Melvyn Bragg and guests discuss the emergence of the world’s first organic matter nearly four billion years ago. Scientists have named 1.5 million species of living organism on the land, in the skies and in the oceans of planet Earth and a new one is classified every day.  Estimates of how many species remain to be discovered vary wildly, but science accepts one categorical point – all living matter on our planet, from the nematode to the elephant, from the bacterium to the blue whale, is derived from a single common ancestor. What was that ancestor?  Did it really emerge from a ‘primordial soup’? And what, in the explanation of evolutionary science, provided the catalyst to start turning the cycle of life?With Richard Dawkins, Charles Simonyi Professor of the Public Understanding of Science at Oxford University; Richard Corfield, Visiting Senior Lecturer at the Centre for Earth, Planetary, Space and Astronomical Research at the Open University; Linda Partridge, Biology and Biotechnology Research Council Professor at University College London.

Melvyn Bragg and guests discuss the history of the most detailed number in nature. In the Bible's description of Solomon's temple it comes out as three, Archimedes calculated it to the equivalent of 14 decimal places and today's super computers have defined it with an extraordinary degree of accuracy to its first 1.4 trillion digits. It is the longest number in nature and we only need its first 32 figures to calculate the size of the known universe within the accuracy of one proton. We are talking about Pi, 3.14159 etc, the number which describes the ratio of a circle's diameter to its circumference. How has something so commonplace in nature been such a challenge for maths? And what does the oddly ubiquitous nature of Pi tell us about the hidden complexities of our world? With Robert Kaplan, co-founder of the Maths Circle at Harvard University, Eleanor Robson, Lecturer in the Department of History and Philosophy of Science at Cambridge University; and Ian Stewart, Professor of Mathematics at the University of Warwick.

Melvyn Bragg and guests discuss Renaissance obsession with Magic. In 1461 one of the powerful Medici family’s many agents carried a mysterious manuscript into his master’s house in Florence. It purported to be the work of an ancient Egyptian priest-king and magician called Hermes Trismegistus. When Cosimo de Medici saw the new discovery, he ordered his translations of Plato to be stopped so that work could begin on the new discovery at once. Hermes promised secret knowledge to his initiates and claimed to have spoken with the spirits and turned base metal into gold. His ideas propelled natural magic into the mainstream of Renaissance intellectual thought, as scholars and magi vied to understand the ancient secrets that would bring statues to life and call the angels down from heaven.But why did magic appeal so strongly to the Renaissance mind? And how did the scholarly Magus, who became a feature of the period, manage to escape prosecution and relate his work to science and the Church?With Peter Forshaw, Lecturer in Renaissance Philosophies at Birkbeck, University of London; Valery Rees, Renaissance historian and a translator of Ficino’s letters; Jonathan Sawday, Professor of English Studies at the University of Strathclyde.

Melvyn Bragg and guests discuss our knowledge of the planets in both our and other solar systems. Tucked away in the outer Western Spiral arm of the Milky Way is a middle aged star, with nine, or possibly ten orbiting planets of hugely varying sizes. Roughly ninety-two million miles and third in line from that central star is our own planet Earth, in thrall to our Sun, just one of the several thousand million stars that make up the Galaxy.Ever since Galileo and Copernicus gave us a scientific model of our own solar system, we have assumed that somewhere amongst the myriad stars there must be other orbiting planets, but it took until 1995 to find one. ‘51 Pegasus A’ was discovered in the Pegasus constellation and was far bigger and far closer to its sun than any of our existing theories could have predicted. Since then 121 new planets have been found. And now it is thought there may be more planets in the skies than there are stars.What causes a planet to form? How do you track one down? And how likely is there to be another one out there with properties like the Earth’s?With Paul Murdin, Senior Fellow at the Institute of Astronomy in Cambridge; Hugh Jones, planet hunter and Reader in Astrophysics at Liverpool John Moores University; Carolin Crawford, Royal Society Research Fellow at the Institute of Astronomy in Cambridge.

Melvyn Bragg and guests discuss the history of the number between 1 and -1, which has strange and uniquely beguiling qualities. Shakespeare’s King Lear warned, “Nothing will come of nothing”. The poet and priest John Donne said from the pulpit, “The less anything is, the less we know it: how invisible, unintelligible a thing is nothing”, and the English monk and historian William of Malmesbury called them “dangerous Saracen magic”. They were all talking about zero, the number or symbol that had been part of the mathematics in the East for centuries but was finally taking hold in Europe.What was it about zero that so repulsed their intellects? How was zero invented? And what role does zero play in mathematics today?With Robert Kaplan, co-founder of the Maths Circle at Harvard University and author of The Nothing That Is: A Natural History of Zero; Ian Stewart, Professor of Mathematics at the University of Warwick; Lisa Jardine, Professor of Renaissance Studies at Queen Mary, University of London.

