What is the Poincaré Conjecture?
Q: What is the Poincaré Conjecture?
A: The Poincaré Conjecture is a question about spheres in mathematics, named after Henri Poincaré, which asks whether certain properties of the 2-sphere are also true for the 3-sphere.
Q: What property does the 2-sphere have?
A: The 2-sphere has the property that any loop on it can be contracted to a point.
Q: Is this property unique to the 2-sphere?
A: This property is unique to the 2-sphere in terms of small spaces that do not have edges. However, an infinitely large plane and a regular disk (a circle and its interior) are both simply connected but they do have edges.
Q: Who proved that it was true for higher dimensional spheres?
A: In 1960, Smale proved it to be true for 5-spheres, 6-spheres and higher, and in 1982 Freedman proved that it was also true for 4-dimensional spheres.
Q: Who solved the Poincaré conjecture?
A: The Poincaré conjecture was solved by Grigori Perelman, a Russian mathematician who used methods from geometry to show that it is indeed true.
Q: What awards did Perelman receive for his work?
A: Perelman received a Fields Medal and $1 million Millennium Prize for his work on solving the Poincaré conjecture; however he declined both awards.
