Topology

Geometry stretched rubbery: the study of properties preserved under continuous deformation, where a doughnut and a mug are the same.

Core Principles & Analysis

• Born from Euler's 1736 Konigsberg bridge problem and the polyhedron formula V − E + F = 2.
• Its central objects — manifolds, knots, surfaces — are classified by invariants that survive stretching.
• The Poincaré conjecture, posed 1904, was the last of the Millennium Problems to fall, in 2003.