Every simple closed curve in the plane divides the plane into exactly two regions, an interior and an exterior, and the curve is the common boundary of both. Named for Camille Jordan, its statement is visually obvious but its rigorous proof is surprisingly delicate.
Facts
Disputed
Proof YearJordan published a claimed proof in 1887; for decades many mathematicians considered that proof flawed and credited Oswald Veblen with the first rigorous proof, but this assessment has since been challenged by Thomas Hales and others, so which proof was genuinely first and correct is not settled among historians of mathematics. StatementEvery simple closed curve in the plane divides the plane into exactly two regions, a bounded interior and an unbounded exterior, and any continuous path from a point in one region to a point in the other must cross the curve. 1 Classification
Statement FormCharacterization Theorem 1 Jordan Curve Theorem
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Source MacTutor History of Mathematics: Camille Jordan - MacTutor biography
Source Oswald Veblen (Wikipedia)
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1. Jordan Curve Theorem (Wikipedia)
Wikimedia FoundationLead section
For decades, mathematicians generally thought that this proof was flawed and that the first rigorous proof was carried out by Oswald Veblen; however, this notion has been overturned by Thomas C. Hales and others.
In Group: Geometric and Differential Topology, Lead paragraph
In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every simple closed curve in the plane (known as a Jordan curve) divides the plane into two regions: the interior, bounded by the curve, and an unbounded exterior, containing all of the nearby and faraway exterior points.
View the Source MacTutor History of Mathematics: Camille Jordan - MacTutor biography
MacTutor History of MathematicsPrincipal Result Of: Camille Jordan, Biography textQuote, Principal Result Of: Camille Jordan, Biography text
Jordan is best remembered today among analysts and topologists for his proof that a simply closed curve divides a plane into exactly two regions, now called the Jordan curve theorem .
Oswald Veblen (Wikipedia)
Principal Result Of: Oswald Veblen, Lead, principal resultQuote, Principal Result Of: Oswald Veblen, Lead, principal result
He proved the Jordan curve theorem in 1905
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