Melvyn Bragg and guests discuss a problematic notion which can be an emotional condition, a syndrome, an extreme or over-reaction, or the physical signs of trauma. The term ‘hysteria’ was first used in Greece in the 5th century BC by Hippocratic doctors. They were trying to explain an illness whose symptoms were breathing difficulties and a sense of suffocation, and whose sufferers were seen chiefly to be recently bereaved widows. The explanation was thought to be a wandering womb putting pressure on other organs. The use that Sigmund Freud put to the term was rather different, but although there is no wandering womb in his notion of hysteria, there is still a mysterious leap from the emotional to the physical, from the mind to the body. What is hysteria? How can emotional experiences cause physical illnesses? And has hysteria’s association with old stereotypes of femininity put it off the modern medical map? With Juliet Mitchell, Professor of Psychoanalysis and Gender Studies at the University of Cambridge and author of Mad Men and Medusas: Reclaiming Hysteria and the Effects of Sibling Relations on the Human Condition; Rachel Bowlby, Professor of English at the University of York who has written the introduction to the latest Penguin translation of Sigmund Freud and Joseph Breuer’s Studies in Hysteria; Brett Kahr, Senior Clinical Research Fellow in Psychotherapy and Mental Health at the Centre for Child Mental Health in London.

Melvyn Bragg and guests discuss the 30 year search to solve all the biggest questions in physics. At the end of the last century, brave voices were predicting that all the big questions of physics were on the verge of being answered by a Theory of Everything. The disparity between the physics of the very small would finally be reconciled with the very large, and the four forces of nature would finally be united with a single set of equations. It was suggested that with such a theory we might solve the riddle of black holes, unlock the secrets of the Big Bang, probe other universes and even uncover the mystery of travelling through time. But Stephen Hawking, who once said that with a Theory of Everything “we would know the mind of God”, has changed his mind and now says that it may not be possible after all. So what are the prospects for a Theory of Everything? Why do we need one? How do we get one? And what would it mean if we did? With Brian Greene, Professor of Physics and Mathematics at Columbia University and author of The Fabric of the Cosmos; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and author of The Constants of Nature; Dr Val Gibson, particle physicist from the Cavendish Laboratory and Fellow of Trinity College, Cambridge.

Melvyn Bragg and guests discuss the interpretation of dreams. Over a hundred years ago, Sigmund Freud declared confidently, “The interpretation of dreams is the royal road to a knowledge of the unconscious activities of the mind”. He was writing in his famous volume, The Interpretation of Dreams and his ideas made a huge impact on the century that was to follow. However, despite the cultural influence of his work, there is still no agreement in neuroscience as to the function or mechanism of dreaming; this is partly because for much of the century the prevailing wisdom was that there was no meaning to dreams at all.What is the mental circuitry that creates our dreams? If they have no meaning, why do we dream them? And why is the tide turning with neuroscientists starting to find reasons to take dreams seriously again?With Professor V S Ramachandran, Director of the Center for Brain and Cognition at the University of California, San Diego; Mark Solms, Professor of Neuropsychology at the University of Cape Town; Martin Conway, Professor of Psychology at the University of Durham.

Melvyn Bragg and guests discuss Ernest Rutherford. He was the father of nuclear science, a great charismatic figure who mapped the landscape of the sub-atomic world. He identified the atom’s constituent parts, discovered that elemental decay was the cause of radiation and became the first true alchemist in the history of science when he forced platinum to change into gold. He was born at the edge of the Empire in 1871, the son of Scottish immigrant farmers and was working the fields when a telegram came from the great British physicist J J Thomson asking him to come to Cambridge. Rutherford immediately laid down his spade saying "that’s the last potato I ever dig". It was. He went on to found a science, win a Nobel Prize and pioneer the ‘big science’ of the twentieth century. With Simon Schaffer, Professor in the History and Philosophy of Science at the University of Cambridge; Jim Al–Khalili, Senior Lecturer in Physics at the University of Surrey; Patricia Fara, Fellow of Clare College, Cambridge.

Melvyn Bragg and guests discuss the origins and history of codes. In October 1586, in the forbidding hall of Fotheringhay Castle, Mary Queen of Scots was on trial for her life. Accused of treason and denied legal representation, she sat alone in the shadow of a vast and empty throne belonging to her absent cousin and arch rival Elizabeth I of England. Walsingham, Elizabeth’s Principal Secretary, had already arrested and executed Mary’s fellow conspirators, her only hope lay in the code she had used in all her letters concerning the plot. If her cipher remained unbroken she might yet be saved. Not for the first time the life of an individual and the course of history depended on the arcane art of Cryptography.What are the origins of this secretive science? And what links the ‘Caesar Cipher’ with the complex algorithms which underpin so much of our modern age?With Simon Singh, science writer and author of The Code Book: The Secret History of Codes and Code-Breaking; Professor Fred Piper, Director of the Information Security Group at Royal Holloway, University of London and co-author of Cryptography: A Very Short Introduction; Lisa Jardine, Professor of Renaissance Studies at Queen Mary, University of London and author of Ingenious Pursuits.