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Ian Stewart

Why Beauty is Truth

Although symmetry seems to be predominantly a geometrical property, Why Beauty is Truth: A History of Symmetryshows that it really gained its importance in mathematics and physics via a different route - that of the solutions of polynomial equations. Ian Stewart starts at the time of the Babylonians, who were able to solve quadratic equations, and moves through the solutions of the cubic and quartic in the Renaissance. Hence we get to the work of Abel and Galois, who demonstrated the insolubility of the quintic by radicals. This was the start of group theory, and the rest of the book shows how this had much influence in later mathematics and physics.

Stewart shows how Sophus Lie applied the notion of a group to continuous systems. He describes the work of Einstein, as well as the development of quantum theory, showing how symmetry has a natural place in modern physics. There is also a chapter on Edward Witten and Superstring theory. Stewart also clearly has a soft spot for quaternions and octonions, showing how these almost forgotten structures may yet play an important part in physics.

The book gives prominence to biographies of the mathematicians concerned, and some people might feel that there isn't enough maths, however I felt that Stewart struck the right balance, and so kept the book accessible to a wide readership.

Amazon.com info

Hardcover 304 pages
ISBN: 046508236X
Salesrank: 409756
Weight:1.25 lbs

Published: 2007 Basic Books

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Amazon.co.uk info

Hardcover 304 pages
ISBN: 046508236X
Salesrank: 340354
Weight:1.25 lbs

Published: 2007 Basic Books

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Amazon.ca info

Hardcover 304 pages
ISBN: 046508236X
Salesrank: 181360
Weight:1.25 lbs

Published: 2007 Basic Books

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Product Description
An eminent teacher and writer explores an idea both simple and complex, both multidisciplinary and unifying--the story of symmetry. At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions--groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe.

Product Description

An eminent teacher and writer explores an idea both simple and complex, both multidisciplinary and unifying--the story of symmetry.

At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry.

In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published.

Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions--groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe.

I wasn't fully able to grasp the beauty ****
This book has many good points, and some drawbacks. I think my own lack of mathematical knowledge held me back from fully appreciating it. (I got A in O level maths in 1981. I enjoyed maths at school, and felt I was getting to the interesting bits when I was forced towards physics chemistry and biology for A levels- looking back I wish I had the chance to do all four subjects) The good points are that is well written with a clear narrative showing how our mathematical thinking has developed over time. It shows well how seemingly abstract problems lead on to many insights that may be interesting of themselves (pure maths) or may help solve practical problems. (applied maths) What seems like purely abstract mathematics may later turn out to be the route to new applied knowledge. The "unreasonable effectiveness" of mathematics is shown in many examples throughout the book. The discussion of the relationship between truth and beauty is well nuanced, and it seems likely that truth will be beautiful, and that a current "ugly" or "messy" formulation is one awaiting its simplification. At school I was just beginning to get the idea that graphs, coordinates, geometry, equations and matrices were all ways of expressing the same idea in different formats. This book shows how these relationships come about, and evolve out from one another. The drawbacks of the book for me was that the final 100 pages largely lost me. I got certain headline points, but I did not understand the ideas behind group theory, Lie groups, Hamilton's work, Killing's work. I think this is a reflection of my ignorance, not the author's writing. My feeling about this book is that it would be a great read for someone studying maths at A level or university and wanting to get an idea of how maths has developed and where it is going. It would whet the appetite and encourage their studies.

I wasn't fully able to grasp the beauty ****

This book has many good points, and some drawbacks. I think my own lack of mathematical knowledge held me back from fully appreciating it. (I got A in O level maths in 1981. I enjoyed maths at school, and felt I was getting to the interesting bits when I was forced towards physics chemistry and biology for A levels- looking back I wish I had the chance to do all four subjects)

The good points are that is well written with a clear narrative showing how our mathematical thinking has developed over time. It shows well how seemingly abstract problems lead on to many insights that may be interesting of themselves (pure maths) or may help solve practical problems. (applied maths) What seems like purely abstract mathematics may later turn out to be the route to new applied knowledge. The "unreasonable effectiveness" of mathematics is shown in many examples throughout the book. The discussion of the relationship between truth and beauty is well nuanced, and it seems likely that truth will be beautiful, and that a current "ugly" or "messy" formulation is one awaiting its simplification. At school I was just beginning to get the idea that graphs, coordinates, geometry, equations and matrices were all ways of expressing the same idea in different formats. This book shows how these relationships come about, and evolve out from one another.

