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    Continuum Hypothesis

    Statement

    The continuum hypothesis states that there is no infinite set with a cardinal number between that of the

    Solution

    undecidable

    Alternate names

    Cantor's problem of the cardinal number of the continuum | Hilbert's first problem

    History

    formulation date | 1877 (147 years ago) formulator | Georg Cantor status | ambiguous proof date | 1963 (86 years later) (61 years ago) provers | Kurt Gödel | Paul Joseph Cohen additional people involved | David Hilbert

    Current evidence

    Proved by Gödel and Cohen to be undecidable within Zermelo-Frankel set theory with or without the axiom of choice, but there is no consensus on whether this is a solution to the problem.

    Associated prizes

    prize awarded for solution | Paul Cohen received the Fields Medal in 1966 for showing that if set theory is consistent, then no contradiction would arise if the negation of the continuum hypothesis was added to set theory.

    Classes

    Hilbert's original 10 problems | Hilbert's 23 problems | mathematical hypotheses | undecidable mathematics problems

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