π唰囙 唳膏唳� 唳灌Ο唳监 唳Α唳监啷� 唳唳ㄠ唳� 唳樴Α唳监 唳嗋Μ唳苦Ψ唰嵿唳距Π 唳曕Π唰囙唰� 唳膏Ξ唳唳曕 唳忇唳熰 唳涏唰� 唳唳侧 唳曕唳� 唳膏唳� 唳曕Π唰� 唳唳侧Μ唳距Π 唳溹Θ唰嵿Ο啷� 唳樴Α唳监 唳ㄠ 唳ム唳曕Σ唰� 唳唳多唳� 唳唳膏唳む唳� 唳膏Ξ唳唰囙Π 唳曕唳� 唳唳ㄠ唳︵唳む 唳嗋Ξ唳班 唳嗋唳� 唳む 唳曕唳ㄠ 唳唳澿Δ唰囙 唳唳班Δ唳距Ξ 唳ㄠ (唳忇唳ㄠ 唳 唳栢唳� 唳唳班 唳む唳� 唳ㄠΟ唳�, 唳むΜ唰� 唳忇唳熰 唳о唳班Γ唳� 唳呧Θ唰嵿Δ唳� 唳曕Π唳む 唳唳班)啷� 唳呧Ξ唰佮 唳曕唳溹唳� 唳班唳む 唳曕Π唰� 唳︵唳 唳Σ唳侧 唳む 唳栢唳� 唳唳唳班唳ㄠ唳む唳曕Π 唳多唳ㄠ唳, 唳曕唳班Γ 唳班唳� 唳呧Θ唰囙唳椸唳侧 唳呧Θ唰嵿Η唳曕唳� 唳膏Ξ唳唰囙Π 唳唳椸Λ唳�; 唳班唳む 唳曕唳� 唳曕唳溹唳� 唳灌Μ唰� 唳む 唳ㄠ唳多唳氞唳� 唳灌唳唳� 唳唳唳ㄠ啷� 唳班唳� 唳ㄢ€權唳距Ο唳� 唳曕Π唰� 唳︵唳 唳Σ唳侧 唳唳ム唳熰 唳Π唳苦Ψ唰嵿唳距Π 唳灌Ο唳监 唳唳啷� 唳膏Ξ唳唰囙Π 唳忇 唳膏唳苦 唳Π唳苦Ξ唳距Κ唰囙Π 唳溹Θ唰嵿Ο唳� 唳唳ㄠ唳� 唳樴Α唳监唳む 唳膏Ξ唳唳曕 唰оЖ 唳熰 唳唳椸 唳唳� 唳曕Π唰� 唳ㄠ唳唰囙唰囙イ 唳膏Ξ唰€唳曕Π唳� 唳膏Ξ唳距Η唳距Θ唰囙Π 唳曕唳粪唳む唳班唳� 唳忇 唳唳︵唳о 唳栢唳熰唳ㄠ 唳唳啷�
唳氞唳む唳班唳� 唳樴Α唳监唳熰 唳唳囙Ν-唳曕唳侧 唳呧唳唳班唳ムΞ唰囙唳苦 唳膏唳膏唳熰唳イ 唰� 唳ム唳曕 唰� 唳樴Π 唳膏唳Θ唰� 唳嗋唳距Σ唰� 唳嗋Ξ唳班 唰� 唳� 唳唳佮唳距, 唳呧Π唰嵿Ε唳距, 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唳唳栢唳ㄠ 唰� + 唰� = 唰�, 唳唳囙Ν-唳曕唳侧 唳呧唳唳班唳ムΞ唰囙唳苦 唳膏唳膏唳熰唳 唰� + 唰� = 唰︵イ 唰� 唳ム唳曕 唰� 唳樴Π 唳膏唳Θ唰� 唳嗋唳距Σ唰� 唳唳佮唳距 唰� 唳忇イ 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唰� + 唰� = 唰�, 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唰� + 唰� = 唰р€︵唳む唳唳︵啷�
唳撪Κ唳班 唳夃Σ唰嵿Σ唰囙唳苦Δ x^3 鈥� x^2 = y^2 + y 唳膏Ξ唰€唳曕Π唳｀唳苦Π 唳膏Ξ唳距Η唳距Θ 唰唳苦
x = 0, y = 0
x = 0, y = 4
x = 1, y = 0
x = 1, y = 4
唳多唳� 唳膏Ξ唳距Η唳距Θ唳熰 (x = 1, y = 4) 唳膏唳о唳班Γ 唳椸唳｀唳む唳� 唳灌唳膏唳 唳犩唳� 唳椸唳班唳｀Ο唰嬥唰嵿Ο 唳ㄠ 唳灌Σ唰囙 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唳唳 唳唳 唳唳侧 唳唳唳�
x^3 鈥� x^2 = y^2 + y
1^3 -1^2 = 4^2 + 4
1-1 = 16 + 4
0 = 20
唳唳灌唳む 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唰� = 唰�, 唰� 唳忇Π 唳膏唳� 唳椸唳｀唳む唳� (唰�, 唰оЕ, 唰оЙ, 唰ㄠЕ鈥︹€�) 唳む唳� 唰� 唳� 唳灌Μ唰囙イ 唰�-唳樴Α唳监 唳Ζ唰嵿Η唳む唳む 唳膏唳栢唳 唳涏唳侧 唰唳� (唰�,唰�,唰�,唰�,唰�), 唳嗋Π 唳膏Ξ唳距Η唳距Θ 唳涏唳侧 唰唳�, 唳む唳� 唳忇唰� E5 = 4 唳侧唳栢 唳灌Ο唳监イ 唳Ζ唳� 唰� 唳樴Α唳监 唳Ζ唰嵿Η唳む 唳唳Μ唳灌唳� 唳曕Π唳� 唳灌Δ唰� (唳呧Π唰嵿Ε唳距 唳樴Α唳监唳む 唳︵唳唳� 唳膏唳栢唳唳椸唳侧 唳灌Δ唰� 唰�,唰�,唰�,唰�,唰�,唰�,唰�) 唳む唳灌Σ唰� 唳膏Ξ唳距Η唳距Θ 唳灌Δ唰� 唰唳苦イ 唳忇唳距唰� 唳忇唳� 唳忇唳熰 唳膏唳班唳� 唳嗋唳距Π唰� 唳侧唳栢 唳唳侧 唳唳む 唳唳班唳� (E 唳膏唳班唳�)
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March 10, 2009
I guess the author does a reasonable job. But when I reached the end, I still didn't feel I understood at all how the proof worked. Probably that's just because it's so bloody hard. I got a lot more though out of Prime Obsession, Derbyshire's book on the Riemann Hypothesis, where the author opens up the box and shows you some of the actual math...
June 20, 2011
This is the kind of book that we non mathematical minds can easily digest and love. It gives you an epic scope of the number of minds that it takes to build new ideas. I doubt if Fermat had actually solved this theorem correctly, but this is impossible to prove. Fermat's theorem however was not impossible to prove! It was solved! Thanks to the efforts of many men (and women!) over many lifetimes and one final man who had the determination and persistence to finish the unthinkable. This book has a lot of wonderful elements, and really exemplifies a love of mathematics. Although if you want to actually understand the theorem this book may not be for you! I can honestly say reading it did not put the theorem in any more digestible light than it started out with. Perhaps it was to the authors advantage to skip the technicalities and focus on the enjoyment of the journey. I personally loved this approach, but it may not be for everyone, especially if you are actually looking to understand the theorem (a massive undertaking that is really not in my repertoire to comment on).
December 3, 2011
Simon converts what could have been a dry chronicle of proofs into an ode full of excitement, inspiration and intrigue worthy of a gothic love affair. Full review to follow.
June 30, 2023
This is the first popular maths book I ever read - and the one that persuaded me I wanted to be involved in the field of popular science. Just as the US publishers of Harry Potter and the Philosopher鈥檚 Stone reckoned the US public couldn鈥檛 cope with the word 鈥榩hilosopher鈥� and changed the title, this was originally called Fermat鈥檚 Enigma in the US, but such is its longstanding acclaim it's ended up with the correct name there too. Crazy assumptions from publishers apart, it鈥檚 the superb story of a bizarre little problem that no one could solve until the ever-wily mathematician Fermat scribbled in a margin that he had a wonderful solution, only there wasn鈥檛 room to write it down.
Fermat may well have been boasting, but his marginal claim threw down a gauntlet to hundreds of mathematicians who were to follow in his footsteps and fail, until it was finally achieved in the 20th century. Don鈥檛 worry if the maths itself isn't of great interest to you 鈥� the story will, both in its historical context and in the insight into the work and nature of modern mathematicians - at least, relatively modern given the book is a good 25 years old now.
In some ways the star of the book is Andrew Wiles, the British mathematician who pretty well single-handedly cracked the problem with an unusual level of secrecy, rather than the typical sharing approach of the profession. But equally it鈥檚 Fermat himself.
Whether or not Fermat actually had a solution is a moot point 鈥� but he certainly didn鈥檛 have Wiles鈥� complex approach and it's entirely possible it was a boast that he could have fulfilled. It seems so difficult to come up with a straightforward solution to this problem that Fermat has to be more than a little doubted. The nature of Wiles' solution is such that many mathematicians struggled with it, and Singh can only really give us an impression of what was involved. Any attempt to give meaning to the 100 plus page proof requires mathematics that is beyond the casual reader, and it's probably fair to say that bringing any clarity to the nature of the proof is the weakest part of this book.
Like all the best popular science books 鈥� and this certainly is one of the best 鈥� it brings in a whole range of extras historically and mathematically to add to the fascinating cast. Singh's writing style is fluid and genial. He came from a TV background, and the book combines the accessibility of that genre with the ability to go into far more depth than a TV documentary can. It's a milestone in the development of the popular science genre.
Fermat may well have been boasting, but his marginal claim threw down a gauntlet to hundreds of mathematicians who were to follow in his footsteps and fail, until it was finally achieved in the 20th century. Don鈥檛 worry if the maths itself isn't of great interest to you 鈥� the story will, both in its historical context and in the insight into the work and nature of modern mathematicians - at least, relatively modern given the book is a good 25 years old now.
In some ways the star of the book is Andrew Wiles, the British mathematician who pretty well single-handedly cracked the problem with an unusual level of secrecy, rather than the typical sharing approach of the profession. But equally it鈥檚 Fermat himself.
