When was this proved...............?

Question

When was the Poincare conjecture proved and is it also known as Thurston's conjecture?.Also,what is the theory behind the Poincare conjecture?

Answer 1

According to Wikipedia, Grigori Perelman attempted a proof in 2002-03 which is still under scrutiny. Mean while, big money is being offered to find someone who can definitely prove it. It appears to still be a hypothesis
"The conjecture concerns a space that locally looks like ordinary three dimensional space but is finite in size and lacks any boundary (a closed 3-manifold)."
"The conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere. and is unproven."

Answer 2

After nearly a century of effort by mathematicians, a series of papers made available in 2002 and 2003 by Grigori Perelman, following the program of Richard Hamilton, sketched a solution. Three groups of mathematicians have produced works filling in the details of Perelman's proof.

The Poincaré conjecture is one of the most important questions in topology. It is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute is offering a $1,000,000 prize for a correct solution. Perelman's work is under review and the prize money could be awarded if the proof is considered valid two years after publication

If by theory behind it, you mean what does it conjecture? A compact statement would be: Every simply connected compact 3-manifold (without boundary) is homeomorphic to a 3-sphere.

In english the conjecture concerns a space that locally looks like ordinary three dimensional space but is finite in size and lacks any boundary (a closed 3-manifold). The conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.

Thurston's conjecture is a more general statement that IMPLIES Poincare's conjecture. Specifically Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed into pieces with geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in 1982, and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture.