Melvyn Bragg and guests discuss the power-packs within cells in all complex life on Earth. Inside each cell of every complex organism there are structures known as mitochondria. The 19th century scientists who first observed them thought they were bacteria which had somehow invaded the cells they were studying. We now understand that mitochondria take components from the food we eat and convert them into energy. Mitochondria are essential for complex life, but as the components that run our metabolisms they can also be responsible for a range of diseases – and they probably play a role in how we age. The DNA in mitochondria is only passed down the maternal line. This means it can be used to trace population movements deep into human history, even back to an ancestor we all share: mitochondrial Eve. With Mike Murphy Professor of Mitochondrial Redox Biology at the University of Cambridge Florencia Camus NERC Independent Research Fellow at University College London and Nick Lane Professor of Evolutionary Biochemistry at University College London Producer Luke Mulhall

Melvyn Bragg and guests discuss the life, ideas and legacy of the pioneering Swedish botanist Carl Linnaeus (1707 – 1778). The philosopher Jean-Jacques Rousseau once wrote: "Tell him I know no greater man on earth". The son of a parson, Linnaeus grew up in an impoverished part of Sweden but managed to gain a place at university. He went on to transform biology by making two major innovations. He devised a simpler method of naming species and he developed a new system for classifying plants and animals, a system that became known as the Linnaean hierarchy. He was also one of the first people to grow a banana in Europe. With Staffan Muller-Wille University Lecturer in History of Life, Human and Earth Sciences at the University of Cambridge Stella Sandford Professor of Modern European Philosophy at Kingston University, London and Steve Jones Senior Research Fellow in Genetics at University College, London Producer Luke Mulhall

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.

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