| 1 | Wagner's, Poincare's, and Descartes' experiences are representative of countless others in every field of culture. | |
| 2 | Given that we live in a world with three spatial dimensions, the Poincaré conjecture tells us ultimately what shape our universe could be. | |
| 3 | The Sunday Telegraph tracked down the eccentric recluse who stunned the maths world when he solved a century-old puzzle known as the Poincaré Conjecture. | |
| 4 | With the help of Poincare mapping, the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane. | |
| 5 | This is what Poincaré and Thurston say about the world of 3-manifolds: there are no manifolds besides those which has been already discovered. |
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