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Mathematics

The Continuum Hypothesis and Its Independence from ZFC

Quick fact

In 1963, Paul Cohen proved that the continuum hypothesis is independent of ZFC: it can be neither proven nor disproven using the standard axioms of set theory. This result, which relies on a technique called forcing, earned him a Fields Medal in 1966.

Why this is interesting

You've probably heard that there are different sizes of infinity. But did you know that the question of whether there is an infinity strictly between the size of the natural numbers and the real numbers cannot be answered using the standard axioms of mathematics?