Customer Reviews

Symmetry: A Journey into the Patterns of Nature

5 star:		(7)
4 star:		(1)
3 star:		(3)
2 star:		(3)
1 star:		(0)

 

 

I read this book in 2 weeks, can't stop admiring the way the author managed to explain so many interesting modern math concepts in layman's terms. Below are some astonishing math knowledge which worth the book price you pay for.

1) Quintic Equation: Both Abel and Galois proved the quintic equations have no radical solutions. Abel proved 'No solution' by reductio ad absurdum; while Galois proved 'Why No?' with the beautiful Group Theory. How could a 19-year-old French boy thought of such grand math theory? It was a shame he was not recognised by the grand mathematicians like Cauchy, Gauss, Fourier, etc. He wrote the Group Theory down the night before his deadly duel and scribbled "Je n'ai pas le temps" (I have no time)... it took another 10 years for Group Theory to be rediscoverd by Prof Liouville of the Ecole Polytechniques (whose ignorant examiners ironically failed Galois twice in Entrance Concours Exams).

2) Moonshine: Monster Group dimensions (dj) & relationship with Fourier expansion of coefficients (cj) in Modular Function (page 333):
x^-1 + 744+196,884x + 21,493,760 x^2 + 864,229,970x^3 +...
cn= c1+c2+...cn-1 + dn
where d1 = 196,883
d2 = 21,296,876
d3 = 842,609,326
and c1 = 1+ d1 = 196,884
c2 = c1+d2 = 21,493,760
c3 = c1 + c2 + d3 = 864,229,970
What a coincidence! no wonder Conway said this discovery was the most exciting event in his life.
3) 'Atlas of Finite Group': the book covered the insider story of the 5 Cambridge mathematicians led by Conway, in an attempt to create the 'Periodic Table' of Group's building blocks (Monster Group is the last one).
3) Icosahedron symmetry (20-sided polygon of triangular faces): this is the way viruses 'trick' our body cells to reproduce for them, by this deadly icosaherdon beauty. In nature, bees are tricked by flowers' symmetry. In human, we are 'tricked' by opposite sex's body symmetry:)
4) Arche de la Defense @ Paris: a Hypercube architecture (cube of 4-dimensions), shows us we can visualize 4-dimension objects in our 3-dimension world.
5) Chap 7 (Revolution) compared the Anglo-Saxon and French Math culture:
"Anglo-saxon temperament tend towards the nitty-gritty, revelling in strange examples and anomalis. The French, in contrast, love grand abstract theories and are masters at inventing language to articulate new and difficult structures." I agreed, having been taught in anglo-saxon (UK, USA) math before entering into French Grande Ecole (Engineering University), I found great difficulty to compete with French classmates in abstract math, but beat them in applied math by my high-school 'anglo-saxon' math training. You notice France has never won IMO Math Olympiad Championship like USA, China do, but France invented most of the modern algebra and modern analysis.
Conclusion:
This book is a grand-tour of the most exciting modern math - Group Theory. For all math students who hate reading the boring abstract modern math textbooks, you will be 'hooked' by the underlying beauty of modern math after reading du Sautoy's Symmetry.
Bon Courage!

Symmetry is something that is easy for us to appreciate. It might be that we have an evolutionary taste for symmetric creatures; we suspect there is something wrong if a horse has an uneven gait, and it has been shown that we prefer symmetric faces. Of course symmetry is part of our art and architecture. So it is an inherently interesting subject for everyone, but mathematicians have taken the study of symmetry to heights that the rest of us can barely imagine. One of those mathematicians is Marcus du Sautoy, who has shown in his previous _The Music of the Primes_ that he has the capability of descending from the mathematical summits enough to have readers understand a bit of what mathematicians do. Now in _Symmetry: A Journey into the Patterns of Nature_ (Harper), du Sautoy has told the story of a mathematical quest that has gone on for centuries and which, it seems, was essentially completed in the 1980s. There are lots of different symmetries, some of which have complicated ways of being manipulated in dimensions higher than anyone will ever be able to depict. To prove that every single symmetry has been mathematically classified was a real triumph of a branch of mathematics known as Group Theory. The scale of the triumph only mathematicians will come close to fully understanding, but the rest of us can get an idea of how monumental a victory this was from du Sautoy's engaging look at how the job was done.

