The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry



The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of SymmetryWhat Do Bach S Compositions, Rubik S Cube, The Way We Choose Our Mates, And The Physics Of Subatomic Particles Have In Common All Are Governed By The Laws Of Symmetry, Which Elegantly Unify Scientific And Artistic Principles Yet The Mathematical Language Of Symmetry Known As Group Theory Did Not Emerge From The Study Of Symmetry At All, But From An Equation That Couldn T Be Solved For Thousands Of Years Mathematicians Solved Progressively Difficult Algebraic Equations, Until They Encountered The Quintic Equation, Which Resisted Solution For Three Centuries Working Independently, Two Great Prodigies Ultimately Proved That The Quintic Cannot Be Solved By A Simple Formula These Geniuses, A Norwegian Named Niels Henrik Abel And A Romantic Frenchman Named Variste Galois, Both Died Tragically Young Their Incredible Labor, However, Produced The Origins Of Group Theory The First Extensive, Popular Account Of The Mathematics Of Symmetry And Order, The Equation That Couldn T Be Solved Is Told Not Through Abstract Formulas But In A Beautifully Written And Dramatic Account Of The Lives And Work Of Some Of The Greatest And Most Intriguing Mathematicians In History.

Is a well-known author, some of his books are a fascination for readers like in the The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry book, this is one of the most wanted Mario Livio author readers around the world.

!!> Reading ➳ The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry ➬ Author Mario Livio – Heartforum.co.uk
  • Paperback
  • 368 pages
  • The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
  • Mario Livio
  • English
  • 09 July 2017
  • 0743258215

10 thoughts on “The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

  1. Suzanne says:

    This book brought back some of thefascinating things I learned in my upper division graduate classes on group theory It is approachable, yet I m sure challenging to those without a mathematics background I love thinking about the way too short lives of those brilliant mathematicians who invented group theory the political and social environments at the time were rough, and what they accomplished was amazing And symmetry is applicable to so many areas it is a fascinating topic.

  2. Greg says:

    This is a book about a genius Livio quotes George Bernard Shaw early and appropriately to describe Abel and Galois The reasonable man adapts himself to the world the unreasonable one persists in trying to adapt the world to himself Therefore all progress depends on the unreasonable man 3 It is a very, very true statement.Livio traces the development in mathematics over the broad strokes of history It is a history of brilliant minds solving progressivelydifficult algebraic equatio This is a book about a genius Livio quotes George Bernard Shaw early and appropriately to describe Abel and Galois The reasonable man adapts himself to the world the unreasonable one persists in trying to adapt the world to himself Therefore all progress depends on the unreasonable man 3 It is a very, very true statement.Livio traces the development in mathematics over the broad strokes of history It is a history of brilliant minds solving progressivelydifficult algebraic equations With the quintic equations, however, no solution could be found for over 300 years Abel and Galois came at the problem from a completely different line of thinking, and their revolution which has come to manifest itself in modern group theory changed the way we understand the world Ultimately, they came to define the properties of a group as 1 Closure The offspring of any two members combined by the operation must itself be a member 2 Associativity when combining by the operation three ordered members, you may combine any two of the first, and the result is the same, unaffected by the way they are bracketed 3 Identity element The group has to contain an identity element such that when combined with any member, it leaves the member unchanged 4 Inverse For every member in the group there must exist an inverse When a member is combined with its inverse, it gives the identity element 46 Livio goes on to explore the line of thinking further At times he s a bit breathless So, how did Galois prove his inventive propositions Even just the essence of Galois s proof is somewhat technical, but it provides such a unique window into his unsurpassed creativity that it is definitely worth the effort required to penetrate it Following the logical steps of the proof is like having walked through the labyrinth of Mozart s mind while he composed one of his symphonies 169 Before Galois, equations were always classified only by their degree quadratic, cubic, quantic, and so on Galois discovered that symmetry was aimportant characteristic Classifying equations by their degree is analogous to grouping the wooden building blocks in a toy box according to their sizes Galois s classification by symmetry properties is equivalent to the realization that the shape of the blocks round, square, or triangular isfundamental 170 Livio completes his overview by talking about the modern uses of this mathematical approach To me the most interesting is that of Einstein Suspicious at first Einstein slowly began to grasp the incredible power of symmetry If the laws of nature are to remain unchanged for moving observers, not only do the equations describing these laws need to obey Lorentz covariance, the laws themselves may actually be deduced from the requirement of symmetry This profound realization has literally reversed theological process that Einstein and many of the physicists who followed him employed to formulate the laws of nature 204 Livio quotes Owen Meredith pseudonym of Edward Robert Bulwer Lytton, earl of Lytton ultimately in describing how important thinkers like Abel and Galois are in our world Genius does what it must, and Talent does what it can 263 He finishes with a quick analysis of how these mathematicians are able to be so innovative Psychologists John Dacey and Kathleen Lennon emphasize tolerance of ambiguity the ability to think, operate, and remain open minded in situations where the rules are unclear, where there are no guidelines, or where the usual support systems have collapsed Indeed, without the competence to function where there are no rules, Picasso would have never invented cubism and Galois would not have come up with group theory Tolerance of ambiguity is a necessary condition for creativity 265 This conclusion is applicable to all of us

  3. Ami Iida says:

    it is written about symmetry and group theory.they had made impressive upon the human being from mathThere are lots of games coming from symmetry.ex tetrishttps en.wikipedia.org wiki TetrisPolyominohttps en.wikipedia.org wiki Polyomino15 puzzlehttps en.wikipedia.org wiki 15_puzzleRubik s Cubehttps en.wikipedia.org wiki Rubik%2etc.you can play every games coming from symmetry LOL LOL LOL it is written about symmetry and group theory.they had made impressive upon the human being from mathThere are lots of games coming from symmetry.ex tetrishttps en.wikipedia.org wiki TetrisPolyominohttps en.wikipedia.org wiki Polyomino15 puzzlehttps en.wikipedia.org wiki 15_puzzleRubik s Cubehttps en.wikipedia.org wiki Rubik%2etc.you can play every games coming from symmetry LOL LOL LOL

  4. Jessica says:

    This was definitelyreadable than most of the books about math I have read There was plenty in it that I didn t understand, but it didn t take away from the point of the book Any mathematician who gets killed in a duel over a girl at age 20 after spending a year in prison for revolutionary activities is worth reading aboutespecially if he made a discovery that revolutionized mathematics.

