Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject. He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics. He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days. With Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge and Andrew Treglown Associate Professor in Mathematics at the University of Birmingham The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.

In 1957 Stevie Smith published a poetry collection called Not Waving But Drowning – and its title poem gave us a phrase which has entered the language. Its success has overshadowed her wider work as the author of more than half a dozen collections of poetry and three novels, mostly written while she worked as a secretary. Her poems, printed with her pen and ink sketches, can seem simple and comical, but often beneath the surface lurk themes of melancholy, loneliness, love and death. With Jeremy Noel-Tod Associate Professor in the School of Literature, Drama and Creative Writing at the University of East Anglia Noreen Masud Lecturer in Twentieth Century Literature at the University of Bristol and Will May Professor of Modern and Contemporary Literature at the University of Southampton The photograph above shows Stevie Smith recording her story Sunday at Home, a finalist in the BBC Third Programme Short Story competition in 1949.

On 21 May 1838 an estimated 150,000 people assembled on Glasgow Green for a mass demonstration. There they witnessed the launch of the People’s Charter, a list of demands for political reform. The changes they called for included voting by secret ballot, equal-sized constituencies and, most importantly, that all men should have the vote. The Chartists, as they came to be known, were the first national mass working-class movement. In the decade that followed, they collected six million signatures for their Petitions to Parliament: all were rejected, but their campaign had a significant and lasting impact. With Joan Allen Visiting Fellow in History at Newcastle University and Chair of the Society for the Study of Labour History Emma Griffin Professor of Modern British History at the University of East Anglia and President of the Royal Historical Society and Robert Saunders Reader in Modern British History at Queen Mary, University of London. The image above shows a Chartist mass meeting on Kennington Common in London in April 1848.

Melvyn Bragg and guests discuss the pioneering Danish astronomer Tycho Brahe (1546 – 1601) whose charts offered an unprecedented level of accuracy. In 1572 Brahe's observations of a new star challenged the idea, inherited from Aristotle, that the heavens were unchanging. He went on to create his own observatory complex on the Danish island of Hven, and there, working before the invention of the telescope, he developed innovative instruments and gathered a team of assistants, taking a highly systematic approach to observation. A second, smaller source of renown was his metal prosthetic nose, which he needed after a serious injury sustained in a duel. The image above shows Brahe aged 40, from the Atlas Major by Johann Blaeu. With Ole Grell Emeritus Professor in Early Modern History at the Open University Adam Mosley Associate Professor of History at Swansea University and Emma Perkins Affiliate Scholar in the Department of History and Philosophy of Science at the University of Cambridge.

Melvyn Bragg and guests discuss the discovery made in 1911 by the Dutch physicist Heike Kamerlingh Onnes (1853-1926). He came to call it Superconductivity and it is a set of physical properties that nobody predicted and that none, since, have fully explained. When he lowered the temperature of mercury close to absolute zero and ran an electrical current through it, Kamerlingh Onnes found not that it had low resistance but that it had no resistance. Later, in addition, it was noticed that a superconductor expels its magnetic field. In the century or more that has followed, superconductors have already been used to make MRI scanners and to speed particles through the Large Hadron Collider and they may perhaps bring nuclear fusion a little closer (a step that could be world changing). The image above is from a photograph taken by Stephen Blundell of a piece of superconductor levitating above a magnet. With Nigel Hussey Professor of Experimental Condensed Matter Physics at the University of Bristol and Radbout University Suchitra Sebastian Professor of Physics at the Cavendish Laboratory at the University of Cambridge And Stephen Blundell Professor of Physics at the University of Oxford and Fellow of Mansfield College Producer: Simon Tillotson