As part of the BBC's year of science programming, Melvyn Bragg looks at the history of the oldest scientific learned society of them all: the Royal Society. The horrors of the First World War were a shocking indictment of the power of science. Picking up the thread at this hiatus in scientific optimism, this programme, recorded in the current home of the Royal Society in Carlton House Terrace in London, looks at the more subtle, discreet role the Society played in the 20th century, such as secretly arranging for refugee scientists to flee Germany, co-ordinating international scientific missions during the Cold War and quietly distributing government grant money to fund the brightest young researchers in the land. As ever more important scientific issues face the world and Britain today, the programme asks how well placed the Royal Society is to take an important lead in the future.

As part of the BBC's year of science programming, Melvyn Bragg looks at the history of the oldest scientific learned society of them all: the Royal Society. The 19th century blooms scientifically with numerous alternative, specialist learned societies and associations, all threatening the Royal Society's pre-eminence. Attempts to reform the membership criteria - marking scientific leadership's painful transition from patronage to expertise - are troubled, and organisations such as the British Association for the Advancement of Science (now the BSA) excite and enliven scientific discourse outside of London. Science becomes a realistic career and a path of improvement, and by the time HG Wells writes science fiction at the end of the 19th century, there are sufficient numbers of interested, informed readers to suggest that Edwardian society contained the beginnings of a scientific society.

As part of the BBC's year of science programming, Melvyn Bragg looks at the history of the oldest scientific learned society of them all: the Royal Society. Programme two begins in the coffee house Isaac Newton and the fellows of the early 18th century frequented. At the Royal Observatory, Greenwich, we learn how Newton's feud with the Astronomer Royal John Flamsteed tested the lines between government-funded research and public access. In the age of exploration, senior fellows accompany naval expeditions, such as Cook's expedition to Tahiti and subsequent discovery of Australia. International relations are fostered between scientists such as Benjamin Franklin, whose house in London serves as live-in lab and de facto American embassy. By the end of the century the President, Sir Joseph Banks, successfully embeds the Royal Society in the imperial bureaucratic hub of the new Somerset House. But while senior fellows concentrated on foreign fields, a more radical, dissident science and manufacturing base wrought the Industrial Revolution right under their noses.

As part of the BBC's year of science programming, Melvyn Bragg looks at the history of the oldest scientific learned society of them all: the Royal Society. Melvyn travels to Wadham College, Oxford, where under the shadow of the English Civil War, the young Christopher Wren and friends experimented in the garden of their inspirational college warden, John Wilkins. Back in London, as Charles II is brought to the throne from exile, the new Society is formally founded one night in Gresham College. When London burns six years later, it is two of the key early Fellows of the Society who are charged with its rebuilding. And, as Melvyn finds out, in the secret observatory in The Monument to the fire, it is science which flavours their plans.

Melvyn Bragg and guests Serafina Cuomo, John O'Connor and Ian Stewart discuss the ideas and influence of the Greek mathematician Pythagoras and his followers, the Pythagoreans.The Ancient Greek mathematician Pythagoras is probably best known for the theorem concerning right-angled triangles that bears his name. However, it is not certain that he actually developed this idea; indeed, some scholars have questioned not only his true intellectual achievements, but whether he ever existed. We do know that a group of people who said they were followers of his - the Pythagoreans - emerged around the fifth century BC. Melvyn Bragg and his guests discuss what we do and don't know about this legendary figure and his followers, and explore the ideas associated with them. Some Pythagoreans, such as Philolaus and Archytas, were major mathematical figures in their own right. The central Pythagorean idea was that number had the capacity to explain the truths of the world. This was as much a mystical belief as a mathematical one, encompassing numerological notions about the 'character' of specific numbers. Moreover, the Pythagoreans lived in accordance with a bizarre code which dictated everything from what they could eat to how they should wash. Nonetheless, Pythagorean ideas, centred on their theory of number, have had a profound impact on Western science and philosophy, from Plato through astronomers like Copernicus to the present day.Serafina Cuomo is Reader in Roman History at Birkbeck College, University of London; John O'Connor is Senior Lecturer in Mathematics at the University of Saint Andrews; Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick.

Melvyn Bragg and guests Jim Al-Khalili, Frank Close and Frank James discuss the history of the discovery of radiation.Today the word 'radiation' conjures up images of destruction. But in physics, it simply describes the emission, transmission and absorption of energy, and the discovery of how radiation works has allowed us to identify new chemical elements, treat cancer and work out what the stars are made of.Over the course of the 19th century, physicists from Thomas Young, through Michael Faraday to Henri Becquerel made discovery after discovery, gradually piecing together a radically new picture of reality. They explored the light beyond the visible spectrum, connected electricity and magnetism, and eventually showed that heat, light, radio and mysterious new phenomena like 'X-rays' were all forms of 'electromagnetic wave'. In the early 20th century, with the discovery of radioactivity, scientists like Max Planck and Ernest Rutherford completed the picture of the 'electromagnetic spectrum'. This was a cumulative achievement that transformed our vision of the physical world, and what we could do in it.Jim Al-Khalili is Professor of Theoretical Physics and Chair in the Public Engagement in Science at the University of Surrey; Frank Close is Professor of Physics at Exeter College, University of Oxford; Frank James is Professor of the History of Science at the Royal Institution.

Melvyn Bragg and guests Richard Corfield, Jane Francis and Sanjeev Gupta discuss the geological formation of Britain.Around 600 million years ago the island that we now call Britain was in two parts, far to the south of the Equator. Scotland and north-western Ireland were part of a continent (Laurentia) that also included what is now North America. To the south-east, near the Antarctic Circle, meanwhile, you would have found southern Ireland, England and Wales. They formed a mini-continent (Avalonia) with what is now Newfoundland.Over the course of hundreds of millions of years, as they inched their way north, the two parts came together - first as part of a vast unitary continent (Pangaea), later as a promontory on the edge of Europe, and eventually, as sea levels rose, as an island. The story of how Britain came to be where it is now, in its current shape - from the separation of North America and Europe to the carving out of the English Channel - is still being uncovered today.Richard Corfield is Visiting Senior Resarch Fellow at Oxford University; Jane Francis is Professor of Palaeoclimatology at the University of Leeds; Sanjeev Gupta is a Royal Society-Leverhulme Trust Research Fellow at Imperial College London.

Melvyn Bragg discusses the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented an astonishingly powerful new mathematical tool - calculus. Both claimed to have conceived it independently, but the argument soon descended into a bitter battle over priority, plagiarism and philosophy. Set against the backdrop of the Hanoverian succession to the English throne and the formation of the Royal Society, the fight pitted England against Europe, geometric notation against algebra. It was fundamental to the grounding of a mathematical system which is one of the keys to the modern world, allowing us to do everything from predicting the pressure building behind a dam to tracking the position of a space shuttle.Melvyn is joined by Simon Schaffer, Professor of History of Science at the University of Cambridge and Fellow of Darwin College; Patricia Fara, Senior Tutor at Clare College, University of Cambridge; and Jackie Stedall, Departmental Lecturer in History of Mathematics at the University of Oxford.

Melvyn Bragg and guests Martin Brasier, Richard Corfield and Rachel Wood discuss the Ediacara Biota, the Precambrian life forms which vanished 542 million years ago, and whose discovery proved Darwin right in a way he never imagined. Darwin was convinced that there must have been life before the Cambrian era, but he didn't think it was possible for fossils like the Ediacara to have been preserved. These sea-bed organisms were first unearthed in the 19th century, but were only recognised as Precambrian in the mid-20th century. This was an astonishing discovery. Ever since, scientists have been working to determine its significance. Were the Ediacara the earliest forms of animal life? Or were they a Darwinian dead end? Either way, it is argued, they reveal some of the secrets of the workings of evolution. Richard Corfield is Senior Lecturer in Earth Sciences at the Open University; Martin Brasier is Professor of Palaeobiology at the University of Oxford; Rachel Wood is Lecturer in Carbonate Geoscience at the University of Edinburgh.

Melvyn Bragg discusses Logical Positivism, the eye-wateringly radical early 20th century philosophical movement. The Logical Positivists argued that much previous philosophy was built on very shaky foundations, and they wanted to go right back to the drawing board. They insisted that philosophy - and science - had to be much more rigorous before it started making grand claims about the world. The movement began with the Vienna Circle, a group of philosophically-trained scientists and scientifically-trained philosophers, who met on Thursdays, in 'Red Vienna', in the years after the First World War. They were trying to remould philosophy in a world turned upside down not just by war, but by major advances in science. Their hero was not Descartes or Hegel but Albert Einstein. The group's new doctrine rejected great swathes of earlier philosophy, from meditations on the existence of God to declarations on the nature of History, as utterly meaningless. When the Nazis took power, they fled to England and America, where their ideas put down new roots, and went on to have a profound impact.Melvyn is joined by Barry Smith, Professor of Philosophy at the University of London; Nancy Cartwright, Professor of Philosophy at the London School of Economics; and Thomas Uebel, Professor of Philosophy at Manchester University.