Poincaré Conjecture: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

In a 1904 paper, the French mathematician Jules Henri Poincare stated that every closed simply connected 3-manifold is homeomorphic to the 3-sphere. Dr. Grigory Perelman of the Steklov Institute of Mathematics (part of the Russian Academy of Sciences in St. Petersburg) solved the 100-year-old Poincare conjecture. The ICM awarded Perelman the Field Medal (Noble Prize of Mathematics) for his work, but Perelman refused the Medal.

**Links to the proof:**

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