Whether or not Fermat actually had a solution is a moot point 鈥� but he certainly didn鈥檛 have Wiles鈥� complex approach and it's entirely possible it was a boast that he could have fulfilled. It seems so difficult to come up with a straightforward solution to this problem that Fermat has to be more than a little doubted. The nature of Wiles' solution is such that many mathematicians struggled with it, and Singh can only really give us an impression of what was involved. Any attempt to give meaning to the 100 plus page proof requires mathematics that is beyond the casual reader, and it's probably fair to say that bringing any clarity to the nature of the proof is the weakest part of this book.
Like all the best popular science books 鈥� and this certainly is one of the best 鈥� it brings in a whole range of extras historically and mathematically to add to the fascinating cast. Singh's writing style is fluid and genial. He came from a TV background, and the book combines the accessibility of that genre with the ability to go into far more depth than a TV documentary can. It's a milestone in the development of the popular science genre.
January 17, 2016
From my reading journal:
May 31, 2009.
Yesterday I finished reading Fermat's Last Theorem. I plan to write a glowing book review but this space is too limited to contain it.
April 25, 2019
Strap in, guys. I鈥檓 going to walk you through the history of how Fermat鈥檚 Last Theorum was proved, all in one little (okay, big) review. And I can do this because of this awesome, semi-accessible, frequently tangent-taking, but mostly, this deeply fascinating book.
----------STEP ONE: THE THEORUM----------
For the unenlightened, Fermat鈥檚 Last Theorum is this: you probably know the Pythagorean theorum, a虏 + b虏 = c虏, which explains that if you square the shorter two sides of a right-angled triangle and add them together, you get the value of third side squared. This is easily proved (that is, demonstrated to be completely, utterly, logically true via a mathematical proof, using axioms known to be true, which is just like a logic proof if you鈥檝e done philosophy. Or a geometry proof, if you went to 9th grade). Take any triangle, and this will be true. There are infinite solutions to this equation鈥攍iterally infinite values of A, B, and C which will render this solution true.
However, Fermat discovered that the formula an + bn = cn where n > 2 has NO whole number solutions. (Go ahead, give it a whirl. I鈥檒l wait).
Then he challenged the mathematical community to create a mathematical proof demonstrating this must be true. While tantalizing them with the knowledge he鈥檇 already created a proof for this with a scribbled note in the margin of his notebook: 鈥淚 have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.鈥�
Asshole.
So sparked centuries of people trying to write this proof, to no avail. Until Professor Andrew Wiles (who has the most apropos name ever鈥攈e has wiles indeed) of Cambridge, in 1993.
***
For clarity, this is Fermat鈥檚 Equation (which I鈥檒l refer to as FE): an + bn = cn where n > 2
And THIS is Fermat鈥檚 Last Theorum (which I鈥檒l refer to as FLT): 鈥淭here are no solutions to Fermat鈥檚 Equation鈥�
***
----------TANGENT: GODEL----------
At this point, it鈥檚 been assumed that math is logically perfect鈥攖hat if you correctly build a proof using axioms (like m + n = n + m), it must be true (and if it鈥檚 proven to be true, nothing can prove it to be false). This is known as 鈥渁xiomatic set theory.鈥�
Along came Godel (who is analyzed to death by my beloved, Doug Hofstadter- see here and here). His ideas are as follows:
1. If axiomatic set theory is consistent, then there have to be theorems that can鈥檛 be proved or disproved. Why? Because of paradoxes. Godel translated the following statement into mathematical notation: 鈥淭his statement has no proof.鈥� If that鈥檚 false, then you COULD create a proof for that statement鈥攈owever, that would make the statement false, so how could you have a proof for that? So it has to be true. But if it鈥檚 true, it can鈥檛 be proved because that鈥檚 what it literally says. It鈥檚 a mathematical statement that is true, but could never be proved to be true (an 鈥渦ndecidable statement鈥�).
2. There鈥檚 no way to prove that axiomatic set theory is consistent; in a way, it鈥檚 one of those 鈥渦ndecidable statement鈥� that鈥檚 true but can鈥檛 be proved to be true.
Interestingly, this parallels the physicist Heisenberg鈥檚 discovery of the uncertainty principle, but we won鈥檛 get into that.
Now, there aren鈥檛 very many of those undecidable statements. Godel couldn鈥檛 really point to any other undecidable statements besides the one above, so people assumed they were found only in the most extreme math and would probably never even be encountered.
Welp. A young student named Paul Cohen at Stanford discovered a way to test whether a question is undecidable, and in doing so, discovered several more.
Which sparked some fear in mathematicians. What if Fermat鈥檚 Last Theorum was undecidable?! What if they were wasting their time trying to prove the unprovable?
Interestingly, if it were an undecidable statement, it couldn鈥檛 be proved鈥攜et it would have to be true. The theorum says 鈥渢here are no whole numbers to the equation an + bn = cn where n > 2.鈥� If this were false, then it would be possible to prove this by offering a solution to this鈥攂y finding a whole number N that鈥檚 greater than 2 that allows the equation to be solved. Which would make it a decidable statement, which is a contradiction. So it can鈥檛 be false and also be an undecidable statement. In other words, Fermat鈥檚 Last Theorum might be totally true but there might be no way to prove it.
----------STEP TWO: TANIYAMA-SHIMURA CONJECTURE----------
Modular forms are a mathematical tool, sort of like impossible forms or shapes, that reveal a lot about how numbers are related.
The Taniyama-Shimura Conjecture (TSC), created by two Japanese mathematicians (one of whom tragically and abruptly killed himself quite young) says every modular form is related to a specific elliptic equation (elliptic equations were Andrew Wiles鈥檚 main area of study; they鈥檙e a type of equation, not super important that you understand them).
The fact that these were unified meant there鈥檚 a kind of Rosetta stone that鈥檚 been discovered: 鈥淪imple intuitions in the modular world translate into deep truths in the elliptic world, and vice versa. Very profound problems in the elliptic world can get solved sometimes by translating them using this Rosetta stone into the modular world, and discovering that we have the insights and tools in the modular world to treat the translated problem. Back in the elliptic world we would have been at a loss.鈥�
Beyond that awesomeness, the TSC suggests something even more interesting: that possibly all of mathematics, all the different worlds of mathematics, might have parallels in other worlds, as with the elliptic world and the modular world. All of mathematics might be unified鈥攁rguably the absolute ultimate goal of abstract mathematics, because this would give us the most complete picture, and the biggest arsenal of tools to solve mathematical problems.
----------STEP THREE: RIBET鈥橲 THEORUM----------
This is all important for FLT because of something called Ribet鈥檚 Theorum (Ribet was a colleague of Wiles). Ribet鈥檚 Theorum goes like this: the imagined solution to FE can be translated into an elliptic equation. And that elliptic equation doesn鈥檛 seem to have a modular world equivalent. But the TSC claims that every elliptic equation must be related to a modular form.
So if you can PROVE that the elliptic form of the solution to FE has no modular form (which we can! The proof was done in 1986), the following is true: if the TSC is true (i.e. all elliptic equations have modular forms), and the elliptic form of the imagined solution to FE has no modular form, then the imagined solution cannot exist, proving FLT.
So now, all we have to do is prove that the TSC is true, and FLT is automatically proven to be true.
And this鈥擳HIS鈥攊s what Andrew Wiles focused on. Proving the TSC (Taniyama-Shimura Conjecture).
----------STEP FOUR: PROVING THE THEORUM----------
Wiles finally succeeded when he applied a new method called the Kolyvagin-Flach method, which groups elliptic equations into families and then proves that an elliptic equation in that family has a modular form; if that elliptic equation has a modular form, then all other elliptic equations in that family also has a modular form.
However, the Kolyvagin-Flach method has to be adapted for each family of elliptic equations. Wiles successfully adapted the method for all families of elliptic equations, thereby proving that all elliptic equations have modular forms (which, as a reminder, is basis of the Taniyama-Shimura Conjecture, and proving the TSC proves FLT).
Two months before I was born, in 1993, he proved FLT in a series of 3 lectures.
Kinda. Actually, there was a minor flaw in his proof (essentially, he might have failed to properly adapt the Kolyvagin-Flach method for some of the families of equations) but it doesn鈥檛 really matter because a year later, Wiles published a work-around to that flaw, so he proved FLT once and for all.
----------CONCLUSION----------
All I can think about is: maybe if math looked like this, if THIS had been our material in high school鈥攎aybe then I wouldn鈥檛 have disliked it. Maybe other people wouldn鈥檛, either. What a shoddy job we do teaching our children the wonder of learning.
----------STEP ONE: THE THEORUM----------
For the unenlightened, Fermat鈥檚 Last Theorum is this: you probably know the Pythagorean theorum, a虏 + b虏 = c虏, which explains that if you square the shorter two sides of a right-angled triangle and add them together, you get the value of third side squared. This is easily proved (that is, demonstrated to be completely, utterly, logically true via a mathematical proof, using axioms known to be true, which is just like a logic proof if you鈥檝e done philosophy. Or a geometry proof, if you went to 9th grade). Take any triangle, and this will be true. There are infinite solutions to this equation鈥攍iterally infinite values of A, B, and C which will render this solution true.
However, Fermat discovered that the formula an + bn = cn where n > 2 has NO whole number solutions. (Go ahead, give it a whirl. I鈥檒l wait).
Then he challenged the mathematical community to create a mathematical proof demonstrating this must be true. While tantalizing them with the knowledge he鈥檇 already created a proof for this with a scribbled note in the margin of his notebook: 鈥淚 have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.鈥�
Asshole.
So sparked centuries of people trying to write this proof, to no avail. Until Professor Andrew Wiles (who has the most apropos name ever鈥攈e has wiles indeed) of Cambridge, in 1993.
***
For clarity, this is Fermat鈥檚 Equation (which I鈥檒l refer to as FE): an + bn = cn where n > 2
And THIS is Fermat鈥檚 Last Theorum (which I鈥檒l refer to as FLT): 鈥淭here are no solutions to Fermat鈥檚 Equation鈥�
***
----------TANGENT: GODEL----------
At this point, it鈥檚 been assumed that math is logically perfect鈥攖hat if you correctly build a proof using axioms (like m + n = n + m), it must be true (and if it鈥檚 proven to be true, nothing can prove it to be false). This is known as 鈥渁xiomatic set theory.鈥�
Along came Godel (who is analyzed to death by my beloved, Doug Hofstadter- see here and here). His ideas are as follows:
1. If axiomatic set theory is consistent, then there have to be theorems that can鈥檛 be proved or disproved. Why? Because of paradoxes. Godel translated the following statement into mathematical notation: 鈥淭his statement has no proof.鈥� If that鈥檚 false, then you COULD create a proof for that statement鈥攈owever, that would make the statement false, so how could you have a proof for that? So it has to be true. But if it鈥檚 true, it can鈥檛 be proved because that鈥檚 what it literally says. It鈥檚 a mathematical statement that is true, but could never be proved to be true (an 鈥渦ndecidable statement鈥�).
2. There鈥檚 no way to prove that axiomatic set theory is consistent; in a way, it鈥檚 one of those 鈥渦ndecidable statement鈥� that鈥檚 true but can鈥檛 be proved to be true.
Interestingly, this parallels the physicist Heisenberg鈥檚 discovery of the uncertainty principle, but we won鈥檛 get into that.
Now, there aren鈥檛 very many of those undecidable statements. Godel couldn鈥檛 really point to any other undecidable statements besides the one above, so people assumed they were found only in the most extreme math and would probably never even be encountered.
Welp. A young student named Paul Cohen at Stanford discovered a way to test whether a question is undecidable, and in doing so, discovered several more.
Which sparked some fear in mathematicians. What if Fermat鈥檚 Last Theorum was undecidable?! What if they were wasting their time trying to prove the unprovable?
Interestingly, if it were an undecidable statement, it couldn鈥檛 be proved鈥攜et it would have to be true. The theorum says 鈥渢here are no whole numbers to the equation an + bn = cn where n > 2.鈥� If this were false, then it would be possible to prove this by offering a solution to this鈥攂y finding a whole number N that鈥檚 greater than 2 that allows the equation to be solved. Which would make it a decidable statement, which is a contradiction. So it can鈥檛 be false and also be an undecidable statement. In other words, Fermat鈥檚 Last Theorum might be totally true but there might be no way to prove it.
----------STEP TWO: TANIYAMA-SHIMURA CONJECTURE----------
Modular forms are a mathematical tool, sort of like impossible forms or shapes, that reveal a lot about how numbers are related.
The Taniyama-Shimura Conjecture (TSC), created by two Japanese mathematicians (one of whom tragically and abruptly killed himself quite young) says every modular form is related to a specific elliptic equation (elliptic equations were Andrew Wiles鈥檚 main area of study; they鈥檙e a type of equation, not super important that you understand them).
The fact that these were unified meant there鈥檚 a kind of Rosetta stone that鈥檚 been discovered: 鈥淪imple intuitions in the modular world translate into deep truths in the elliptic world, and vice versa. Very profound problems in the elliptic world can get solved sometimes by translating them using this Rosetta stone into the modular world, and discovering that we have the insights and tools in the modular world to treat the translated problem. Back in the elliptic world we would have been at a loss.鈥�
Beyond that awesomeness, the TSC suggests something even more interesting: that possibly all of mathematics, all the different worlds of mathematics, might have parallels in other worlds, as with the elliptic world and the modular world. All of mathematics might be unified鈥攁rguably the absolute ultimate goal of abstract mathematics, because this would give us the most complete picture, and the biggest arsenal of tools to solve mathematical problems.
----------STEP THREE: RIBET鈥橲 THEORUM----------
This is all important for FLT because of something called Ribet鈥檚 Theorum (Ribet was a colleague of Wiles). Ribet鈥檚 Theorum goes like this: the imagined solution to FE can be translated into an elliptic equation. And that elliptic equation doesn鈥檛 seem to have a modular world equivalent. But the TSC claims that every elliptic equation must be related to a modular form.
So if you can PROVE that the elliptic form of the solution to FE has no modular form (which we can! The proof was done in 1986), the following is true: if the TSC is true (i.e. all elliptic equations have modular forms), and the elliptic form of the imagined solution to FE has no modular form, then the imagined solution cannot exist, proving FLT.
So now, all we have to do is prove that the TSC is true, and FLT is automatically proven to be true.
And this鈥擳HIS鈥攊s what Andrew Wiles focused on. Proving the TSC (Taniyama-Shimura Conjecture).
----------STEP FOUR: PROVING THE THEORUM----------
Wiles finally succeeded when he applied a new method called the Kolyvagin-Flach method, which groups elliptic equations into families and then proves that an elliptic equation in that family has a modular form; if that elliptic equation has a modular form, then all other elliptic equations in that family also has a modular form.
However, the Kolyvagin-Flach method has to be adapted for each family of elliptic equations. Wiles successfully adapted the method for all families of elliptic equations, thereby proving that all elliptic equations have modular forms (which, as a reminder, is basis of the Taniyama-Shimura Conjecture, and proving the TSC proves FLT).
Two months before I was born, in 1993, he proved FLT in a series of 3 lectures.
Kinda. Actually, there was a minor flaw in his proof (essentially, he might have failed to properly adapt the Kolyvagin-Flach method for some of the families of equations) but it doesn鈥檛 really matter because a year later, Wiles published a work-around to that flaw, so he proved FLT once and for all.
----------CONCLUSION----------
All I can think about is: maybe if math looked like this, if THIS had been our material in high school鈥攎aybe then I wouldn鈥檛 have disliked it. Maybe other people wouldn鈥檛, either. What a shoddy job we do teaching our children the wonder of learning.
April 3, 2009
What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the proof to Fermat's Last Theorem, but of much of mathematics (and the lives of mathematicians) since the seventeenth century.
I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book, Fermat's Enigma plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.
Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus' Arithmetica that x^n + y^n 鈮� z^n for any number n greater than 2, a propostion for which he had "a truly marvelous demonstration鈥� which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for over 350 YEARS .
Andrew Wiles published the first (and only?) proof in 1994, and Enigma does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication鈥� what was Fermat's proof?
I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book, Fermat's Enigma plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.
Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus' Arithmetica that x^n + y^n 鈮� z^n for any number n greater than 2, a propostion for which he had "a truly marvelous demonstration鈥� which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for over 350 YEARS .
Andrew Wiles published the first (and only?) proof in 1994, and Enigma does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication鈥� what was Fermat's proof?
December 9, 2007
This book is as interesting as a detective story while being about quite advanced mathematics - as such it is quite a book showing the remarkable skill of its writer to explain complex ideas in ways that are always readable and enjoyable.
A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mathematician jots down that he has found this proof, but not what the proof is. And for hundredsd of years the greatest minds in mathematics have tried to find this simple proof and been beaten by the problem time and again.
This really is a delightful book and one that gives an insight into how mathematicians think about the world. The proof of Pythagoras's theorem given in this book is so simple that the beauty of mathematical proof is made plain to everyone. Just a little knowledge of algebra is needed for this part of the book - the rest requires no maths at all.
A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mathematician jots down that he has found this proof, but not what the proof is. And for hundredsd of years the greatest minds in mathematics have tried to find this simple proof and been beaten by the problem time and again.
This really is a delightful book and one that gives an insight into how mathematicians think about the world. The proof of Pythagoras's theorem given in this book is so simple that the beauty of mathematical proof is made plain to everyone. Just a little knowledge of algebra is needed for this part of the book - the rest requires no maths at all.
August 25, 2017
Un teorema 猫 per sempre
Un tale Fermat, che nel diciassettesimo secolo si dilettava di matematica ed era un po' buontempone, enunci貌 un teorema all'apparenza banale e lasci貌 scritto sul margine di una pagina di un libro:
鈥淒ispongo di una meravigliosa dimostrazione di questo teorema, che non pu貌 essere contenuta nel margine stretto della pagina鈥�
Il teorema era banale, come pure l'affermazione. Non poteva che scaturirne una dimostrazione banale.
Eppure...
La dimostrazione di quell'equazione banale fece perdere il sonno alle maggiori menti matematiche di tutto il mondo, che per 350 anni si arrovellarono per trovare una soluzione. Risultati: zero.
Cos'猫 una dimostrazione? In matematica si ritiene che un teorema sia dimostrato quando con un procedimento logico se ne fornisce inequivocabilmente e incontestabilmente la correttezza.
"La ricerca di una dimostrazione matematica 猫 la ricerca di una conoscenza che 猫 pi霉 assoluta della conoscenza accumulata da ogni altra disciplina. Il desiderio di una verit脿 definitiva ottenuta attraverso il metodo della dimostrazione 猫 ci貌 che ha guidato i matematici negli ultimi duemilacinquecento anni."
Solo nel 1993 un matematico inglese, Andrew Wiles, dopo sette anni di sforzi, ossessioni, notti insonni, incubi, entusiasmi e delusioni riusc矛 a completare la dimostrazione.
Possibile che Fermat avesse trovato una dimostrazione a questo teorema? No, impossibile crederlo; la dimostrazione di Wiles 猫 composta da 200 pagine di matematica estremamente complessa che non poteva assolutamente essere disponibile al tempo di Fermat e che alla fine per貌 猫 servita anche ad approfondire intere branche della matematica.
Ecco, il libro spiega la storia di questa dimostrazione e dei grandi matematici che ci hanno lavorato, spiega la bellezza delle sfide matematiche, l'ostinazione e la determinazione richiesta, l'inventiva necessaria e la potenza di un risultato che diventa "eterno".
La storia di questa dimostrazione 猫 decisamente interessante; per me l'unica carenza nel libro 猫 l'autore, che 猫 "solo" un giornalista e che, poraccio, di matematica ci capisce come io di taglio e cucito. E trasforma la storia in una telecronaca; per consentire ai profani di capire gli aspetti legati alla successione degli eventi d脿 per scontate parecchie cose (pur riportandole) rinunciando a spiegare con semplicit脿, forse perch茅 nemmeno lui ci ha capito un granch茅.
Cartesio disse: "quando sono in discussione questioni trascendentali, siate chiari in modo trascendentale".
Ecco Singh chiaro non 猫. Inutile per me riportare frasi come "Tutto quello che devi fare 猫 aggiungere qualche gamma-zero di struttura (M) e poi ti basta ripercorrere la tua argomentazione ed ecco che funziona" se non se ne spiega il significato. O si omette la frase, o la si spiega.
Riesce pure a mettere errori di matematica nelle definizioni che, mi dispiace, in un libro di matematica noooooo, proprio non accetto!.
In ogni caso la storia 猫 affascinante e il libro riesce a trasmettere interesse e curiosit脿 per la matematica e per queste persone meravigliose che si sono prodigate per trovare soluzioni a problemi veramente complessi.
Fermat era un buontempone e ci ha preso in giro per 350 anni. Ma senza di lui, oggi le nostre conoscenze matematiche sarebbero certamente inferiori...
March 13, 2021
Belas hist贸rias de amor. Do amor dos homens por um teorema: o 煤ltimo Teorema de Fermat.
Uma odisseia matem谩tica cheia de beleza, frustra莽茫o e triunfo. N茫o 茅 apenas a hist贸ria do genial Andrew Wiles; esta 茅 a hist贸ria dos homens que amam a matem谩tica. Sem fins utilit谩rios, sem pretens玫es. De Pit谩goras a Wiles, de 1637 a 1994.
A Fermat faltou espa莽o naquela p谩gina para fazer a sua brilhante demonstra莽茫o, mas 脿s posteriores gera莽玫es de matem谩ticos n茫o faltou coragem. Ser谩 que Fermat estava, mais uma vez, certo?
Esta obra, embora aborde conceitos matem谩ticos [alguns com um elevado grau de complexidade como a conjectura Taniyama-Shimura] e apresente reflex玫es que exigem um apurado racioc铆nio abstracto [sobretudo nesta 谩rea de matem谩tica pura] n茫o pretende excluir aqueles que n茫o se encontram entre os poucos eleitos que compreendem perfeitamente a linguagem dos n煤meros. A leitura, 脿s vezes, apresenta algumas dificuldades (ultrapass谩veis) mas vale muito a pena. Uma obra muito bela e que nos encanta.
Para saber um bocadinho mais:
*
"El recuerdo de Arqu铆medes persistir谩 cuando Esquilo est茅 ya olvidado, porque las lenguas mueren y los conceptos matem谩ticos no. Inmortalidad es tal vez un t茅rmino est煤pido, pero quiz谩 un matem谩tico posea las mayores probabilidades de alcanzarla, sea cual sea su significado." [G.H.Hardy]
Uma odisseia matem谩tica cheia de beleza, frustra莽茫o e triunfo. N茫o 茅 apenas a hist贸ria do genial Andrew Wiles; esta 茅 a hist贸ria dos homens que amam a matem谩tica. Sem fins utilit谩rios, sem pretens玫es. De Pit谩goras a Wiles, de 1637 a 1994.
A Fermat faltou espa莽o naquela p谩gina para fazer a sua brilhante demonstra莽茫o, mas 脿s posteriores gera莽玫es de matem谩ticos n茫o faltou coragem. Ser谩 que Fermat estava, mais uma vez, certo?
Esta obra, embora aborde conceitos matem谩ticos [alguns com um elevado grau de complexidade como a conjectura Taniyama-Shimura] e apresente reflex玫es que exigem um apurado racioc铆nio abstracto [sobretudo nesta 谩rea de matem谩tica pura] n茫o pretende excluir aqueles que n茫o se encontram entre os poucos eleitos que compreendem perfeitamente a linguagem dos n煤meros. A leitura, 脿s vezes, apresenta algumas dificuldades (ultrapass谩veis) mas vale muito a pena. Uma obra muito bela e que nos encanta.
Para saber um bocadinho mais:
*
"El recuerdo de Arqu铆medes persistir谩 cuando Esquilo est茅 ya olvidado, porque las lenguas mueren y los conceptos matem谩ticos no. Inmortalidad es tal vez un t茅rmino est煤pido, pero quiz谩 un matem谩tico posea las mayores probabilidades de alcanzarla, sea cual sea su significado." [G.H.Hardy]
September 23, 2022
The best mathematical nonfiction thriller I've ever read!
Consider this equation: x^n + y^n = z^n (where x,y,z,n are natural numbers with n>2)
Fermat stated that the above equation has no solutions.
It鈥檚 the simplicity of this theorem which is elusive of the nature of its difficulty to be proved!
Stated around 1637, Fermat had scribbled this theorem with a note in the margin - "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
This theorem and other notes were published posthumously by his son. Till date, nobody is aware of the proof that Fermat would have concocted in his mind!
With modern mathematical tools and researches, this theorem which remained unsolved for more than 350 years was finally proved in 1995 by Andrew Wiles.
This book is a tale of how this theorem was pursued for centuries and finally how it was proved.
Loved:
The context setting and remarkable background stories.
Fun trivia on numbers - and how mathematics is the language of nature.
The depth into which many great minds delved and devoted their entire life.
Recommended:
If you've ever been intrigued by Mathematics, this is a must read.
You don't necessarily need to have a grip on Maths to enjoy this book. Explained in layman terms, detailed mathematical proofs and footnotes are all confined to the Appendix section, for the curious minds.
Notes:
How I picked this book - A friend sent greetings at 5:29PM mentioning special time. Though I knew about the magic number, but somehow this message helped me traverse down the rabbit hole.
Ramanujan -> Magic Number -> Taxicab Number -> Fermat near misses -> Fermat's last Theorem... and from thereon it was a different world altogether!
Then last month, I went shopping books on behalf of friends. Someone picked these, which I ended up reading before sending :) [thank you!]
Consider this equation: x^n + y^n = z^n (where x,y,z,n are natural numbers with n>2)
Fermat stated that the above equation has no solutions.
It鈥檚 the simplicity of this theorem which is elusive of the nature of its difficulty to be proved!
Stated around 1637, Fermat had scribbled this theorem with a note in the margin - "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
This theorem and other notes were published posthumously by his son. Till date, nobody is aware of the proof that Fermat would have concocted in his mind!
With modern mathematical tools and researches, this theorem which remained unsolved for more than 350 years was finally proved in 1995 by Andrew Wiles.
This book is a tale of how this theorem was pursued for centuries and finally how it was proved.
Loved:
The context setting and remarkable background stories.
Fun trivia on numbers - and how mathematics is the language of nature.
The depth into which many great minds delved and devoted their entire life.
Recommended:
If you've ever been intrigued by Mathematics, this is a must read.
You don't necessarily need to have a grip on Maths to enjoy this book. Explained in layman terms, detailed mathematical proofs and footnotes are all confined to the Appendix section, for the curious minds.
Notes:
How I picked this book - A friend sent greetings at 5:29PM mentioning special time. Though I knew about the magic number, but somehow this message helped me traverse down the rabbit hole.
Ramanujan -> Magic Number -> Taxicab Number -> Fermat near misses -> Fermat's last Theorem... and from thereon it was a different world altogether!
Then last month, I went shopping books on behalf of friends. Someone picked these, which I ended up reading before sending :) [thank you!]
September 26, 2022
鈥淭he definition of a good mathematical problem is the mathematics it generates rather than the problem itself.鈥�
Fermat's Last Theorem states that: x鈦� + y鈦� = z鈦� has no whole number solutions for any integer n greater than 2. Simon Singh fashions the quest to solve this 350-year-old mathematical enigma into a compelling story. In the 1630s, when Pierre de Fermat scribbled a note on a page of his copy of Diophantus鈥檚 Arithmetica, stating (in Latin) his theorem and indicating 鈥淚 have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.鈥� Singh takes the reader through a series of minibiographies of past mathematicians, ultimately arriving at Andrew Wiles, who spent over eight years developing the 130-page proof.
Along the way, the reader will learn a great deal about number theory, logic, and the rigorous standards required to achieve an absolute proof. This book covers a wide variety of people and their contributions over the years, such as Pythagoras, Leonhard Euler, Sophie Germain, Gabriel Lame鈥�, Augustin Cauchy, Ernst Kummer, David Hilbert, Kurt Godel, Alan Turing, Goro Shimura, and Yutaka Taniyama.
The highlight of the book is, of course, Andrew Wiles who discovered Fermat鈥檚 Last Theorem at the age of ten, and dedicated himself to figuring out a proof, no matter how long it took. Wiles decided to keep his work secret and work alone in his attic. 鈥淵ou might ask how could I devote an unlimited amount of time to a problem that might simply not be soluble. The answer is that I just loved working on this problem and I was obsessed. I enjoyed pitting my wits against it.鈥�
We learn about the Shimura-Taniyama conjecture, and the relationship between elliptic curves and modular forms. Singh never gets bogged down with calculations 鈥� they are instead included in the Appendices. I have a background in mathematics, so this type of subject matter appeals to me, but I daresay it is not required to enjoy this story of challenge, perseverance, and discovery.
4.5
Fermat's Last Theorem states that: x鈦� + y鈦� = z鈦� has no whole number solutions for any integer n greater than 2. Simon Singh fashions the quest to solve this 350-year-old mathematical enigma into a compelling story. In the 1630s, when Pierre de Fermat scribbled a note on a page of his copy of Diophantus鈥檚 Arithmetica, stating (in Latin) his theorem and indicating 鈥淚 have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.鈥� Singh takes the reader through a series of minibiographies of past mathematicians, ultimately arriving at Andrew Wiles, who spent over eight years developing the 130-page proof.
Along the way, the reader will learn a great deal about number theory, logic, and the rigorous standards required to achieve an absolute proof. This book covers a wide variety of people and their contributions over the years, such as Pythagoras, Leonhard Euler, Sophie Germain, Gabriel Lame鈥�, Augustin Cauchy, Ernst Kummer, David Hilbert, Kurt Godel, Alan Turing, Goro Shimura, and Yutaka Taniyama.
The highlight of the book is, of course, Andrew Wiles who discovered Fermat鈥檚 Last Theorem at the age of ten, and dedicated himself to figuring out a proof, no matter how long it took. Wiles decided to keep his work secret and work alone in his attic. 鈥淵ou might ask how could I devote an unlimited amount of time to a problem that might simply not be soluble. The answer is that I just loved working on this problem and I was obsessed. I enjoyed pitting my wits against it.鈥�
We learn about the Shimura-Taniyama conjecture, and the relationship between elliptic curves and modular forms. Singh never gets bogged down with calculations 鈥� they are instead included in the Appendices. I have a background in mathematics, so this type of subject matter appeals to me, but I daresay it is not required to enjoy this story of challenge, perseverance, and discovery.
4.5
January 31, 2024
賰鬲丕亘 乇賷丕囟賷 賲丕鬲毓. 賱賲 兀鬲賵賯毓 兀賳 兀爻鬲賲鬲毓 亘賯乇丕亍丞 賴匕丕 丕賱賰鬲丕亘 廿賱賶 賴匕丕 丕賱丨丿!
賷賰鬲亘 賮賷乇賲丕 賮賷 丕賱賯乇賳 丕賱爻丕亘毓 毓卮乇 毓賱賶 賴丕賲卮 賰鬲丕亘 乇賷丕囟賷 賲毓丕丿賱丞. 賵賷賯賵賱 兀賳賴 賱丕 丨賱賾 賱賴匕賴 丕賱賲毓丕丿賱丞. 賵兀賳賾 賱丿賷賴 亘乇賴丕賳丕賸 賱丕 賲爻丕丨丞 賱賴 賮賷 賴匕丕 丕賱賴丕賲卮 賱賷賰鬲亘賴!
賱爻賳賵丕鬲 胤賵丕賱貨 賷馗賱賾 丕賱乇賷丕囟賷賵賳 賷丨丕賵賱賵賳 廿孬亘丕鬲 賯賵賱賴 兀賵 鬲賮賳賷丿賴. 賵賷氐賷亘賴賲 丕賱廿丨亘丕胤 賮賷 賰賱賾 賲乇丞. 賵鬲禺亘賵 噩匕賵丞 丕賱亘丨孬 夭賲賳丕賸 賱賰賳賴丕 鬲毓賵丿. 廿賱賶 兀賳 賳氐賱 廿賱賶 丕賱毓丕賲 1995. 丨賷孬 鬲購孬亘鬲 賳賴丕卅賷丕 亘廿丿禺丕賱 賯賵丕賳賷賳 丕賱乇賷丕囟賷丕鬲 丕賱丨丿賷孬丞 賵丕賱鬲禺賷賱賷丞 噩丿丕賸!
賵賰兀賳賷 亘賴丕鬲賴 丕賱賲亘乇賴賳丞 賲孬丕賱 丨賯賷賯賷 賱卮毓乇 兀亘賷 丕賱胤賷亘 丕賱賲鬲賳亘賷:
兀賻賳丕賲購 賲賽賱亍賻 噩購賮賵賳賷 毓賻賳 卮賻賵丕乇賽丿賽賴丕..... 賵賻賷賻爻賴賻乇購 丕賱禺賻賱賯購 噩賻乇賾丕賴丕 賵賻賷賻禺鬲賻氐賽賲購
賵賰兀賳賾 賮賷乇賲丕 賱賲 賷賳賲 賮丨爻亘貙 亘賱 賲丕鬲 賲賱亍 噩賮賵賳賴 賵亘賱賶 毓馗丕賲賴貨 賵亘賯賷 丕賱賳丕爻 鈥撡堎勝娯迟堌� 兀賷 賳丕爻- 賷爻賴乇賵賳 噩乇丕賴丕 賵賷禺鬲氐賲賵賳.
賷兀禺匕賳丕 丕賱賰丕鬲亘 丕賱賲丕賴乇 "爻丕賷賲賵賳 爻賷賳噩" 賮賷 賴匕賴 丕賱乇丨賱丞 丕賱賮賰乇賷丞 丕賱賲丿賴卮丞. 賵賮賷 丕爻鬲胤乇丕丿丕鬲 乇丕卅毓丞貙 賳毓賷卮 賲毓 乇賷丕囟賷賷賳 賰孬乇 賮賷 兀夭賲賳丞 賲禺鬲賱賮丞貙 亘丕賴鬲賲丕賲丕鬲賴賲 賵兀爻卅賱鬲賴賲 賵賰卮賵賮丕鬲賴賲.
爻賷丨亘 賴匕丕 丕賱賰鬲丕亘 賲賳 賷丨亘賾 丕賱乇賷丕囟賷丕鬲貙 賵賲賳 賷丨亘賾 賯乇丕亍丞 丕賱爻賷乇貙 賵賲賳 賷丨亘賾 賲鬲丕亘毓丞 丕賱賲睾丕賲乇丕鬲 丕賱賮賰乇賷丞 丕賱鬲賷 賷購爻賱賲賴丕 賰賱賾 噩賷賱 廿賱賶 丕賱匕賷 賷賱賷賴.
鬲乇噩賲丞 丕賱賰鬲丕亘 賲賲鬲丕夭丞貙 賮卮賰乇丕賸 賱賱賲鬲乇噩賲丞 "丕賱夭賴乇丕亍 爻丕賲賷" 毓賱賶 鬲乇噩賲鬲賴丕 丕賱夭丕賴乇丞.
賵卮賰乇 賵丕噩亘 賱賲丐爻爻丞 賴賳丿丕賵賷 丕賱賮賰乇賷丞 丕賱鬲賷 兀爻毓丿鬲賳丕 亘廿氐丿丕乇 賴匕丕 丕賱賰鬲丕亘.
賷賰鬲亘 賮賷乇賲丕 賮賷 丕賱賯乇賳 丕賱爻丕亘毓 毓卮乇 毓賱賶 賴丕賲卮 賰鬲丕亘 乇賷丕囟賷 賲毓丕丿賱丞. 賵賷賯賵賱 兀賳賴 賱丕 丨賱賾 賱賴匕賴 丕賱賲毓丕丿賱丞. 賵兀賳賾 賱丿賷賴 亘乇賴丕賳丕賸 賱丕 賲爻丕丨丞 賱賴 賮賷 賴匕丕 丕賱賴丕賲卮 賱賷賰鬲亘賴!
賱爻賳賵丕鬲 胤賵丕賱貨 賷馗賱賾 丕賱乇賷丕囟賷賵賳 賷丨丕賵賱賵賳 廿孬亘丕鬲 賯賵賱賴 兀賵 鬲賮賳賷丿賴. 賵賷氐賷亘賴賲 丕賱廿丨亘丕胤 賮賷 賰賱賾 賲乇丞. 賵鬲禺亘賵 噩匕賵丞 丕賱亘丨孬 夭賲賳丕賸 賱賰賳賴丕 鬲毓賵丿. 廿賱賶 兀賳 賳氐賱 廿賱賶 丕賱毓丕賲 1995. 丨賷孬 鬲購孬亘鬲 賳賴丕卅賷丕 亘廿丿禺丕賱 賯賵丕賳賷賳 丕賱乇賷丕囟賷丕鬲 丕賱丨丿賷孬丞 賵丕賱鬲禺賷賱賷丞 噩丿丕賸!
賵賰兀賳賷 亘賴丕鬲賴 丕賱賲亘乇賴賳丞 賲孬丕賱 丨賯賷賯賷 賱卮毓乇 兀亘賷 丕賱胤賷亘 丕賱賲鬲賳亘賷:
兀賻賳丕賲購 賲賽賱亍賻 噩購賮賵賳賷 毓賻賳 卮賻賵丕乇賽丿賽賴丕..... 賵賻賷賻爻賴賻乇購 丕賱禺賻賱賯購 噩賻乇賾丕賴丕 賵賻賷賻禺鬲賻氐賽賲購
賵賰兀賳賾 賮賷乇賲丕 賱賲 賷賳賲 賮丨爻亘貙 亘賱 賲丕鬲 賲賱亍 噩賮賵賳賴 賵亘賱賶 毓馗丕賲賴貨 賵亘賯賷 丕賱賳丕爻 鈥撡堎勝娯迟堌� 兀賷 賳丕爻- 賷爻賴乇賵賳 噩乇丕賴丕 賵賷禺鬲氐賲賵賳.
賷兀禺匕賳丕 丕賱賰丕鬲亘 丕賱賲丕賴乇 "爻丕賷賲賵賳 爻賷賳噩" 賮賷 賴匕賴 丕賱乇丨賱丞 丕賱賮賰乇賷丞 丕賱賲丿賴卮丞. 賵賮賷 丕爻鬲胤乇丕丿丕鬲 乇丕卅毓丞貙 賳毓賷卮 賲毓 乇賷丕囟賷賷賳 賰孬乇 賮賷 兀夭賲賳丞 賲禺鬲賱賮丞貙 亘丕賴鬲賲丕賲丕鬲賴賲 賵兀爻卅賱鬲賴賲 賵賰卮賵賮丕鬲賴賲.
爻賷丨亘 賴匕丕 丕賱賰鬲丕亘 賲賳 賷丨亘賾 丕賱乇賷丕囟賷丕鬲貙 賵賲賳 賷丨亘賾 賯乇丕亍丞 丕賱爻賷乇貙 賵賲賳 賷丨亘賾 賲鬲丕亘毓丞 丕賱賲睾丕賲乇丕鬲 丕賱賮賰乇賷丞 丕賱鬲賷 賷購爻賱賲賴丕 賰賱賾 噩賷賱 廿賱賶 丕賱匕賷 賷賱賷賴.
鬲乇噩賲丞 丕賱賰鬲丕亘 賲賲鬲丕夭丞貙 賮卮賰乇丕賸 賱賱賲鬲乇噩賲丞 "丕賱夭賴乇丕亍 爻丕賲賷" 毓賱賶 鬲乇噩賲鬲賴丕 丕賱夭丕賴乇丞.
賵卮賰乇 賵丕噩亘 賱賲丐爻爻丞 賴賳丿丕賵賷 丕賱賮賰乇賷丞 丕賱鬲賷 兀爻毓丿鬲賳丕 亘廿氐丿丕乇 賴匕丕 丕賱賰鬲丕亘.
March 22, 2019
I never watched any documentaries before going to college (and this was about a century and a half ago.. I am getting old -_-. But yeah, 2009 to be precise). I was always interested in NatGeo and History Channel - but they never showed the real deal on television. The documentaries would be mostly half assed, and at worst, total crap. That's also how Indian television landscape can be broadly categorized too, give or take a few exceptions ofcourse. And so I grew up loving the sciences based on what was taught in school curriculum, and elsewhere what I read on the slow 64-bit internet connection.
And then college happened. Parents got me my own laptop - and the college intranet had a ton of stuff that other students shared. That place and that time - was where my love for documentaries was born. I had never been so fascinated with anything before. And the first two that I watched - in a long line of them - were Einstein's Biggest Blunder and BBC's Fermat's Last Theorem. The memory of that sunday afternoon is still pretty fresh.
Back then, I only had a casual interest in astronomy and cosmology, and Einstein's theories were still something exotic. And so I basically understood jackshit from the first documentary. Even more intrigued than before, I started the second one. Fermat's Last Theorem was much more relatable - I had known the theorem, and understood the concept too.
Years later when I joined goodreads, I found out that there was a book too. Keeping in with the tradition of firsts, it became the first book on my TBR pile too. Where it stayed until a few days ago - and I finally marked it as read last night.
To be honest, this isn't the greatest book ever. It isnt even Simon Singh's best, who delivered the goods the much better in Big Bang. But it surely captures the essence of all mathematical and scientific endeavor very well - That every once in a while, in the middle of an ordinary life, science gives us a fairytale
And then college happened. Parents got me my own laptop - and the college intranet had a ton of stuff that other students shared. That place and that time - was where my love for documentaries was born. I had never been so fascinated with anything before. And the first two that I watched - in a long line of them - were Einstein's Biggest Blunder and BBC's Fermat's Last Theorem. The memory of that sunday afternoon is still pretty fresh.
Back then, I only had a casual interest in astronomy and cosmology, and Einstein's theories were still something exotic. And so I basically understood jackshit from the first documentary. Even more intrigued than before, I started the second one. Fermat's Last Theorem was much more relatable - I had known the theorem, and understood the concept too.
Years later when I joined goodreads, I found out that there was a book too. Keeping in with the tradition of firsts, it became the first book on my TBR pile too. Where it stayed until a few days ago - and I finally marked it as read last night.
To be honest, this isn't the greatest book ever. It isnt even Simon Singh's best, who delivered the goods the much better in Big Bang. But it surely captures the essence of all mathematical and scientific endeavor very well - That every once in a while, in the middle of an ordinary life, science gives us a fairytale
July 26, 2024
Why do variables love mathematics?
测鈧赌
测鈧赌
February 19, 2017
Hab铆a le铆do parte de este libro cuando estudiaba periodismo, gracias a Alejandra Carmona, una profe muy inquieta que daba el ramo de Antropolog铆a y que siempre llegaba con lecturas nuevas y actuales. Por ella descubr铆 no s贸lo a autores 鈥渁cad茅micos鈥�, como L茅vi-Strauss y 脕ngel Rama, sino a escritores que cruzan el periodismo con la etnograf铆a y la literatura, como Mart铆n Caparr贸s y Simon Singh, autor de El 脷ltimo Teorema de Fermat. Es un libro hermoso, como hermosas son las matem谩ticas y como hermoso es el problema que hered贸 Fermat a sus colegas por m谩s de 300 a帽os y como hermosa es la historia de traiciones, desaf铆os y sue帽os que est谩n ligados a este acertijo matem谩tico.
Este es un libro que mezcla la investigaci贸n cient铆fica, el periodismo y la literatura. Aprend铆 un mont贸n ley茅ndolo. Est谩 escrito (y traducido) con una prosa limpia, liviana y sencilla, algo muy dif铆cil de lograr, sobre todo cuando se explican temas intrincados, como las matem谩ticas. Salvo por el exceso de adverbios de mente (que, ay, me ponen medio mal) es un placer leer las explicaciones complejas de manera tan amable.
Pienso que la matem谩tica son un universo de l贸gica, absolutismos y armon铆a de un nivel superior. Como toda disciplina y todo arte, aspira a la belleza y los matem谩ticos lo saben, persiguen la belleza de la perfecci贸n de los n煤meros y le achacan a este universo propiedades como la bondad o la amistad, todo a partir de patrones num茅ricos. Se me ocurre que mucha de la filosof铆a matem谩tica refleja la moral de sus autores y, al mismo tiempo, describen tambi茅n las relaciones humanas y la vida.
Me gust贸 mucho que el autor se hiciera cargo, en un apartado, del sesgo hist贸rico de g茅nero que han acompa帽ado las matem谩ticas. 鈥淎 trav茅s de los siglos las mujeres han sido desanimadas a estudiar matem谩ticas, pero a pesar de la discriminaci贸n, ha habido varias matem谩ticas que lucharon contra esa costumbre institucionalizada e inscribieron sus nombres en forma indeleble en los anales de las matem谩ticas鈥�. Y nombra a Hipatia de Alejandr铆a o Sophie Germain, que tuvo que usar el pseud贸nimo de Monsieur Le Blanc para que tomaran en serio su trabajo. Cuando ella debi贸 revelar su identidad, un destacado matem谩tico (que fue su maestro sin saber que ella no era hombre) escribi贸: 鈥淐uando una persona del sexo que, de acuerdo con nuestras costumbres y prejuicios, debe encontrar infinitamente m谩s dificultades para familiarizarse con estas espinosas investigaciones, tiene 茅xito en superar estos obst谩culos y penetrar las partes m谩s oscuras de ellas, entonces sin ninguna duda debe tener el m谩s noble coraje, talentos verdaderamente extraordinarios y una genialidad superior鈥�.
Cuando yo estaba en octavo b谩sico era muy porra. Me iba mal en el colegio. No estudiaba demasiado. Ese mismo a帽o me puse a pololear con un chico dos a帽os mayor que yo, que era escandalosamente estudioso. Me acuerdo cuando me explic贸 las potencias. Yo me hab铆a sacado un rojo en la prueba y 茅l, con mucha paciencia y amor, me explic贸 esta materia que en realidad es s煤per f谩cil y entretenida. De ah铆 en adelante me puse igual de odiosa y matea que 茅l. Sal铆 de cuarto medio con promedio 6,9 en matem谩tica. Despu茅s estudi茅 periodismo y olvid茅 los n煤meros, pero al leer este libro record茅 por qu茅 me gustaban tanto, por qu茅 disfrutaba m谩s resolviendo facs铆miles de la PSU de matem谩ticas que viendo Los Simpsons. Hay tanta perfecci贸n en los n煤meros, tantos juegos posibles.
El libro se trata de c贸mo se resolvi贸 el problema matem谩tico m谩s famoso de la historia: el teorema de Fermat, que sostiene que no hay soluciones posibles al teorema de Pit谩goras cuando la potencia es mayor a 2. El libro explica, tambi茅n, porque esa demostraci贸n es tan endemoniada y dif铆cil. La belleza del problema es que Fermat dijo tener una demostraci贸n, pero que no la pod铆a escribir en el margen de un libro, ya que ese espacio era muy peque帽o. En rigor, no exist铆a la demostraci贸n (no existe, nadie ha visto jam谩s la demostraci贸n de Fermat). Era y es una especie de eslab贸n perdido de las matem谩ticas. 350 a帽os despu茅s, Andrew Wiles plantear铆a su propia soluci贸n, una muy compleja y elegante, que unifica las matem谩ticas y que se sirve de todas las etapas de esta ciencia para lograrlo. Al final, el libro cuenta esa historia y tambi茅n repasa miles de a帽os de epistemolog铆a de las matem谩ticas.
Algunas cosas bell铆simas que se leen en este libro:
鈥斺€淧it谩goras hab铆a descubierto que unas proporciones num茅ricas simples eran responsables de la armon铆a de la m煤sica鈥�.
鈥斺€淟a raz贸n entre la longitud real de los r铆os desde su nacimiento hasta su desembocadura y su longitud en l铆nea recta (鈥�) es aproximadamente 3,14: n煤mero cercano al valor de 蟺鈥�.
鈥斺€淟as matem谩ticas son el lenguaje que permite describir la naturaleza del universo鈥�.
鈥斺€淟a raz贸n por la cual se le atribuye el teorema a Pit谩goras es porque fue 茅l quien primero demostr贸 su validez universal鈥�.
鈥斺€淟a llamada demostraci贸n cient铆fica depende de la observaci贸n y la percepci贸n, las cuales son falibles y s贸lo suministran aproximaciones (鈥�) [la demostraci贸n matem谩tica] tiene una verdad m谩s profunda que cualquier otra verdad, porque es el resultado de un proceso l贸gico. Las matem谩ticas son una materia de estudio no subjetiva (鈥�) independiente de la opini贸n鈥�. Es decir, una demostraci贸n matem谩tica es una verdad absoluta y se aplica para un caso espec铆fico como para todos los de su serie hasta el infinito. Es loca esa hue谩, ojal谩 las ciencias sociales funcionaran as铆.
鈥斺€淔ermat y Pascal habr铆an de descubrir las primeras demostraciones y certezas absolutas de la teor铆a de la probabilidad, una materia que es, en esencia, incierta鈥�.
鈥� 鈥淸Pascal] sostuvo que 鈥榣a emoci贸n que un apostador siente cuando hace una apuesta es igual a la cantidad que puede ganar multiplicada por la probabilidad de que gane鈥�.
鈥斺€淓l primer director del departamento de matem谩ticas (de la Universidad de Alejandr铆a) fue, ni m谩s ni menos, Euclides鈥�.
鈥擲obre la destrucci贸n de la biblioteca de Alejandr铆a: 鈥淓n el a帽o 642, un ataque musulm谩n culmin贸 con 茅xito aquello en lo que los cristianos hab铆an fracasado鈥�. Quemaron todo por fanatismo dogm谩tico. Maldita religi贸n.
鈥� 鈥淓l crecimiento de cualquier disciplina depende de su capacidad para comunicar y desarrollar ideas鈥�.
鈥斺€淟os n煤meros amigos son parejas de n煤meros tales que cada uno de ellos es igual a la suma de los divisores del otro鈥�.
鈥斺€淸En matem谩tica] las ideas no corroboradas son infinitamente menos valiosas y se conocen como conjeturas鈥�.
鈥斺€淓s impensable para los matem谩ticos no poder, al menos en teor铆a, contestar todas las preguntas, y esta necesidad se llama completud鈥�.
鈥斺€淟os te贸ricos de los n煤meros consideran a los n煤meros primos como los m谩s importantes de todos, porque son los 谩tomos de las matem谩ticas鈥�.
鈥斺€淒ios existe puesto que las matem谩ticas son consistentes, y el diablo existe puesto que no podemos demostrarlo鈥�, Andr茅 Weil.
鈥擲obre Galois, un maestro escribi贸: 鈥渓a locura matem谩tica domina a este muchacho鈥�.
鈥斺€淐uando se discuten cuestiones trascendentales, hay que ser trascendentalmente claro鈥�.
鈥� Y la frase que escribi贸 Wiles cuando termin贸 su demostraci贸n del teorema de Fermat frente a la comunidad matem谩tica m谩s importante: 鈥淐reo que me detendr茅 aqu铆鈥� <3
Este es un libro que mezcla la investigaci贸n cient铆fica, el periodismo y la literatura. Aprend铆 un mont贸n ley茅ndolo. Est谩 escrito (y traducido) con una prosa limpia, liviana y sencilla, algo muy dif铆cil de lograr, sobre todo cuando se explican temas intrincados, como las matem谩ticas. Salvo por el exceso de adverbios de mente (que, ay, me ponen medio mal) es un placer leer las explicaciones complejas de manera tan amable.
Pienso que la matem谩tica son un universo de l贸gica, absolutismos y armon铆a de un nivel superior. Como toda disciplina y todo arte, aspira a la belleza y los matem谩ticos lo saben, persiguen la belleza de la perfecci贸n de los n煤meros y le achacan a este universo propiedades como la bondad o la amistad, todo a partir de patrones num茅ricos. Se me ocurre que mucha de la filosof铆a matem谩tica refleja la moral de sus autores y, al mismo tiempo, describen tambi茅n las relaciones humanas y la vida.
Me gust贸 mucho que el autor se hiciera cargo, en un apartado, del sesgo hist贸rico de g茅nero que han acompa帽ado las matem谩ticas. 鈥淎 trav茅s de los siglos las mujeres han sido desanimadas a estudiar matem谩ticas, pero a pesar de la discriminaci贸n, ha habido varias matem谩ticas que lucharon contra esa costumbre institucionalizada e inscribieron sus nombres en forma indeleble en los anales de las matem谩ticas鈥�. Y nombra a Hipatia de Alejandr铆a o Sophie Germain, que tuvo que usar el pseud贸nimo de Monsieur Le Blanc para que tomaran en serio su trabajo. Cuando ella debi贸 revelar su identidad, un destacado matem谩tico (que fue su maestro sin saber que ella no era hombre) escribi贸: 鈥淐uando una persona del sexo que, de acuerdo con nuestras costumbres y prejuicios, debe encontrar infinitamente m谩s dificultades para familiarizarse con estas espinosas investigaciones, tiene 茅xito en superar estos obst谩culos y penetrar las partes m谩s oscuras de ellas, entonces sin ninguna duda debe tener el m谩s noble coraje, talentos verdaderamente extraordinarios y una genialidad superior鈥�.
Cuando yo estaba en octavo b谩sico era muy porra. Me iba mal en el colegio. No estudiaba demasiado. Ese mismo a帽o me puse a pololear con un chico dos a帽os mayor que yo, que era escandalosamente estudioso. Me acuerdo cuando me explic贸 las potencias. Yo me hab铆a sacado un rojo en la prueba y 茅l, con mucha paciencia y amor, me explic贸 esta materia que en realidad es s煤per f谩cil y entretenida. De ah铆 en adelante me puse igual de odiosa y matea que 茅l. Sal铆 de cuarto medio con promedio 6,9 en matem谩tica. Despu茅s estudi茅 periodismo y olvid茅 los n煤meros, pero al leer este libro record茅 por qu茅 me gustaban tanto, por qu茅 disfrutaba m谩s resolviendo facs铆miles de la PSU de matem谩ticas que viendo Los Simpsons. Hay tanta perfecci贸n en los n煤meros, tantos juegos posibles.
El libro se trata de c贸mo se resolvi贸 el problema matem谩tico m谩s famoso de la historia: el teorema de Fermat, que sostiene que no hay soluciones posibles al teorema de Pit谩goras cuando la potencia es mayor a 2. El libro explica, tambi茅n, porque esa demostraci贸n es tan endemoniada y dif铆cil. La belleza del problema es que Fermat dijo tener una demostraci贸n, pero que no la pod铆a escribir en el margen de un libro, ya que ese espacio era muy peque帽o. En rigor, no exist铆a la demostraci贸n (no existe, nadie ha visto jam谩s la demostraci贸n de Fermat). Era y es una especie de eslab贸n perdido de las matem谩ticas. 350 a帽os despu茅s, Andrew Wiles plantear铆a su propia soluci贸n, una muy compleja y elegante, que unifica las matem谩ticas y que se sirve de todas las etapas de esta ciencia para lograrlo. Al final, el libro cuenta esa historia y tambi茅n repasa miles de a帽os de epistemolog铆a de las matem谩ticas.
Algunas cosas bell铆simas que se leen en este libro:
鈥斺€淧it谩goras hab铆a descubierto que unas proporciones num茅ricas simples eran responsables de la armon铆a de la m煤sica鈥�.
鈥斺€淟a raz贸n entre la longitud real de los r铆os desde su nacimiento hasta su desembocadura y su longitud en l铆nea recta (鈥�) es aproximadamente 3,14: n煤mero cercano al valor de 蟺鈥�.
鈥斺€淟as matem谩ticas son el lenguaje que permite describir la naturaleza del universo鈥�.
鈥斺€淟a raz贸n por la cual se le atribuye el teorema a Pit谩goras es porque fue 茅l quien primero demostr贸 su validez universal鈥�.
鈥斺€淟a llamada demostraci贸n cient铆fica depende de la observaci贸n y la percepci贸n, las cuales son falibles y s贸lo suministran aproximaciones (鈥�) [la demostraci贸n matem谩tica] tiene una verdad m谩s profunda que cualquier otra verdad, porque es el resultado de un proceso l贸gico. Las matem谩ticas son una materia de estudio no subjetiva (鈥�) independiente de la opini贸n鈥�. Es decir, una demostraci贸n matem谩tica es una verdad absoluta y se aplica para un caso espec铆fico como para todos los de su serie hasta el infinito. Es loca esa hue谩, ojal谩 las ciencias sociales funcionaran as铆.
鈥斺€淔ermat y Pascal habr铆an de descubrir las primeras demostraciones y certezas absolutas de la teor铆a de la probabilidad, una materia que es, en esencia, incierta鈥�.
鈥� 鈥淸Pascal] sostuvo que 鈥榣a emoci贸n que un apostador siente cuando hace una apuesta es igual a la cantidad que puede ganar multiplicada por la probabilidad de que gane鈥�.
鈥斺€淓l primer director del departamento de matem谩ticas (de la Universidad de Alejandr铆a) fue, ni m谩s ni menos, Euclides鈥�.
鈥擲obre la destrucci贸n de la biblioteca de Alejandr铆a: 鈥淓n el a帽o 642, un ataque musulm谩n culmin贸 con 茅xito aquello en lo que los cristianos hab铆an fracasado鈥�. Quemaron todo por fanatismo dogm谩tico. Maldita religi贸n.
鈥� 鈥淓l crecimiento de cualquier disciplina depende de su capacidad para comunicar y desarrollar ideas鈥�.
鈥斺€淟os n煤meros amigos son parejas de n煤meros tales que cada uno de ellos es igual a la suma de los divisores del otro鈥�.
鈥斺€淸En matem谩tica] las ideas no corroboradas son infinitamente menos valiosas y se conocen como conjeturas鈥�.
鈥斺€淓s impensable para los matem谩ticos no poder, al menos en teor铆a, contestar todas las preguntas, y esta necesidad se llama completud鈥�.
鈥斺€淟os te贸ricos de los n煤meros consideran a los n煤meros primos como los m谩s importantes de todos, porque son los 谩tomos de las matem谩ticas鈥�.
鈥斺€淒ios existe puesto que las matem谩ticas son consistentes, y el diablo existe puesto que no podemos demostrarlo鈥�, Andr茅 Weil.
鈥擲obre Galois, un maestro escribi贸: 鈥渓a locura matem谩tica domina a este muchacho鈥�.
鈥斺€淐uando se discuten cuestiones trascendentales, hay que ser trascendentalmente claro鈥�.
鈥� Y la frase que escribi贸 Wiles cuando termin贸 su demostraci贸n del teorema de Fermat frente a la comunidad matem谩tica m谩s importante: 鈥淐reo que me detendr茅 aqu铆鈥� <3
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July 8, 2024
4-Stars - I Really Liked It
I first read this as a paperback in about 2000. I also listened to an (unfortunately abridged) audiobook narrated by David Rintoul in about 2008, prior to my joining 欧宝娱乐 in 2011.
I cannot competently write a review now about "Fermat's Last Theorem", but I do remember that I enjoyed very much both reading and hearing this most interesting book.
I first read this as a paperback in about 2000. I also listened to an (unfortunately abridged) audiobook narrated by David Rintoul in about 2008, prior to my joining 欧宝娱乐 in 2011.
I cannot competently write a review now about "Fermat's Last Theorem", but I do remember that I enjoyed very much both reading and hearing this most interesting book.
June 2, 2022
This is a very interesting book. Don't be scared about the contents, it's an enjoyable read even if you don't know anything about mathematics.
September 10, 2023
def gonna read simon singh's other books!
September 19, 2012
Lectura en 2012
Este a帽o tom茅 nuevamente el libro del Enigma de Fermat, s铆mplemente porque me gust贸 bastante
Las matem谩ticas fueron una de esas cosas con las que siempre tuve un romance eterno. Leyendo nuevamente pude recordar esos episodios en clases en que el maestro en turno lleg贸 un d铆a y anot贸 este mismo teorema en la pizarra. Nos dej贸 toda la clase tratando de solucionarlo y obviamente al final nos inform贸 que el mismo no estaba resuelto (o al menos eso recuerdo, porque en ese a帽o ya deber铆a de haber estado).
Mas detalladamente me hizo recordar a varios amigos que hac铆an las demostraciones de distintas f贸rmulas y me las entregaban como si fueran cartas rom谩nticas (todav铆a las guardo).
La forma en que esta escrita, en ning煤n momento te hace sentir tedio. Agus dice que son mas bien chismorreos alrededor de la vida de los matem谩ticos (seg煤n como se lo iba contando), y precisamente eso es lo que lo hace interesante. Es la vida de personas que significaron algo para que este teorema existiera y para que finalmente fuera solucionado.
El gran enigma matem谩tico ha muerto.
(en serio, leanlo)
................................................
Lectura en 2006
Finalmente llegamos a lo que fu茅 mi 煤ltimo libro del a帽o (2006 para los despistados). Durante las fiestas me encontr茅 en casa de mis abuelos, y el apartado en donde vive mi hermana, actuaria y fan谩tica de las matem谩ticas. Lo lamentable es que la mayor parte de los libros que lee yo se los recomiendo, as铆 que la mayor铆a de los que encontr茅 en su librero ya los hab铆a le铆do.
Encontr茅 tres libros entre los cuales elegir, sin embargo este brillo llamando mi atenci贸n debido a una an茅cdota. Cuando mi hermana todav铆a estudiaba, viajaba a casa en autob煤s cada dos o tres meses. Entre sus compa帽eras hubo una que le presto este libro y en una ocasi贸n el libro viaj贸 con ella鈥� sin embargo hay que a帽adir que mi hermana es algo despistada as铆 que en esa ocasi贸n el libro qued贸 en el autob煤s. No s茅 qu茅 fu茅 lo que le ha dado m谩s coraje en esa ocasi贸n, perder un libro prestado o no poder seguirlo leyendo. Tuvo que comprarlo para devolverlo y adem谩s se compr贸 su propia edici贸n (que todav铆a le tengo que devolver).
El enigma de Fermat es una novela de matem谩ticas. Mediante un poco de historia Singh nos va narrando la evoluci贸n de las matem谩ticas como un arte, muy lejos de aquellas matem谩ticas aplicadas. Las matem谩ticas como algo abstracto que es hermoso por s铆 mismo, porque tiene un orden y una l贸gica, porque en s铆 misma engloba misterios y permite que los descubras mediante una relaci贸n con ella.
Declaro que de ni帽a me gustaba leer el Baldor y en mi 煤ltimo a帽o de preparatoria acab茅 con todas las operaciones integrales en todos mis libros (y no ten铆a s贸lo dos) y este libro ha sido recordar las horas que le dediqu茅.
Que hermosas eran para m铆 las matem谩ticas.
Fue un hermoso fin de a帽o.