Imagine an equilateral triangle. You can leave it where it is, or you can rotate it around by a third, or by two thirds, and it looks just the same. You can flip it around three different axes, and it looks the same. Those are its six symmetries. The Greeks were fascinated with the symmetry of solid figures, the Muslims with that of tiles and plane figures. But shapes and tilings are not all there is to symmetry; different ways of shuffling a pack of cards have symmetry, as does the number lock on a piece of luggage. The change ringers who team up to ring five bells in the exactly 120 different orders in which five bells can be rung are performing a symmetrical operation. There are symmetries of many properties of matter and physics, and it might be that they will help explain string theory. Indeed, the great story here is that like prime numbers, symmetric groups are at the heart of the mathematics of our universe, but unlike prime numbers, there is only a finite number of symmetries, and they have all now been found. It was thought in the 1920s that group theory had reached a dead end and there were no further families of symmetry to be found. But in 1965, a new group was found that didn't fit into any of the previous families, and like the athletes who found themselves able to do a four minute mile once one person had done so, mathematicians were inspired by this discovery into finding further such groups. The largest of the groups is called the Monster. "The Monster is like some huge, great symmetrical snowflake that you can see only when you get to 196,883-dimensional space," says John Horton Conway, one of the heroes of the quest described here. Forget the six symmetries of that equilateral triangle; there are more symmetries in the Monster than there are atoms in the Sun. Even more wonderful is that there are mathematicians like Conway who somehow can picture such an object in their minds, and have included it and all the other possible symmetries in the massive, inclusive _Atlas of Finite Groups_. If the math (even at the level of this popularization) gets dense, there are always funny stories about mathematicians, who are often just as strange as you would expect such eggheads to be.

Symmetries is not a textbook on symmetry, and the concepts here require not only textbooks but mathematical textbooks, textbooks only a few people, even a few mathematicians, are ever going to read. What du Sautoy has done is to give a feeling of the importance of the hunt and the excitement of it. He has also done readers the service of explaining just what a mathematician does. "Many of my friends have the impression that I'm sitting in my office doing long division to a lot of decimal places, and wonder why a computer hasn't put me out of a job by now." It is hunting for patterns and discovering them that keeps him going. The twelve chapters here not only go through the history of group theory but each tells of a month in his life, the joys and frustrations of mathematical research, of mathematical teamwork and competition, or of the push to publish one's ideas. Maybe you will never master group theory, but if you want to know what mathematicians do, and why it is important, this is a wonderful guide.

This is overall a good book. The author devoted one full chapter on the obvious geometric symmetry studies in the walls and floors of the Spanish Al-Hambra palace in Granada. Then he slowly develops the Galois group theory and the more abstract part of the symmetry. He continues his discussions on the various parts of his research life, his collaborations, conferences, his digressions into Japanese episodes, how he feels about his students (his "mathematical children") etc. This is in contrast with Hermal Weyl's famous "Symmtery" book published many years ago. In this book, the author depicts a personal journey into the abstract beauty of mathematical symmetry, how he entangles problems in group theory in his own research. This personal journey is juxtaposed with historical figures like Galois, Cauchy, Abel, Lie and their stories of making key contributions to the field of group symmetry studies. Not only the past giants, but also recent luminaries are also mentioned as studies in mathematics of group symmetry is an ongoing process. Any scientific endeavour should not be completely decoupled from personal struggles, since this is the person that drives the passion of originality. For impersonal accounts, there are the corpus of journal papers. But it is also instructive to see what and how the person felt at the 'moment of epiphany'. This book is for sure not meant for an expert's reading. It is meant for budding mathematicians, to motivate their interest in mathematics. This book should be of general interest to the layperson having some sort of math background.

I had read and enjoyed the author's previous "Music of the Primes" and so gave this new work in the author's research area a read. It was not as coherent and informative as the previous work. There is an attempt to give a glimpse of what it is like to be a working mathematician and a person rather than really delving deeply into the subject matter of finite simple groups and moonshine. For the latter I found Ronan's "Symmetry and the Monster" to be excellent at bringing into view the players and the concepts. As for a portrait of a working mathematician, the present work feels incomplete like the author really hasn't gotten to a stopping point in his research that allows us to understand the journey.

Prof du Sautoy's book is a great read on many levels: it explains some very pure (call it hardcore) mathematics in an understandable way, without shying away from a formula here or there; it shows a bit of the reality of doing mathematical research and the life in academia (the choices you need to make, the highs and lows you encounter); and it gives plenty of colorful anecdotes and mathematical history to create a sense of a larger whole, of mathematics being done by people--some very odd ones, true, but people nonetheless, who like the rest of us get sick, try to raise families, and make bad choices on occasion.

The book could have used a little tighter editing--some glaring typos in the math and imprecise language were a distraction at times, but only because of the high quality of the book as a whole. For me it was a pleasure to read!

Of the many books on the market today explaining some aspect of science for a general audience this is one of the best. I've read enough books to know that even with an editor (though sometimes I wonder if there was a conscious editor) making a science subject generally approachable is a rare gift.