  5. Mii says:

    How fascinating What an intriguing start to the new year

  6. Nguyễn says:

    This book is a comprehensive introduction to a very hard problem of mathematics finding the general solution for a general equation, along with the story of two genius Niels Hendrik Abel and especially Evarist Galois In my opinion, the author has spent much time to collect the documents related to Galois s life, so that he has described Galois s story truthfully in a very scientific way That makes sense for the other books on Galois or the same topics always tried to describes Galois s story This book is a comprehensive introduction to a very hard problem of mathematics finding the general solution for a general equation, along with the story of two genius Niels Hendrik Abel and especially Evarist Galois In my opinion, the author has spent much time to collect the documents related to Galois s life, so that he has described Galois s story truthfully in a very scientific way That makes sense for the other books on Galois or the same topics always tried to describes Galois s story as much fictonal as possible The language of symmetry is also a major topic of this book, and Mario Livio has developed them as the vertical axis of the whole story So that physics came in, with applications of group theory in the unifying question for the universe In some last pages, the appearance of the applications of symmetry in biology and sex which I do think that it is not appropriate reduce the value of this book, and it made me unable to appreciate the book

  7. Natan says:

    I have a BA in physics, and even though this book is not a physics book, I learned just how much I didn t learn in my degree and how awful my teachers were Livio obviously doesn t go into equations and mathematical derivations, but instead explains the reasoning behind them and how different branches of physics are actually connected something they don t bother teaching you.

  8. Rossdavidh says:

    This has got to be the geekiest book I ve read in a long time It s all about math, for goodness sake How do you stay awake through a book on math Well, the duel, and the murder mystery, and the tragic poverty, and the backstabbing, and the mental illness all helped.Because it s not really a book about math, it s a book about mathematicians Very different subject, really There is the baffling tale, which I m still not certain if I believe, that in 1500 s Venice, mathematicians would face off This has got to be the geekiest book I ve read in a long time It s all about math, for goodness sake How do you stay awake through a book on math Well, the duel, and the murder mystery, and the tragic poverty, and the backstabbing, and the mental illness all helped.Because it s not really a book about math, it s a book about mathematicians Very different subject, really There is the baffling tale, which I m still not certain if I believe, that in 1500 s Venice, mathematicians would face off to see who could solve the most fifth degree equations in the least time Crowds showed up to watch this, and to make wagers on the outcome I say we dress Lee and Phil in high Renaissance garb and make them do this in public.Then there is Niels Henrik Abel, who live a poverty stricken life, narrowly missing numerous opportunities to find a position that would provide him enough of an income to allow him to marry his long suffering fiancee Unfortunately, his results were ahead of their time, and therefore misunderstood or simply not understood , and he ended up dying of consumption tuberculosis at the age of 25 His deathbed wish to a friend was to see that his fiancee was taken care of his friend married her.The main figure is Evariste Galois, who the author has clearly become fascinated with The fellow was a French revolutionary, put on trial as a teenager for having threatened the life of the King in public, who died under mysterious circumstances involving a duel with an unknown opponent at age 20 He apparently knew he would lose the duel he spent the night before furiously scribbling out a few letters to his friends, and above all fleshing out his mathematical legacy, which was to become the foundation of group theory.From there, we move on to group theory, seeing how the methods of inverting or turning a pair of trousers can be mathematically identical to certain manipulations of Venn diagrams, and the marriage taboos of the Kariera, a tribe of Australian Aboriginals Those wacky mathematicians Livio is good at finding examples of abstract math that are goofy enough to keep the reader s interest.In fact, though, the writing of a book on symmetry in mathematics was obviously hijacked midway through by the writer s interest in Galois the last chapter is Requiem for a Romantic Genius Which is either a shame or a relief, depending on your opinion It worked for me

  9. Jake Berlin says:

    while this book has muchof a uniting scientific idea than the other livio i read brilliant blunders , it s actually muchscattered is it a big idea book, or a biography of galois why are there random throwaway chapters on evolution and music there are absolutely some interesting ideas here i would very much like to read a top notch book about symmetry but it mostly fails as a work of popular science writing.

  10. Sarah says:

    Whoever wrote the copy for the jacket of this book should get a raise The jacket makes you think the book will be really interesting, and instead it sof a history of how certain mathematical equations finally were solved, the people who solved them, and how symmetry became an important part of mathematics The first half of the book was VERY slow, and it wasn t until the author started actually talking about the key mathematicians and their life stories that it became interesting Perha Whoever wrote the copy for the jacket of this book should get a raise The jacket makes you think the book will be really interesting, and instead it sof a history of how certain mathematical equations finally were solved, the people who solved them, and how symmetry became an important part of mathematics The first half of the book was VERY slow, and it wasn t until the author started actually talking about the key mathematicians and their life stories that it became interesting Perhaps a good read for people interested in the history of the quadratic equation, etc., but not anywhere near as fascinatingly gripping as the cover would have you believe

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