7. Crisis and Uncertainty

Adrian Moore’s series on philosophical thought on infinity finds him mired in a near meltdown in mathematics.

Adrian tells the story of the controversy caused by the work of the German mathematician, Georg Cantor, on the infinite. In a world of paradoxes, we meet the nun who can't decide whether to pray for herself. Her dilemma is beautifully explained by Marcus Giaquinto, Emeritus Professor of Philosophy at UCL, in conversation with Adrian.

And we find out how an associated paradox, first posed by one of the giants of 20th century philosophy, Bertrand Russell, devastated the career of another German mathematician and philosopher.

The arguments of the early 20th century no longer plague modern mathematics in the way that they did. As Adrian explains however, by subjecting the infinite to formal scrutiny, mathematicians have ended up confronting puzzles at the very heart of their discipline.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.