Discovery is the essence of mathematics, lets see some of the latest discoveries of the 21'st century.
The proof of poincaré conjecture, a revolutionary discovery by Grigori Perelman which contributed in geometry. The poincaré conjecture formulated by Henri Poincaré in 1904 left a question in topology about the classification of three-dimensional objects called manifolds. In 2003, Perelman presented proof, introducing mathematical techniques and insights. His work solved a century old problem, and confirmed Poincaré’s intuition about the structure of three-dimensional spaces. This resulted in the advancement of topology, providing insights about the geometric properties of manifolds, inspiring further research in related areas, making it a revolutionary milestone and discovery for geometry.