Geometry

Study of shape, size and space — from Euclid's axioms to curved manifolds and algebraic varieties defined by polynomial equations.

Core Principles & Analysis

• Euclid's Elements axomatized geometry around 300 BC and ruled mathematics for two millennia.
• Non-Euclidean geometries in the 1830s dropped the parallel postulate and curved the plane itself.
• Riemann's 1854 lecture generalized geometry to manifolds, the language general relativity later borrowed.