The Poincare Conjecture
豆瓣
In Search of the Shape of the Universe
O'Shea, Donal
簡介
"O'Shea tells the fascinating story of this mathematical mystery and its solution by the eccentric Mr. Perelman."--"Wall Street Journal "In 1904, Henri Poincare, a giant among mathematicians who transformed the fledging area of topology into a powerful field essential to all mathematics and physics, posed the Poincare conjecture, a tantalizing puzzle that speaks to the possible shape of the universe. For more than a century, the conjecture resisted attempts to prove or disprove it. As Donal O'Shea reveals in his elegant narrative, Poincare's conjecture opens a door to the history of geometry, from the Pythagoreans of ancient Greece to the celebrated geniuses of the nineteenth-century German academy and, ultimately, to a fascinating array of personalities--Poincare and Bernhard Riemann, William Thurston and Richard Hamilton, and the eccentric genius who appears to have solved it, Grigory Perelman. The solution seems certain to open up new corners of the mathematical universe.
目錄
Contents
Preface
1. Cambridge, April 2003
2. The Shape of the Earth
3. Possible Worlds
4. The Shape of the Universe
5. Euclid's Geometry
6. The Non-Euclideans
7. Bernhard Riemann's Probationary Lecture
8. Riemann's Legacy
9. Klein and Poincare
10. Poincare's Topological Papers
11. The Great Savants
12. The Conjecture Takes Hold
13. Higher Dimensions
14. A Solution in the New Millennium
15. Madrid, August 2006
Notes
Glossary of Terms
Glossary of Names
Timeline
Bibliography
Further Reading
Art Credits
Acknowledgments
Index