The drawbacks of the book for me was that the final 100 pages largely lost me. I got certain headline points, but I did not understand the ideas behind group theory, Lie groups, Hamilton's work, Killing's work. I think this is a reflection of my ignorance, not the author's writing.

My feeling about this book is that it would be a great read for someone studying maths at A level or university and wanting to get an idea of how maths has developed and where it is going. It would whet the appetite and encourage their studies.

Bad writing style for an otherwise stellar topic and approach ***
I very much agree with Israel Ramirez's review. I love the topic and the approach the author used. Math history is fascinating and I'm sure more people would understand and appreciate math if it were taught with more of a historical perspective rather than the rote learning approach used in most k-12 education these days in north america. I found this book to drag on at times and not go into enough depth on what it promised to discuss - group theory. Reading was made difficult by the fact that everything happened at the same level of discourse. Whether it was a pages long setup starting with Maxwell's grandparents, The author's opinion on how 2 historians recordings differ on a less important fact of Sumarrian school children, or the Ah Ha! moment that revolutionized mathematics from a study of quantitative calculations to the analysis of the abstract, it's all written in a way that holds the same level of importance. That being said I also cried my eyes out with his recounting of Galois's untimely death - something I never thought possible of a math book. Why beauty is Truth is more than a simple book about math and group theory but a book about humanity's attempt to understand the natural world culminating with the latest triumphs in theoretical physics. However, this book could have easily been half the length and still kept all the main points. It was very hard to get into a rhythm while reading since it was hard to tell what points were important and what points made up the background information.

Bad writing style for an otherwise stellar topic and approach ***

I very much agree with Israel Ramirez's review.

I love the topic and the approach the author used. Math history is fascinating and I'm sure more people would understand and appreciate math if it were taught with more of a historical perspective rather than the rote learning approach used in most k-12 education these days in north america.

I found this book to drag on at times and not go into enough depth on what it promised to discuss - group theory.

Reading was made difficult by the fact that everything happened at the same level of discourse. Whether it was a pages long setup starting with Maxwell's grandparents, The author's opinion on how 2 historians recordings differ on a less important fact of Sumarrian school children, or the Ah Ha! moment that revolutionized mathematics from a study of quantitative calculations to the analysis of the abstract, it's all written in a way that holds the same level of importance.

That being said I also cried my eyes out with his recounting of Galois's untimely death - something I never thought possible of a math book.

Why beauty is Truth is more than a simple book about math and group theory but a book about humanity's attempt to understand the natural world culminating with the latest triumphs in theoretical physics. However, this book could have easily been half the length and still kept all the main points. It was very hard to get into a rhythm while reading since it was hard to tell what points were important and what points made up the background information.

An inspired but muddled mess ***
I agree completely with the review by Israel Ramirez. Stewart religiously avoids mathematical expressions throughout, assuming his audience will choke on anything more than a polynomial equation, but he doesn't think twice about spewing esoteric math and physics jargon when attempting to explain fantastically complicated concepts in words. To his credit, it works some of the time, but any honest reader will admit it doesn't work much of the time. As others have noted, there are many positive things about the book, but by the end the author is throwing new thoughts into the mix helter skelter as if cleaning out his ideas closet, and it all just falls apart. What are we supposed to take away from nonsense such as: "So now the general opinion is that the exceptional Lie groups exist because of the wisdom of the deity in permitting the octonions to exist."??

An inspired but muddled mess ***

I agree completely with the review by Israel Ramirez. Stewart religiously avoids mathematical expressions throughout, assuming his audience will choke on anything more than a polynomial equation, but he doesn't think twice about spewing esoteric math and physics jargon when attempting to explain fantastically complicated concepts in words. To his credit, it works some of the time, but any honest reader will admit it doesn't work much of the time. As others have noted, there are many positive things about the book, but by the end the author is throwing new thoughts into the mix helter skelter as if cleaning out his ideas closet, and it all just falls apart. What are we supposed to take away from nonsense such as: "So now the general opinion is that the exceptional Lie groups exist because of the wisdom of the deity in permitting the octonions to exist."??

Nice Overview ****
Professor Stewart is to be commended for a nice "walking tour" (to quote another reviewer) of mathematic history. He makes the topic accessible for the non-mathematician, and combined with an obvious passion for the topic maintains the reader's attention. The book starts off well, but stumbles here and there before Prof Steward hits his stride in the 18th and 19th centuries. His account of this period is fascinating and well-written. This was a fun read and recommended for anyone wanting a nice diversion into the field of mathematics, with a smidgen of physics thrown in for good measure. One last thing: given the format, the illustrations for this book are top-drawer and accessible---a great aid to those of us non-mathematician types.

