The P=NP problem; the ramifications could boost the world's GDP by several % in one fell swoop (or not; depends on what you prove
).The Poincare Conjecture is a mathematical theorem proposed by Henri Poincare in 1904. It states that any closed 3-dimensional object is equivalent to a 3-sphere, which is a shape similar to a 3-dimensional ball.
The Poincare Conjecture is considered one of the most significant and challenging problems in mathematics. Its proof has many implications in various fields, including topology, geometry, and physics.
The Poincare Conjecture remained unsolved for over 100 years. It was finally solved by Russian mathematician Grigori Perelman in 2003. However, his proof was not officially recognized until 2006.
Perelman used a combination of techniques, including Ricci flow and Hamilton's program, to prove the Poincare Conjecture. He also built upon the work of other mathematicians, such as Richard Hamilton and William Thurston.
The solution to the Poincare Conjecture opened up new areas of research in mathematics, such as geometric topology and differential geometry. It also inspired further work in the study of 3-manifolds and their properties.