introduction

Part 1: The Story of Euclid
1.
First revolution
2.
The Geometry of Taxes
3.
As one of the seven wise men
4.
secret group
5.
Euclid's Manifesto
6.
Beautiful Women, Libraries, and the End of Civilization

Part 2: The Story of Descartes
7.
The revolution of location
8.
The origin of latitude and longitude
9.
The ruined legacy of Rome
10.
The subtle charm of graphs
11.
A soldier's story
12.
trapped in ice by the Snow Queen

Part 3: The Story of Gauss
13.
Revolution in Curved Space
14.
Ptolemy's mistake
15.
Napoleon's hero
16.
The Fifth Axiom of the Wooden Lock
17.
I'm stuck in hyperbolic space
18.
Some insects called humans
19.
The Legend of the Two Aliens
20.
Reconstruction 2,000 years later

Part 4: The Einstein Story
21.
Revolution at the speed of light
22.
Theory of Relativity and Another Albert
23.
Materials of space
24.
Temporary Level 3 Technical Specialist
25.
A relatively Euclidean approach
26.
Einstein's Apple
27.
From inspiration to effort
28.
Blue-haired Victory

Part 5: The Witten Story
29.
Strange Revolution
30.
Ten things I hate about your theory
31.
The inevitable uncertainty of existence
32.
Clash of the Masters
33.
Kalucha-Klein Letter in a Bottle
34.
The Birth of a String
35.
Particles, common particles!
36.
Problems with string theory
37.
The theory formerly called string theory

Epilogue
main
Acknowledgements
Translator's Note
Biographical Index

Mlodinow reveals how the first revolution in geometry began with a “small” technique devised by Pythagoras.
It was a system of abstract rules that could model the universe.
That small idea was the foundation of scientific civilization.
But further progress stalled as the Western mind fell into the slumber of the Dark Ages.
Finally, in the 14th century, news of the next revolution arrived with the discovery of graphs by an unknown French bishop: the union of geometry and numbers.
Then, in a time when daring sailors were crossing the Atlantic to reach new worlds, a 15-year-old boy genius realized that space could be curved like the surface of the Earth.
Can parallel lines really intersect? Can the sum of the interior angles of a triangle be greater than—or less than—180 degrees? The revolution of curved space has transformed both mathematics and physics.
The revolution also allowed a patent office clerk named Einstein to include time within the dimensions of space.
His great geometric revolution ushered in a new era in physics.

Today we are in the midst of a new revolution.
At universities around the world, including Caltech and Princeton, scientists are realizing that all the diverse and mysterious forces of nature can be understood through geometry—a bizarre new geometry.
That geometry is the exciting mathematics of added twisted dimensions.
In that mathematics, space and time, matter and energy are all intertwined, and it is revealed that they are all products of a deeper, more fundamental structure.


This book is based on Mlodinow's extensive collection of sources.
He studied scholars like Feynman and Kip Thorne, and conversed with pioneering physicists and mathematicians like Gell-Mann, Witten, and Green.
He also presents an original argument for the leading position of geometry, skillfully combining rigorous and authoritative research with accessible and entertaining narrative.
Anyone who sees the world through this book will see space, objects, and time in a completely different way than before.

This book is so restrained in its use of mathematical jargon and formulas that it can feel a bit overwhelming in some parts.
Therefore, for those who have a fear of math, this is a book that is more welcome than any other.
Mlodinow wrote his book with precisely such people in mind.
But the mathematics that this book mentions and only partially explains the core points—especially physics—is by no means easy.

Readers interested in geometry, mathematics, physics, and the history of science and mathematics will likely find this book hard to put down.
Because it is so entertaining and packed with balanced information that satisfies the needs of those seeking holistic insight.
This book will help you approach geometry, which has always felt distant, in a more familiar way.