Nice Overview ****

Professor Stewart is to be commended for a nice "walking tour" (to quote another reviewer) of mathematic history. He makes the topic accessible for the non-mathematician, and combined with an obvious passion for the topic maintains the reader's attention. The book starts off well, but stumbles here and there before Prof Steward hits his stride in the 18th and 19th centuries. His account of this period is fascinating and well-written.
This was a fun read and recommended for anyone wanting a nice diversion into the field of mathematics, with a smidgen of physics thrown in for good measure.
One last thing: given the format, the illustrations for this book are top-drawer and accessible---a great aid to those of us non-mathematician types.

Nearly gets the balance of history and math right ****
This book tries to pull off a difficult trick: being both a history of mathematics and mathematicians, and also a primer on group theory and symmetry. Glossing over the real technical details, Stewart does a good job explaining the math, but a good deal of it still went over my head--although he tries to keep things simple, he expects you to actually remember some key parts of high-school math. Math sections alternate with passages about the lives of the discoverers of various theoretical advances. As much as the math gets simplified, so does the history. Facts, people, and context go whipping by at points, reducing some important information down to single lonely sentences. And amazingly, for a book titled "Why Beauty is Truth", there's no single clear definition of what (mathematical) "beauty" is. There are plenty of references to "elegant" equations, or even beautiful ones, but no statement about why mathematicians might find them so, even though I think such a definition is quite simple. David Gelernter's wonderful definition from Machine Beauty would be ideal: "simplicity plus power equals beauty." That is, an equation which is simpler, and which gives useful leverage or has predictive abilities, is elegant and beautiful. A long equation tailored to a specific problem is merely functional. The most compelling idea in the book, which appears a few times, is that the structure of mathematics is not merely an analogy or functional metaphor for "the real world" but is an actual, literal description of it and can even make testable predictions about it. The terrific book Strange Matters: Undiscovered Ideas at the Frontiers of Space and Time looks at that predictive power in more depth, specifically in the field of cosmology.

Nearly gets the balance of history and math right ****

This book tries to pull off a difficult trick: being both a history of mathematics and mathematicians, and also a primer on group theory and symmetry. Glossing over the real technical details, Stewart does a good job explaining the math, but a good deal of it still went over my head--although he tries to keep things simple, he expects you to actually *remember* some key parts of high-school math.

Math sections alternate with passages about the lives of the discoverers of various theoretical advances. As much as the math gets simplified, so does the history. Facts, people, and context go whipping by at points, reducing some important information down to single lonely sentences.

And amazingly, for a book titled "Why Beauty is Truth", there's no single clear definition of what (mathematical) "beauty" is. There are plenty of references to "elegant" equations, or even beautiful ones, but no statement about why mathematicians might find them so, even though I think such a definition is quite simple. David Gelernter's wonderful definition from Machine Beauty would be ideal: "simplicity plus power equals beauty." That is, an equation which is simpler, and which gives useful leverage or has predictive abilities, is elegant and beautiful. A long equation tailored to a specific problem is merely functional.

The most compelling idea in the book, which appears a few times, is that the structure of mathematics is not merely an analogy or functional metaphor for "the real world" but is an actual, literal description of it and can even make testable predictions about it. The terrific book Strange Matters: Undiscovered Ideas at the Frontiers of Space and Time looks at that predictive power in more depth, specifically in the field of cosmology.

Why Beauty is Truth ****
A fascinating account of significant developments in Mathematics and the intriguing characters who made them. It explained several things I never understood studying Chemistry at University. I reckon you'd need at least A-level Maths to make much of it.

Why Beauty is Truth ****

A fascinating account of significant developments in Mathematics and the intriguing characters who made them. It explained several things I never understood studying Chemistry at University.

I reckon you'd need at least A-level Maths to make much of it.

Not what I expected but informative ***
I had bought this being interested in maths many years ago in particular the concept of 'Beauty' in nature and art and how that correlated to symmetry and maths. I had hoped it would touch on fractals and logorithmic sequences and how objects such as seashells and cabbages grow in these formations. Sadly none of this was touched on and I'm not what I would call heavily into advanced mathematics. However I did persevere and read the entire book although far from understanding the concepts in it. I very much enjoyed the humour and the history surrounding how mathmatical concepts were discovered. It reminded me very much of Bill Bryson's writting and not that of a stale Maths book at all. The book gets heavier towards the end when it starts talking of Quantum maths where it pretty much lost me completely. If you are interested in Mathmatical concepts and discoveries this is a very entertaining and informative read but for me the cover was rather misleading. I would be interested to hear a review by a Maths scholar.

