The Poincaré conjecture is a famous problem in the field of topology, a branch of mathematics that studies the properties of space. Proposed by the French mathematician Henri Poincaré in 1904, it suggests that any closed three-dimensional shape, known as a 3-manifold, that is simply connected (meaning it has no holes) is equivalent to a three-dimensional sphere. After many years of research, the conjecture was proven true by the Russian mathematician Grigori Perelman in 2003. His proof built upon the work of others and used advanced techniques in geometric analysis. The resolution of the Poincaré conjecture was a significant milestone in mathematics, earning Perelman the prestigious Fields Medal, which he famously declined.