Dr. Marcus du Sautoy does this using several techniques:

- By relating the story of symmetry through the lives of mathematicians. From the ancient Greeks who were just beginning to understand the nature of prime numbers and first understood the beauty of (what we call) the Platonic Solids, to contemporary group theorists. Along the way filling in important parts contributed by Islamic thinkers in the Golden Age of Islam (esp. al-Khwarizmi) and the Persian Umar al-Khayyami about 200 years later, to the Renaissance and on into the early 18th Century. From there the coverage of personalities is essentially continuous, though by no means complete, right up to the present.

- By relating the story of symmetry through his own life in autobiographical flashbacks and diary-like commentary throughout the year he took to write this book. One of the funnier bits comes near the end of the book where Dr. du Sautoy gives an outline of the typical personalities of professors in mathematics. It seems a predilection with logic and systematization tends to curb empathic and other social functions. Which is to say they are quite the quirky bunch. A condition commonly called Asperger's Syndrome today. Interestingly the three-star review by Michael Hambro highlights this very characteristic by failing to see how others (most others) less gifted in mathematics might be better carried along using these literary techniques. Or in his words, "Would have liked a somewhat more mathematical angle. Chatty about irrelevant and uninteresting family life". Ah, the voice of Asperger's.

- By ignoring the minutia and many numerological dead ends that often plague the daily pursuit of pure mathematics. To be sure we get an inkling of the years of toil and frustration for those who pursue pure mathematics but Dr. du Sautoy spares us the bulk of the tedium.

- By relating symmetry to our daily lives. Especially our general human partiality towards finding beauty or aesthetic pleasure in symmetry. As seen in all mediums of art from architecture to painting to sculpture and to music. Indeed his (all too short) chapter (9th) on music and symmetry is a far better primer on the depth of meaning of music for the human condition than most books devoted to the topic. Dr. du Sautoy makes many other connections for our need of symmetry, some firm, some just a thread, that touch upon subjects as diverse as cosmology to chemistry to subatomic particles.

- And by abjuring Hawking's dictum Dr. du Sautoy has leave to place a few score equations in his book. Some of them are as simple as 1 + 196,883 = 196,884 but many are rather more complex algebraic functions and diagrams. The many economically drawn diagrams definitely help for those of us whose spatial intelligence lies near the norm.

So, if you find yourself interested in mathematics in general and symmetry especially then buy this book and read it.

This book is an insightful read and provides exercise to the logical thought process.
It is somewhat technical and illustrates concrete examples of mathematical concepts; and yet, it is a really fun read. I enjoyed it.

Like some other reviewers on this page, I came to this book with certain expectations. I thought it would be a popular (yet in depth) treatment of the subject matter announced by its title. Though it proved to be a fairly detailed treatment of such, it also proved to be much more: a history of mathematics, in brief, and a kind of mathematical memoir. History of math one can find elsewhere. Overviews of symmetry and group theory one can as well (though perhaps not ones so artful as this). But the truly accessible and inspiring mathematical memoir is rare indeed. Du Sautoy leads the reader by the hand from discovery to discovery, along the way explaining the many ways that mathematicians think, write, and create, and the many drives that propel them down this most complex path of study. He does a brilliant job of humanizing a discipline that -- to the non-initiate -- could not seem more remote from ordinary experience. Time and again, in my reading, I paused to think: if only I, too, were a mathematician!

Du Sautoy is one of those mathematicians who can do it all. He is the best popularizer of mathematics I have read so far.
I liked the way he introduces the ideas of symmetry throughout the book, one at a time, and shows their beauty and relevance.
Another very cool feature of this book is that it incorporates the author's own personal journey through mathematics and his discoveries along the route of beautiful aspects of symmetry.
Who can resist a guy who takes his young son to museums to show him displays of ancient artifacts and explains their mathematical properties.
This is one great read.

I purchased this book because I hoped to gain a better understanding of group theory evolution. It does an excellent job of introducing symmetry and providing a historical context of its mathematical introduction. After the introductory chapters it goes downhill fast. It does not adequately address the explosive development of group theory during the mid 20th century. A previous NYTimes review also stated that the book described how group theory was instrumental in the development of advanced physics (unified field theory) in the latter 20th century. It mentions only sparingly and superficially the connection between group theory and physics.

In summary it seems to be primarily a history of the mathematical personalities involved in group theory research -- an ego quest, perhaps. The author focuses most of his attention later in the book on personal anecdotes related to 'great' mathematicians he has known.

A history of personalities without a corresponding effective history of the concepts is not worth the time it takes to read.