Melvyn Bragg and his guests discuss the role played by women in Enlightenment science. During the eighteenth century the opportunities for women to gain a knowledge of science were minimal. Universities and other institutions devoted to research were the preserve of men. Yet many important contributions to the science of the Enlightenment were made by women. These ranged from major breakthroughs like those of the British astronomer Caroline Herschel, the first woman to discover a comet, to important translations of scientific literature such as Emilie du Chatelet's French version of Newton's Principia - and all social classes were involved, from the aristocratic amateur botanists to the women artisans who worked in London's workshops manufacturing scientific instruments. The image above, of Emilie du Chatelet, is attributed to Maurice Quentin de La Tour.WithPatricia Fara Senior Tutor at Clare College, University of CambridgeKaren O'Brien Professor of English at the University of WarwickJudith Hawley Professor of 18th Century Literature at Royal Holloway, University of LondonProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the history of logic. Logic, the study of reasoning and argument, first became a serious area of study in the 4th century BC through the work of Aristotle. He created a formal logical system, based on a type of argument called a syllogism, which remained in use for over two thousand years. In the nineteenth century the German philosopher and mathematician Gottlob Frege revolutionised logic, turning it into a discipline much like mathematics and capable of dealing with expressing and analysing nuanced arguments. His discoveries influenced the greatest mathematicians and philosophers of the twentieth century and considerably aided the development of the electronic computer. Today logic is a subtle system with applications in fields as diverse as mathematics, philosophy, linguistics and artificial intelligence.With:A.C. GraylingProfessor of Philosophy at Birkbeck, University of LondonPeter MillicanGilbert Ryle Fellow in Philosophy at Hertford College at the University of OxfordRosanna KeefeSenior Lecturer in Philosophy at the University of Sheffield.Producer: Thomas Morris.

Melvyn Bragg and his guests discuss imaginary numbers. In the sixteenth century, a group of mathematicians in Bologna found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an "imaginary" number.The name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves. With Marcus du SautoyProfessor of Mathematics at Oxford University Ian StewartEmeritus Professor of Mathematics at the University of WarwickCaroline SeriesProfessor of Mathematics at the University of WarwickProducer: Thomas Morris.

Melvyn Bragg and his guests discuss Pliny's Natural History.Some time in the first century AD, the Roman scholar Pliny the Elder published his Naturalis Historia, or Natural History, an enormous reference work which attempted to bring together knowledge on every subject under the sun. The Natural History contains information on zoology, astronomy, geography, minerals and mining and - unusually for a work of this period - a detailed treatise on the history of classical art. It's a fascinating snapshot of the state of human knowledge almost two millennia ago.Pliny's 37-volume magnum opus is one of the most extensive works of classical scholarship to survive in its entirety, and was being consulted by scholars as late as the Renaissance. It had a significant influence on intellectual history, and has provided the template for every subsequent encyclopaedia.With:Serafina CuomoReader in Roman History at Birkbeck, University of LondonAude DoodyLecturer in Classics at University College, DublinLiba TaubReader in the History and Philosophy of Science, Cambridge UniversityProducer: Thomas Morris.

Explore the history and discovery of Antarctica, including the triumphs and tragedies of human exploration. Learn about the geological history of the continent and its breakup from the ancient landmass of Gondwana. Discover the challenges faced by early explorers and the impact of commercial exploitation on wildlife. Dive into the heroic age of exploration and the changing research objectives in Antarctica. Delve into the value of meteorological records and the significance of water cavity systems under the ice sheet.

Experts discuss the lives and behaviors of Neanderthals, their extinction, the impact of climate change on human evolution, the relationship between Neanderthals and Homo sapiens, the range and boundaries of Neanderthals, their behaviors and societal structure, and the language abilities and possible interbreeding with Homo sapiens.

From the 1600s to the 1800s, scientific research in Britain was not yet a professional, publicly-funded career.So the wealth, status and freedom enjoyed by British aristocrats gave them the opportunity to play an important role in pushing science forwards - whether as patrons or practitioners.The Cavendish family produced a whole succession of such figures.In the 1600s, the mathematician Sir Charles Cavendish and his brother William collected telescopes and mathematical treatises, and promoted dialogue between British and Continental thinkers. They brought Margaret Cavendish, William's second wife, into their discussions and researches, and she went on to become a visionary, if eccentric, science writer, unafraid to take on towering figures of the day like Robert Hooke.In the 1700s, the brothers' cousin's great-grandson, Lord Charles Cavendish, emerged as a leading light of the Royal Society.Underpinned by his rich inheritance, Charles' son Henry became one of the great experimental scientists of the English Enlightenment.And in the 1800s, William Cavendish, Henry's cousin's grandson, personally funded the establishment of Cambridge University's Cavendish Laboratory. In subsequent decades, the Lab become the site of more great breakthroughs.With:Jim BennettDirector of the Museum of the History of Science at the University of OxfordPatricia FaraSenior Tutor of Clare College, University of CambridgeSimon SchafferProfessor of History of Science at the University of Cambridge and Fellow of Darwin College, CambridgeProducer - Phil Tinline.

