{READ KINDLE} Ó The Poincaré Conjecture: In Search of the Shape of the Universe Õ eBook or E-pub free

So the shape of the universe It s a giant ball, right Especially when you think of its beginning in a big bang But that brings up the awkward question of what s outside the ball Space universe is not infinite It s believed to be finite, but without a boundary It becomes easier to understand this if you consider two dimensional beings living in a spherical the two dimensional surface of a ball universe Their universe is finite, but has no boundaries There are no edges, and if they s So the shape of the universe It s a giant ball, right Especially when you think of its beginning in a big bang But that brings up the awkward question of what s outside the ball Space universe is not infinite It s believed to be finite, but without a boundary It becomes easier to understand this if you consider two dimensional beings living in a spherical the two dimensional surface of a ball universe Their universe is finite, but has no boundaries There are no edges, and if they start off from one point and keep going in the same direction they ll come back to where they started Our universe is finite and without boundary in the same way If you get on a spaceship and keep going in the same direction, eventually you ll be back in the same neighborhood This one is harder to imagine, isn t it In the case of two dimensional people living on a sphere, we can see how it can be finite but without boundary because we can see how the sphere bends in a third dimension But how is it for our three dimensional universe There s no fourth dimension to bend in Reading this book didn t make it any easier for me to really understand how the universe can be finite but without a boundary All I can do is quote the two dimensional analogy, but I m still a three dimensional earthling But even assuming that the universe is finite and without boundary is it a three sphere To go back to the two sphere analogy, just because Magellan sailed in the same direction and came back to where he started doesn t mean that the earth is a sphere It can also be doughnut shaped, and the same would still happen No one really knows what the shape of the universe is There s a lot of evidence for it being flat whatever that means And the Poincare Conjecture It says that a finite, no boundary space that is simply connected is a three sphere This question is obviously of great interest both to mathematicians and to the physicists studying the geometry of the universe We still don t know if the universe is simply connected or not A ball is simply connect, but something like a doughnut is not simply connected Unlike Reimann s Hypothesis, the Poincare Conjecture was finally proved after much heartbreak and agony by an eccentric Russian mathematician named Gregori Perelman who didn t even accept the award for it The book tells the story of the conjecture and the man who proved it Good pop science and math history I ve been interested in the Millennium problems since I first read about them several years ago It was exciting to read about the first one to be solved I never took topology in college, though, so I have to admit that much of this went right over my head If you wanted to know without reading all the math, yes, the Poincare conjecture turned out to be true Pretty cool stuff There was some explanation earlier in the book, but later explanation was poor I came away with little understanding of how the Poincare conjecture was solved The book was a disappointment, but did provide a reference to book by Jeffrey Weeks that might offer better layman level explanations of topological concepts. Why is this book notwidely read It s at least as good as books like Fermat s Last Theorem, with farmathematical content If any layman wants a glimpse into the world of top level mathematics, I cannot recommend a better book. As a recent grad student in mathematics I found this book incredibly interesting It made me want to go on and get my Ph.D in manifold theory. This book was in the mathematics section in the library and I was expecting somethingmathematics focused Hence I was disappointed by the history lesson this book turned out to be Except for the initial confusion, it was a nice read. The fact is I would need infinitive sets of lifes to read all the books I want and another set of infinitive lifes to put into practice everything I read in all the books I would achieve to read in those other infinite sets of lifes certainly, an infinite number of books And yet, I would need an infinite memory to recall all the things I learn from them and correct, maybe, all the infinite sets of mistakes I would make during my infinite learning If infinite books available, I might The fact is I would need infinitive sets of lifes to read all the books I want and another set of infinitive lifes to put into practice everything I read in all the books I would achieve to read in those other infinite sets of lifes certainly, an infinite number of books And yet, I would need an infinite memory to recall all the things I learn from them and correct, maybe, all the infinite sets of mistakes I would make during my infinite learning If infinite books available, I might not be able to start anew with the first book, but having enough infinite time, who knows Life would be infinite, even if memory would not.I finished this book with a feeling of satisfaction, with the great pleasure of having touched, albeit with the points of my fingers, the fascinating world of topology and geometry and while I want to learnI get the feeling I will not have enough time in this life to grasp this incredible world it s been opened to me to understand all the nuancies, not even the most simple ones It is a very sad moment to realise this life is