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Melvyn Bragg and guests discuss the nature and existence of mathematical infinity. Jonathan Swift encapsulated the counter-intuitive character of infinity with insouciant style:鈥淪o, naturalists observe, a fleaHath smaller fleas on him that preyAnd these hath smaller fleas to bite 鈥榚mAnd so proceed ad infinitum.鈥滱las, the developing utility mathematicians put to the idea of infinity did not find the English philosopher Thomas Hobbes quite so relaxed. When confronted with a diagram depicting an infinite solid whose volume was finite, he wrote, 鈥淭o understand this for sense, it is not required that a man should be a geometrician or logician, but that he should be mad鈥�. Yet philosophers and mathematicians have continued to grapple with the unending, and it is a core concept in modern maths.So, what is mathematical infinity? Are some infinities bigger than others? And does infinity exist in nature?With Ian Stewart, Professor of Mathematics at the University of Warwick; Robert Kaplan,聽co-founder of The Math Circle聽at Harvard University and author of The Art of the Infinite: Our Lost Language of Numbers; Sarah Rees, Reader in Pure Mathematics at the University of Newcastle.