Este a帽o tom茅 nuevamente el libro del Enigma de Fermat, s铆mplemente porque me gust贸 bastante
Las matem谩ticas fueron una de esas cosas con las que siempre tuve un romance eterno. Leyendo nuevamente pude recordar esos episodios en clases en que el maestro en turno lleg贸 un d铆a y anot贸 este mismo teorema en la pizarra. Nos dej贸 toda la clase tratando de solucionarlo y obviamente al final nos inform贸 que el mismo no estaba resuelto (o al menos eso recuerdo, porque en ese a帽o ya deber铆a de haber estado).
Mas detalladamente me hizo recordar a varios amigos que hac铆an las demostraciones de distintas f贸rmulas y me las entregaban como si fueran cartas rom谩nticas (todav铆a las guardo).
La forma en que esta escrita, en ning煤n momento te hace sentir tedio. Agus dice que son mas bien chismorreos alrededor de la vida de los matem谩ticos (seg煤n como se lo iba contando), y precisamente eso es lo que lo hace interesante. Es la vida de personas que significaron algo para que este teorema existiera y para que finalmente fuera solucionado.
El gran enigma matem谩tico ha muerto.
(en serio, leanlo)
................................................
Lectura en 2006
Finalmente llegamos a lo que fu茅 mi 煤ltimo libro del a帽o (2006 para los despistados). Durante las fiestas me encontr茅 en casa de mis abuelos, y el apartado en donde vive mi hermana, actuaria y fan谩tica de las matem谩ticas. Lo lamentable es que la mayor parte de los libros que lee yo se los recomiendo, as铆 que la mayor铆a de los que encontr茅 en su librero ya los hab铆a le铆do.
Encontr茅 tres libros entre los cuales elegir, sin embargo este brillo llamando mi atenci贸n debido a una an茅cdota. Cuando mi hermana todav铆a estudiaba, viajaba a casa en autob煤s cada dos o tres meses. Entre sus compa帽eras hubo una que le presto este libro y en una ocasi贸n el libro viaj贸 con ella鈥� sin embargo hay que a帽adir que mi hermana es algo despistada as铆 que en esa ocasi贸n el libro qued贸 en el autob煤s. No s茅 qu茅 fu茅 lo que le ha dado m谩s coraje en esa ocasi贸n, perder un libro prestado o no poder seguirlo leyendo. Tuvo que comprarlo para devolverlo y adem谩s se compr贸 su propia edici贸n (que todav铆a le tengo que devolver).
El enigma de Fermat es una novela de matem谩ticas. Mediante un poco de historia Singh nos va narrando la evoluci贸n de las matem谩ticas como un arte, muy lejos de aquellas matem谩ticas aplicadas. Las matem谩ticas como algo abstracto que es hermoso por s铆 mismo, porque tiene un orden y una l贸gica, porque en s铆 misma engloba misterios y permite que los descubras mediante una relaci贸n con ella.
Declaro que de ni帽a me gustaba leer el Baldor y en mi 煤ltimo a帽o de preparatoria acab茅 con todas las operaciones integrales en todos mis libros (y no ten铆a s贸lo dos) y este libro ha sido recordar las horas que le dediqu茅.
Que hermosas eran para m铆 las matem谩ticas.
Fue un hermoso fin de a帽o.
July 10, 2023
A genuinely engaging, exciting and informative book!
October 4, 2011
If you buy the latest Jilly Cooper instead of this you WILL go to hell!
This one languished on my bookshelf for the best part of a year as I was too scared to pick it up & start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that...
YOU DON'T NEED ANY MATHS TO READ THIS!
What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it.
Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion.
All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am.
I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.
This one languished on my bookshelf for the best part of a year as I was too scared to pick it up & start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that...
YOU DON'T NEED ANY MATHS TO READ THIS!
What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it.
Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion.
All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am.
I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.
June 13, 2018
螒蟻蠂喂魏维 谓伪 蟺慰蠉渭蔚 蠈蟿喂 未蔚谓 蔚委谓伪喂 位慰纬慰蟿蔚蠂谓委伪. 螠慰蠀 蟿慰 蔚委蠂伪谓 蟺蟻慰蟿蔚委谓蔚喂 渭伪味委 渭蔚 魏维蟺慰喂伪 尾喂尾位委伪 蔚蟺喂蟽蟿畏渭慰谓喂魏萎蟼 蠁伪谓蟿伪蟽委伪蟼 魏伪喂 蟽蠀谓蔚蟺蠋蟼 蟺蔚蟻委渭蔚谓伪 魏维蟿喂 伪谓蟿委蟽蟿慰喂蠂慰. 螒蠀蟿蠈蟼 萎蟿伪谓 魏伪喂 慰 位蠈纬慰蟼 蟺慰蠀 蟿慰 蟺伪蟻维蟿畏蟽伪 蟽蟿畏谓 蟺蟻蠋蟿畏 伪蟺蠈蟺蔚喂蟻伪.
螌渭蠅蟼, 蔚委谓伪喂 渭喂伪 蔚尉伪喂蟻蔚蟿喂魏萎 魏伪喂 伪蟺位慰蠆魏萎 喂蟽蟿慰蟻委伪 蟿蠅谓 渭伪胃畏渭伪蟿喂魏蠋谓 蟽蔚 蟽蠂蔚未蠈谓 位慰纬慰蟿蔚蠂谓喂魏萎 伪蟺蠈未慰蟽畏. 危委纬慰蠀蟻伪 未蔚谓 渭伪胃伪委谓蔚喂 魏维蟺慰喂慰蟼 渭伪胃畏渭伪蟿喂魏维 渭蔚 伪蠀蟿蠈 蟿慰 尾喂尾位委慰,
伪位位维 渭蟺慰蟻蔚委 谓伪 苇蟻胃蔚喂 蟽蔚 蔚蟺伪蠁萎 渭蔚 蟿喂蟼 蟺位苇慰谓 蟽蠉纬蠂蟻慰谓蔚蟼 渭慰蟻蠁苇蟼 蟿慰蠀蟼 蠂蠅蟻委蟼 喂未喂伪委蟿蔚蟻蔚蟼 纬谓蠋蟽蔚喂蟼.
危蔚 蟿蔚位喂魏萎 伪谓维位蠀蟽畏 畏 喂蟽蟿慰蟻委伪 渭蔚 蟽蠀谓蔚蟺萎蟻蔚 魏伪喂 蟿慰 尾喂尾位委慰 蟽委纬慰蠀蟻伪 维尉喂味蔚 蟿畏谓 未蔚蠉蟿蔚蟻畏 蔚蠀魏伪喂蟻委伪 蟺慰蠀 蟿慰蠀 苇未蠅蟽伪.
螌渭蠅蟼, 蔚委谓伪喂 渭喂伪 蔚尉伪喂蟻蔚蟿喂魏萎 魏伪喂 伪蟺位慰蠆魏萎 喂蟽蟿慰蟻委伪 蟿蠅谓 渭伪胃畏渭伪蟿喂魏蠋谓 蟽蔚 蟽蠂蔚未蠈谓 位慰纬慰蟿蔚蠂谓喂魏萎 伪蟺蠈未慰蟽畏. 危委纬慰蠀蟻伪 未蔚谓 渭伪胃伪委谓蔚喂 魏维蟺慰喂慰蟼 渭伪胃畏渭伪蟿喂魏维 渭蔚 伪蠀蟿蠈 蟿慰 尾喂尾位委慰,
伪位位维 渭蟺慰蟻蔚委 谓伪 苇蟻胃蔚喂 蟽蔚 蔚蟺伪蠁萎 渭蔚 蟿喂蟼 蟺位苇慰谓 蟽蠉纬蠂蟻慰谓蔚蟼 渭慰蟻蠁苇蟼 蟿慰蠀蟼 蠂蠅蟻委蟼 喂未喂伪委蟿蔚蟻蔚蟼 纬谓蠋蟽蔚喂蟼.
危蔚 蟿蔚位喂魏萎 伪谓维位蠀蟽畏 畏 喂蟽蟿慰蟻委伪 渭蔚 蟽蠀谓蔚蟺萎蟻蔚 魏伪喂 蟿慰 尾喂尾位委慰 蟽委纬慰蠀蟻伪 维尉喂味蔚 蟿畏谓 未蔚蠉蟿蔚蟻畏 蔚蠀魏伪喂蟻委伪 蟺慰蠀 蟿慰蠀 苇未蠅蟽伪.
July 13, 2022
Its a simple problem: x^n + y^n = z^n has no positive integer solutions (xyz) for n>2. So why is it so hard to prove? (or disprove). I'm a math/physics nerd so this book has great appeal. I also like Simon Singh's technical writing. He stayed 100% on track as he traced Pythagoras in 6 BC to Andrew Wiles proof in 1994.
We all remember 3-4-5 triangles from geometry/trig, right? Pythagorean Theorem says 3^2 + 4^2 = 5^2. Other famous right triangle uses of these are the 5-12-13 or the 7-24-25, or how about 99-4900 - 4901. So why can't a version of this with cubes, or ^4 or ^5 work?
Andrew Wiles read by Eric Bell when he was 10. He ultimately left Cambridge, England became a math professor at Princeton.
The text kept moving at a strong pace. The greatest minds in math all came into play, with their own focus and contribution to solving this problem. Pierre de Fermat lived 1607-1665. The mathematicians before him that get mentioned all contributed to number theory that had direct bearing on this ultimate math problem. Fermat has scribbled in the margins that he knew the proof, but it simply wouldn't fit in the margins.
Even as computers came into being, the 'brute force' method of MANY trials (with none working) could solve this problem. For even if a million numbers were tried, maybe the next one could work. What was needed was a full mathematical logical proof.
Solid 4.5*. If you like math/physics, then easy 5. If not, then round down to a very readable 4.
We all remember 3-4-5 triangles from geometry/trig, right? Pythagorean Theorem says 3^2 + 4^2 = 5^2. Other famous right triangle uses of these are the 5-12-13 or the 7-24-25, or how about 99-4900 - 4901. So why can't a version of this with cubes, or ^4 or ^5 work?
Andrew Wiles read by Eric Bell when he was 10. He ultimately left Cambridge, England became a math professor at Princeton.
The text kept moving at a strong pace. The greatest minds in math all came into play, with their own focus and contribution to solving this problem. Pierre de Fermat lived 1607-1665. The mathematicians before him that get mentioned all contributed to number theory that had direct bearing on this ultimate math problem. Fermat has scribbled in the margins that he knew the proof, but it simply wouldn't fit in the margins.
Even as computers came into being, the 'brute force' method of MANY trials (with none working) could solve this problem. For even if a million numbers were tried, maybe the next one could work. What was needed was a full mathematical logical proof.
Solid 4.5*. If you like math/physics, then easy 5. If not, then round down to a very readable 4.
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