simply much too short to discover all the beauty hidden behind the walls of ignorance.This is a fascinating book casting the search for a solution for an unsurmountable until Perelman arrived, of course and difficult extremely difficult problem, for performing the task of solving an open question well, rather a conjecture posed by Poincar one of the greatest mathematicians in history in the last page of his last work on topology analysis situs the Poincar s conjecture.I knew little about topology and geometry before reading the book and after reading the book I wantas a physicist I have the right to say I was ignorant before reading the book, but I remain ignorant as well after the reading and this is quite disatisfying.So many brilliant minds failed and then, out of the blue well, a blue which is not at all such looking at the brilliant background of the solver and his career , one clear mind Perelman, of course came from the cold Russia with modesty and right attitude, a bold mind who, after solving such Conjecture, went back to his cave from where he came from to never show up, after saying something similar to hey world, look what I leave for the future of maths Just some notes for you to read By the way, I got solved the Poincar s conjecture, but please leave me alone I was just playing Sudoku Thank you very much.I loved and read with great pleasure the way the author presented the very difficult concepts and math topics to later give a sucint explanation of what was solved by Perelman actually I loved to read the historical overview surrounding the lifes and circumstances, the diffculties and disappointments the many great mathematicians suffere, the context and the background, human and mathematical, until a Russian mathematician came to fill in the void If this is not a fascinating story then you really don t have a sense for beauty and the misterious ways you may need to arrive at it.At times, reading was difficult Mathematical concepts are not easy to explain for the layman, but the author achieves, when necessary, almost always, to use the correct explanation, find the correct example or comparison, to use the right words a clear mind would need to use and an average mind would need to understand Enlightning and absolutely recommendable This was a decent book, but a bit of a hard read.Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail how one concept leads to another how concepts fail to connect For me, at least, this was difficult to follow Granted, in order to truly understand what is being discussed, you would need to understand the mathematics perhaps this is just an insurmountable problem in trying to translate high level and di This was a decent book, but a bit of a hard read.Firstly, the book introduces many concepts by name, with some short descriptions, and then goes on to discuss them in some qualitative detail how one concept leads to another how concepts fail to connect For me, at least, this was difficult to follow Granted, in order to truly understand what is being discussed, you would need to understand the mathematics perhaps this is just an insurmountable problem in trying to translate high level and difficult mathematics into lay language.Secondly, there are too many sections where names and dates and attempted proofs of such and such a conjecture theory etc are listed in these sections it very much feels like the only people who would be able to pull much meaning would be already quite familiar with the topics There is muchof this in the last third or quarter of the book.The middle 85% of the book isn t about the Poincare Conjecture per se In this, I would describe the book as the history of mathematicians and mathematics, from ancient times to today, as told from the point of view of the Poincare Conjecture An analogy might be something like a book that details the life of some famous figure by telling the history of their family ancestry and the times and events their family lived through {READ KINDLE} õ The Poincaré Conjecture: In Search of the Shape of the Universe ⚛ Henri Poincar was one of the greatest mathematicians of the late nineteenth and early twentieth century He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting The Poincar conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single pointPoincar s conjecture is one of the seven millennium problems that bring a one million dollar award for a solution Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in AugustHe also will almost certainly share a Clay Institute millennium awardIn telling the vibrant story of The Poincar Conjecture, Donal O Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman s proof of this famous conjecture This book was about as painful as reading the book of Genesis its pages mostly comprise a chronological list of mathematicians and so and so s work begot so and so s thesis interspersed with definitions sans explanation or example a group, a ring, etc The highlights were the only occasional example of geometry in mathematical physics or when the author found time to elaborate a littleon an interesting property of a certain metric or surface structure In fact, the best part of This book was about as painful as reading the book of Genesis its pages mostly comprise a chronological list of mathematicians and so and so s work begot so and so s thesis interspersed with definitions sans explanation or example a group, a ring, etc The highlights were the only occasional example of geometry in mathematical physics or when the author found time to elaborate a littleon an interesting property of a certain metric or surface structure In fact, the best part of the book is the final two sentences that state for about the 5th time but with the most clarity the thesis of the book as defined by its title Good grief