Not what I expected but informative ***

I had bought this being interested in maths many years ago in particular the concept of 'Beauty' in nature and art and how that correlated to symmetry and maths. I had hoped it would touch on fractals and logorithmic sequences and how objects such as seashells and cabbages grow in these formations. Sadly none of this was touched on and I'm not what I would call heavily into advanced mathematics.

However I did persevere and read the entire book although far from understanding the concepts in it. I very much enjoyed the humour and the history surrounding how mathmatical concepts were discovered. It reminded me very much of Bill Bryson's writting and not that of a stale Maths book at all. The book gets heavier towards the end when it starts talking of Quantum maths where it pretty much lost me completely.

If you are interested in Mathmatical concepts and discoveries this is a very entertaining and informative read but for me the cover was rather misleading. I would be interested to hear a review by a Maths scholar.

I couldn't fully appreciate the beauty ****
This book has many good points, and some drawbacks. I think my own lack of mathematical knowledge held me back from fully appreciating it. (I got A in O level maths in 1981. I enjoyed maths at school, and felt I was getting to the interesting bits when I was forced towards physics chemistry and biology for A levels- looking back I wish I had the chance to do all four subjects) The good points are that is well written with a clear narrative showing how our mathematical thinking has developed over time. It shows well how seemingly abstract problems lead on to many insights that may be interesting of themselves (pure maths) or may help solve practical problems. (applied maths) What seems like purely abstract mathematics may later turn out to be the route to new applied knowledge. The "unreasonable effectiveness" of mathematics is shown in many examples throughout the book. The discussion of the relationship between truth and beauty is well nuanced, and it seems likely that truth will be beautiful, and that a current "ugly" or "messy" formulation is one awaiting its simplification. At school I was just beginning to get the idea that graphs, coordinates, geometry, equations and matrices were all ways of expressing the same idea in different formats. This book shows how these relationships come about, and evolve out from one another. The drawbacks of the book for me was that the final 100 pages largely lost me. I got certain headline points, but I did not understand the ideas behind group theory, Lie groups, Hamilton's work, Killing's work. I think this is a reflection of my ignorance, not the author's writing. My feeling about this book is that it would be a great read for someone studying maths at A level or university and wanting to get an idea of how maths has developed and where it is going. It would whet the appetite and encourage their studies.

I couldn't fully appreciate the beauty ****

A Book to be Prized. *****
When Ian Stewart writes a book on mathematics it is always something that booklovers look forward too. This book is no exception. Beside explaining complex mathematical ideas in language understandable to non-mathematicians, and making the history of mathematics come to life through linking it with the biographies,and the personal struggles of those who have carried the subject forward through the ages,Ian Stewart does it with a beautiful simplicity. The title of this book is well earned and no one who buys it will be disappointed. A bonus in this book is thatIan Stewart shows with great economy, throughout the book, the very close relationship between the development of mathematics and the progress of physics.The care he takes not to over-reach or simplify the relationship between mathematics and physics is made clear in the final chapter where under the heading: 'Seekers After Truth and Beauty' he states:"But what works in mathematics need not work in physics,and vice versa". This is a book which cannot be too highly recommended.

A Book to be Prized. *****

When Ian Stewart writes a book on mathematics it is always something that booklovers look forward too. This book is no exception. Beside explaining complex mathematical ideas in language understandable to non-mathematicians, and making the history of mathematics come to life through linking it with the biographies,and the personal struggles of those who have carried the subject forward through the ages,Ian Stewart does it with a beautiful simplicity. The title of this book is well earned and no one who buys it will be disappointed. A bonus in this book is thatIan Stewart shows with great economy, throughout the book, the very close relationship between the development of mathematics and the progress of physics.The care he takes not to over-reach or simplify the relationship between mathematics and physics is made clear in the final chapter where under the heading: 'Seekers After Truth and Beauty' he states:"But what works in mathematics need not work in physics,and vice versa". This is a book which cannot be too highly recommended.

Ian Stewart has done it again! *****
What more can I say? Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth. A MUST for anybody with an interest in mathematics.

Ian Stewart has done it again! *****

What more can I say?

Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.

A MUST for anybody with an interest in mathematics.