A prodigy in Leningrad
Conquering the Poincaré conjecture
The refusal of fame and fortune
Topology and the shape of reality
How many geometric types did William Thurston conjecture could describe all three-dimensional shapes?
diego Stretch and morph 3D shapes to discover how topology defines the true shape of reality.
diego Proving the Poincaré conjecture helps scientists understand the possible shapes of the entire cosmos.
diego Topology and the Poincaré Conjecture
With no holes inside, any closed space bends into a sphere.
diego Perelman actually proved a much larger theory that classified all three-dimensional shapes.
What larger mathematical theory, proposed by William Thurston, did Perelman have to prove first?
Mug or donut: In the mathematical field of topology, a coffee mug and a donut are considered the exact same shape because both have one hole.
Which area of modern physics uses Perelman's refined mathematical tools to study black holes?
The study of the properties of geometric figures that remain unchanged under continuous deformation. Grigori Perelman utilized this mathematical discipline to solve the historic Poincaré conjecture in 2002.