Jordan curve theorem
Teorema de la curva de Jordan
- Date
- 1887 · confidence high
- Place
- Paris, France
- Credited to
- Camille Jordan; first rigorous proof by Oswald Veblen, 1905
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
States that every simple closed curve in the plane divides it into two regions, a bounded interior and an unbounded exterior, and that any path between them must cross the curve. It seems obvious but is very hard to prove rigorously.
For decades Jordan's original 1887 proof was considered flawed, and Oswald Veblen's 1905 proof was regarded as the first truly rigorous one; this assessment has since been nuanced.
What it led to
- Development of modern algebraic topology
- Generalisations to higher-dimensional spaces