The continuum hypothesis is a mathematical proposition concerning the sizes of infinite sets. It specifically states that there is no set whose size is strictly between that of the integers and the real numbers. In simpler terms, it suggests that the only sizes of infinite sets are either countable, like the set of integers, or uncountable, like the set of real numbers. This hypothesis was first proposed by the mathematician Georg Cantor in the late 19th century. It became a significant topic in set theory and was shown to be independent of the standard axioms of set theory, meaning it can neither be proven nor disproven using those axioms.