Loading... ## The equation that couldn't be solved : how mathematical genius discovered… (original 2005; edition 2005)## by Mario Livio
## Work detailsThe Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio (2005)
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Sign up for LibraryThing to find out whether you'll like this book. No current Talk conversations about this book. Like reading five books , so much information. I keep picturing Galois ( group theory ) as being Elric from Full Metal Alchemist. ( Probably not far off really ) " ANYTHING can be transformed ! " ( ) While the concept of symmetry is fascinating I think that it's application to particle physics may be like applying circles to planetary motions. Nature just isn't symmetric. This book includes a great history of the mathematics of Group Theory. This book would make a good biography of Abel and Galois but is really a book about maths and not a maths book (if you can see the distinction). We get the intimate details of the two mathematicians' lives but their actual discoveries seem to be an addendum to the book as a whole. If you want a popular history and have a basic mathematical knowledge this is for you but I wouldn't recommend it if you want to exit the process knowing something about Galois theory. How ignorant I am. In Chapter One, Mario Livio promises to open our eyes to the magic of symmetry through the language of mathematics. To do so, he first acquaints us with group theory of modern algebra. A group is any collection of elements (they need not be numbers) that have the properties of (1) closure, (2) associativity, (3) an identity element, and (4) an inverse operation. The fact that this simple definition leads to a theory that unifies all symmetries amazes even mathematicians. Livio give us a little of the history of algebra, beginning with the ancient Greeks and Hindus, who solved the general quadratic. The story of the solution of the general cubic is a fascinating one involving allegations of cheating and libel among 16th century Italian mathematicians. Moreover, the solution required the invention of imaginary numbers. Once the cubic was solved, the solution or the quadratic quickly followed, but the quintic remained a mystery. Even Euler and Gauss were stumped by the quintic, and they began to think the problem was insoluble. In fact, the work of two very young mathematicians, Niels Henrik Abel and Evariste Galois, proved that there could be no general solution to the general form of the quintic equation. The solution proved to be a surprise in that it depended on the relations among the coefficients of the variables. Only those quintics with a proper symmetry among the coefficients can be solved by purely algebraic operations. Livio does not actually show why the previous statement is true, probably because it requires real math. Nevertheless, the conclusion is pretty startling even to a math tyro like me. The book gets a bit bogged down in its biographical sections, devoting more time to Galois’s life than I found interesting. Nevertheless, it is worth reading. (JAB) no reviews | add a review
References to this work on external resources. ## Wikipedia in English (4)
What 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. |
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