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Symmetry: A Journey into the Patterns of Nature Paperback – Illustrated, March 3, 2009
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About the Author
Marcus du Sautoy is a professor of mathematics and the Simonyi Professor for the Public Understanding of Science at Oxford University. He is a frequent contributor on mathematics to The Times, The Guardian, and the BBC, and he lives in London.
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bells, Bach Golberg Variations, DNA sequences, RNA viruses invasions, and secret codes.
When Phil Anderson, a Nobel laureate, said that physics is basically the study of symmetry, he was actually modest. Symmetry is not only out there in nature, but in our brain too. Mirror neurons in the brain, allow us to empathize, to understand other people feelings by becoming "symmetric" with them.
This is not a book about the mathematics of symmetry, but more about the symmetry in mathematics, mind, arts and nature.
For doing this in an engaging way, Marcus du Sautoy deserves to be widely read.
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.
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.
It is somewhat technical and illustrates concrete examples of mathematical concepts; and yet, it is a really fun read. I enjoyed it.
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.
Top international reviews
This is not an "in-depth" book about simmetry, it is more an informative book, easy to read and very entertaining.
I am sure this author could have written such a book, but this isn't it. It has been dumbed down far too much (I suspect at the insistence of the publisher). He avoids simple group theory terminology, so instead of writing about "how many groups there are with 27 elements", he has "how many objects there are with 27 symmetries", which isn't going to help anyone, and is going to confuse those who understand just a little of his subject matter. Yet he mentions zeta functions several times, though without any clue as to what they are.
In chapter three he states, repeatedly, that the Alhambra palace contains examples of all 17 symmetries (he means wallpaper groups); and there are pictures of some of them. I wonder why he chose not to have a page or two illustrating all 17? This would have been interesting, or at least fun to look at, for all readers, however dumb the publisher takes them to be.
The best feature of the book is not its abortive attempts to discuss mathematics, but its anecdotes about mathematicians. If these are what you want, the book is worth buying.