The Poincaré Conjecture is a famous problem in the field of topology, which studies the properties of space that are preserved under continuous transformations. Proposed by the French mathematician Henri Poincaré in 1904, the conjecture states that any simply connected, closed 3-manifold is homeomorphic to the 3-sphere. In simpler terms, if a three-dimensional shape has no holes and is finite in extent, it can be transformed into a sphere without tearing or gluing. After many years of effort by mathematicians, the conjecture was proven by Grigori Perelman in 2003. His proof built upon the work of others in geometric analysis and was verified by the mathematical community. The resolution of the Poincaré Conjecture was a significant milestone in mathematics, earning Perelman the prestigious Fields Medal, which he famously declined.