The Cool Universe is the name astronomers give to the matter between the stars.These great clouds of dust and gas are not hot enough to be detected by optical telescopes.But over the last few decades, they have increasingly become the focus of infrared telescopy.Astronomers had long encountered dark, apparently starless patches in the night sky. When they discovered that these were actually areas obscured by dust, they found a way to see through these vexing barriers, using infrared telescopes, to the light beyond.However, more recently, the dust itself has become a source of fascination.The picture now being revealed by infrared astronomy is of a universe that is dynamic.In this dynamic universe, matter is recycled - and so the dust and gas of the Cool Universe play a vital role. They are the material from which the stars are created, and into which they finally disintegrate, enriching the reservoir of cool matter from which new stars will eventually be formed. As a result of the new research, we are now beginning to see first-hand the way our planet was formed when the solar system was born.With:Carolin CrawfordMember of the Institute of Astronomy, and Fellow of Emmanuel College, at the University of CambridgePaul MurdinVisiting Professor of Astronomy at Liverpool John Moores University's Astronomy Research InstituteMichael Rowan-RobinsonProfessor of Astrophysics at Imperial College, LondonProducer: Phil Tinline.

Melvyn Bragg and guests Usha Goswami, Annette Karmiloff-Smith and Denis Mareschal discuss what new research reveals about the infant brain.For obvious reasons, what happens in the minds of very young, pre-verbal children is elusive. But over the last century, the psychology of early childhood has become a major subject of study. Some scientists and researchers have argued that children develop skills only gradually, others that many of our mental attributes are innate. Sigmund Freud concluded that infants didn't differentiate themselves from their environment. The pioneering Swiss child psychologist Jean Piaget thought babies' perception of the world began as a 'blooming, buzzing confusion' of colour, light and sound, before they developed a more sophisticated worldview, first through the senses and later through symbol. More recent scholars such as the leading American theoretical linguist Noam Chomsky have argued that the fundamentals of language are there from birth. Chomsky has famously argued that all humans have an innate, universally applicable grammar.Over the last ten to twenty years, new research has shed fresh light on important aspects of the infant brain which have long been shrouded in mystery or mired in dispute, from the way we start to learn to speak to the earliest understanding that other people have their own minds. With:Usha Goswami, Professor of Education at the University of Cambridge and Director of its Centre for Neuroscience in Education Annette Karmiloff-Smith, Professorial Research Fellow at the Centre for Brain and Cognitive Development at the Department of Psychological Sciences, Birkbeck College, University of LondonDenis Mareschal, Professor of Psychology at the Centre for Brain and Cognitive Development at Birkbeck College, University of London.

Melvyn Bragg and guests John Barrow, Colva Roney-Dougal and Marcus du Sautoy explore the unintended consequences of mathematical discoveries, from the computer to online encryption, to alternating current and predicting the path of asteroids.In his book The Mathematician's Apology (1941), the Cambridge mathematician GH Hardy expressed his reverence for pure maths, and celebrated its uselessness in the real world. Yet one of the branches of pure mathematics in which Hardy excelled was number theory, and it was this field which played a major role in the work of his younger colleague, Alan Turing, as he worked first to crack Nazi codes at Bletchley Park and then on one of the first computers.Melvyn Bragg and guests explore the many surprising and completely unintended uses to which mathematical discoveries have been put. These include:The cubic equations which led, after 400 years, to the development of alternating current - and the electric chair.The centuries-old work on games of chance which eventually contributed to the birth of population statistics.The discovery of non-Euclidean geometry, which crucially provided an 'off-the-shelf' solution which helped Albert Einstein forge his theory of relativity.The 17th-century theorem which became the basis for credit card encryption.In the light of these stories, Melvyn and his guests discuss how and why pure mathematics has had such a range of unintended consequences.John Barrow is Professor of Mathematical Sciences at the University of Cambridge and Professor of Geometry at Gresham College, London; Colva Roney-Dougal is Lecturer in Pure Mathematics at the University of St Andrews; Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford.