» Fearless Symmetry: Exposing the Hidden Patterns of Numbers (New Edition)

Fearless Symmetry: Exposing the Hidden Patterns of Numbers (New Edition) Reviews

Customer Rating:
Summary: Promised but not delivered.
Comment: This is my first review and it will be a short one. Like I said in the title, I expected much of this reading. From the authors and the fact of having having Mazur's blessing in the preface, such expectation is well placed. Unfortunately, the book doesn't rise to this expectation.

If you are unfamiliar with number theory and/or higher mathematics in general, you'll fnd the first two chapters quite entertaining and will feel the story building up for a climax that, in my opinion, did not come. The later chapters are hard to digest and you'll have the feeling of "?!??!!?" (if you know what I mean).

If on the other hand, you're familiar with algebraic number theory and just want to know more about Galois representations then you'll conclude that the book could well be written in half the number of pages and still explain better the later chapters.

Not everything is bad tough: I highlight the chapter on Varieties. It accomplishes what the whole book should have (which is difficult of course): it explains an important idea in familiar terms for the newcomers and still focus on interesting modern approaches (or not so modern anymore) like the functor of points.

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Customer Rating:
Summary: quite possibly the best recreational math book explaining groups
Comment: Fearless Symmetry is an engaging, entertaining, wonderful piece of literary mathematics. It gives a concise view of number theory without the dryness of a textbook. The authors do a wonderful job of explaining and solidifying the abstraction in mathematics, bringing the average non-mathematically minded reader into the realm of modern mathematics.
This book is a 'must read' for any undergraduate student of mathematics who may be experiencing difficulty understanding the basic concepts of modern algebra.

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Customer Rating:
Summary: Far too elementary for the initiated; far too abstruse for those who aren't
Comment: This book explains a great deal of elementary mathematical material without making it interesting. Somewhere around the 2/3 mark the abstractness of the material skyrockets, leaving anyone but a trained mathematician to wonder why they wasted their time.

But the trained mathematicians will not want to waste *their* time reading all the introductory material. Even the last 1/3 of the book, which discusses a huge pile of tremendously abstract material, continues to discuss it as though to beginners, with virtually no motivation.

During most of this latter portion of the book I felt as though I was stumbling through a thick forest at night, only able to see 5 feet in front of me.

At no time was the payoff clear. I just learned a lot of abstract concepts that seemed to have no intrinsic interest and no punchline.

In summary, there is really no audience that this book is suitable for.

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Customer Rating:
Summary: Let me Inject Some Reality into Discussion
Comment: In spite of some of the comments posted already and in spite of what is on the book's back cover - this is a math book - this is a serious math book. I personally don't see that average person getting anything out of this if they hadn't had say Linear Algebra in particular. Calculus is not required but higher alegra is.

The reason I bought this book is that I read Ian Stewert's book on Symmetry and Beauty and found it lacking as it was not very mathematical.
I was not dissapointed in the level of math in this book. If anything, I got overwhelmed by the end.

I call this type of book "drill deep" but not wide. I like that idea.

The author's have a real ambitious goal. It's laid out on pages 11 and 12:
"in this book we explore ..representations...we consider sets, groups, matrices and functions between them. We show you in detail in one particular case that we develop throughout the book that sets us to our goal: mod p linear representations of Galois groups."

THIS IS THE GOAL OF THIS BOOK. They are not kidding this is what the book sets out to do and I belive accomplishes.


The authors are true to this goal in the "drill deep" mode. Example: Chapter 2 is Groups - not everything about Group Theory is presented but enough that is needed for the rest of the book. In a similar manner one chapter is on so called reciprocity laws. Chapter 4 is on Modular Arithmetic a crucial aspect to this book.

One prior reviewer indicated that each chapter is far more difficult than the last; this is sortof the general tenure of the book - but with exceptions if you know that material. Example, Chapter 5, Complex Numbers, for me was a relief sandwiched in between Modular Artimetic and Equations and Varieties. I can attest that for the subject "Complex numbers" - that they treated it at a relativley elementary level and focused on just those aspects needed later on. I am sure that for all subjects like "Quadratric reciprocity" that was the case. However, if you hadn't been exposed to quadratic reciprocity and Legendre symbols it is a tough slog.

For me the high point of the book was Chapter 8, I felt that I understood the difficult concept of the the Absolute group of the field of algebraic numbers by the end of the chapter. It is an infinite group that only elements can really be enumerated - Identity and complex conjugation. It fills in some (but not all) of the points in the number line between the group of rational numbers and the line with no gaps the field of real numbers.

Chapters 13 to 22 my ability to follow went way downhill and I just skimmed to get some highpoints.

I might return to this book in the future. I like the idea of not having to learn every aspect of something like alebraic ring theory , then every aspect of permutation theory etc. but just learning enough to accomplish some higher level of understanding like ultimatley how Fermat's Last Therom was solved.

I would recomend Stwert's book on Symmetry and Beauty first if you feel you want a more general understanding of this subject as opposed to a real math book which this is.

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Customer Rating:
Summary: From the Earth to the stars
Comment:
The book has a goal which is very difficult to reach: introducing people without every mathematical background to the contemporary research in Galois Theory, Number Theory and Diophantine Geometry. In such a situation it is always very hard to choose the best proofs to be written in the book, the best examples and the best way... Maybe, if was the author, I would have made more proofs in the second part of the book, and have chosen other examples for this part. However --- it is so light to criticize --- and the author achieved his goal in proportion of at least 80%, which is not less for an impossible goal!

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