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Home > Education > Mathematics > 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 Symmetry

by Livio, Mario
 
 
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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
"What do the music of J. S. Bach, the basic forces of nature, Rubik's Cube, and the selection of mates have in common? They are all characterized by certain symmetries. Symmetry is the concept that bridges the gap between science and art, between the world of theoretical physics and the everyday world we see around us. Yet the ""language"" of symmetry--group theory in mathematics--emerged from a most unlikely source: an equation that couldn't be solved. Over the millennia, mathematicians solved progressively more difficult algebraic equations until they came to what is known as the quintic equation. For several centuries it resisted solution, until two mathematical prodigies independently discovered that it could not be solved by the usual methods, thereby opening the door to group theory. These young geniuses, a Norwegian named Niels Henrik Abel and a Frenchman named Evariste Galois, both died tragically. Galois, in fact, spent the night before his fatal duel (at the age of twenty) scribbling another brief summary of his proof, at one point writing in the margin of his notebook ""I have no time."" The story of the equation that couldn't be solved is a story of brilliant mathematicians and a fascinating account of how mathematics illuminates a wide variety of disciplines. In this lively, engaging book, Mario Livio shows in an easily accessible way how group theory explains the symmetry and order of both the natural and the human-made worlds. "
Title of ebook: The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
ISBN: 9780743274623
parent-ISBN: 9780743258203
Publisher: Simon & Schuster
Published: 09-2005
Released online for download: 09-01-2005
Author of eBook: Livio, Mario

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The Equation that Couldn't Be Solved

How Mathematical Genius Discovered the Language of Symmetry

Chapter One: Symmetry

An inkblot on a piece of paper is not particularly attractive to the eye, but if you fold the paper before the ink dries, you may get something that looks like figure 1 that is much more intriguing. In fact, the interpretation of similar inkblots forms the basis for the famous Rorschach test developed in the 1920s by the Swiss psychiatrist Hermann Rorschach. The declared purpose of the test is to somehow elicit the hidden fears, wild fantasies, and deeper thoughts of the viewers interpreting the ambiguous shapes. The actual value of the test as an "x-ray of the mind" is vehemently debated in psychological circles. As Emory University psychologist Scott Lilienfeld once put it, "Whose mind, that of the client or the examiner?" Nevertheless, there is no denial of the fact that images such as that in figure 1 convey some sort of attractive and fascinating impression. Why?

Is it because the human body, most animals, and so many human artifacts possess a similar bilateral symmetry? And why do all those zoolog ... read full excerpt from: The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry ebook



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