What is the answer to the Poincare Conjecture?
Poincaré conjecture
| A compact 2-dimensional surface without boundary is topologically homeomorphic to a 2-sphere if every loop can be continuously tightened to a point. The Poincaré conjecture asserts that the same is true for 3-dimensional spaces. | |
|---|---|
| Field | Geometric topology |
| Conjectured by | Henri Poincaré |
| Conjectured in | 1904 |
Who solved Poincaré conjecture?
Grigori “Grisha” Perelman
Russian mathematician Grigori “Grisha” Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only one that’s been solved. Famously, he turned down the $1,000,000 Millennium Prize.
What did Poincare discover?
In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
Who proved the Poincare Conjecture in 2002?
Perelman
In November 2002, Perelman submitted a short paper to the arXiv, followed by two more papers. He demonstrated that, indeed, it was possible to repair all such singularities and offered the first rigorous proof of the Poincaré conjecture.
Who rejected Fields Medal?
Grigori Perelman
| Grigori Perelman | |
|---|---|
| Known for | Riemannian geometry Geometric topology Proof of the soul conjecture Proof of the Poincaré conjecture |
| Awards | Saint Petersburg Mathematical Society Prize (1991), accepted EMS Prize (1996), declined Fields Medal (2006), declined Millennium Prize (2010), declined |
| Scientific career | |
| Fields | Mathematics |
What is Poincare known for?
Henri Poincaré was a mathematician, theoretical physicist and a philosopher of science famous for discoveries in several fields and referred to as the last polymath, one who could make significant contributions in multiple areas of mathematics and the physical sciences.
What was the first scientific achievement of Henri Poincare?
His work on the n-body problem, whose ultimate aim was to determine if the solar system was stable, led to Chaos theory – Poincaré gave the first mathematical description of a dynamic system behaving chaotically. His work in special relativity yielded the modern form of the Lorentz transformations.
What is Poincare Conjecture used for?
The Poincare Conjecture is essentially the first conjecture ever made in topology; it asserts that a 3-dimensional manifold is the same as the 3-dimensional sphere precisely when a certain algebraic condition is satisfied. The conjecture was formulated by Poincare around the turn of the 20th century.