In the context of The Story of Maths, explore the Hilbert's first problem revisited of the "To Infinity and Beyond".
In 1950s American mathematician Paul Cohen took up the challenge of Cantor's Continuum Hypothesis which asks "is there is or isn't there an infinite set of number bigger than the set of whole numbers but smaller than the set of all decimals". Cohen found that there existed two equally consistent mathematical worlds. In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set. Cohen would subsequently work on Hilbert's eighth problem, the Riemann hypothesis, although without the success of his earlier work.
Riemann hypothesis Hilbert's eighth problem Continuum Hypothesis Hilbert's first problem Paul Cohen