George Szpiro
Plume | 2007 | 321 páginas | rar - pdf | 1,6 Mb
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The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it
In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
Contents
Chapter 1: Fit for a King 1
Grigori Perelman’s unprecedented refusal of a Fields Medal for solving one of the greatest problems of our age. The king waits in vain.
Chapter 2: What Flies Know and Ants Don’t 8
The importance of dimensions for Christopher Columbus and for bugs.
Chapter 3: The Forensic Engineer 15
The life of Henri Poincaré, in particular his investigation of a tragedy in a coal mine.
Chapter 4: An Oscar for the Best Script 33
Poincaré’s prizewinning theory of the solar system’s stability...and the scandal.
Chapter 5: Geometry Without Euclid 53 Topology; how this mathematical discipline has developed since Euler.
Chapter 6 : From Copenhagen and Hamburg to Black Mountain, North Carolina 75
Poincaré’s first, incorrect attempt to prove the conjecture...and the parts he got right.
Chapter 7 : What the Conjecture Is Really All About 95
Imaging things that are unimaginable.
Chapter 8 : Dead Ends and a Mysterious Disease 112
Around the world with three-dimensional spheres.
Chapter 9 : Voyage to Higher Dimensions 142
A rock-collecting yippie amazes the world.
Chapter 10 : Inquisition—West Coast Style 172
How other hopefuls ended up with egg on their faces.
Chapter 11 : Watching Things Go “Pop” 186
Richard Hamilton gets going with the Ricci flow . . . and then gets stuck.
Chapter 12 : The Cigar Surgeon 205
The proof lands on the Internet. Swooping up Poincaré, Thurston, and Hamilton. History is made.
Chapter 13 : The Gang of Four, plus Two 226
Vetting the proof, a math professor pushes his protégés into the limelight.
Chapter 14 : The Prize 247
The minor matter of a million dollars. Does money motivate math?
Notes 263
Bibliography 285
Acknowledgments 295
Index 297
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