Melvyn Bragg and guests discuss mysterious phenomena called Gravitational Waves in contemporary physics. The rather un-poetically named star SN 2006gy is roughly 150 times the size of our sun. Last week it went supernova, creating the brightest stellar explosion ever recorded. But among the vast swathes of dust, gas and visible matter ejected into space, perhaps the most significant consequences were invisible – emanating out from the star like the ripples from a pebble thrown into a pond. They are called Gravitational Waves, predicted by Einstein and much discussed since, their existence has never actually been proved but now scientists may be on the verge of measuring them directly. To do so would give us a whole new way of seeing the cosmos. But what are gravitational waves, why are scientists trying to measure them and, if they succeed, what would a gravitational picture of the universe look like?With Jim Al-Khalili, Professor of Physics at the University of Surrey; Carolin Crawford, Royal Society Research Fellow at the Institute of Astronomy, Cambridge; Sheila Rowan, Professor in Experimental Physics in the Department of Physics and Astronomy at the University of Glasgow

Melvyn Bragg and guests discuss symmetry. Found in Nature - from snowflakes to butterflies - and in art in the music of Bach and the poems of Pushkin, symmetry is both aesthetically pleasing and an essential tool to understanding our physical world. The Greek philosopher Aristotle described symmetry as one of the greatest forms of beauty to be found in the mathematical sciences, while the French poet Paul Valery went further, declaring; “The universe is built on a plan, the profound symmetry of which is somehow present in the inner structure of our intellect”.The story of symmetry tracks an extraordinary shift from its role as an aesthetic model - found in the tiles in the Alhambra and Bach's compositions - to becoming a key tool to understanding how the physical world works. It provides a major breakthrough in mathematics with the development of group theory in the 19th century. And it is the unexpected breakdown of symmetry at sub-atomic level that is so tantalising for contemporary quantum physicists.So why is symmetry so prevalent and appealing in both art and nature? How does symmetry enable us to grapple with monstrous numbers? And how might symmetry contribute to the elusive Theory of Everything?With Fay Dowker, Reader in Theoretical Physics at Imperial College, London; Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Ian Stewart, Professor of Mathematics at the University of Warwick.

Melvyn Bragg and guests discuss the history of anaesthetics, from laughing gas in the 1790s to the discovery of “blessed chloroform”. Remembering his unsuccessful stint at Edinburgh Medical school Charles Darwin described the horrors of surgery before anaesthetics : "I attended the operating theatre and saw two very bad operations... but I rushed away before they were completed. Nor did I ever attend again, for hardly any inducement would have been strong enough to make me do so; this being long before the blessed days of chloroform. The two cases fairly haunted me for many a long year."The suffering Darwin witnessed is almost unimaginable. In the 19th Century, a simple fracture often led to amputation carried out on a conscious patient, whose senses would be dulled only by brandy or perhaps some morphine. Many patients died of shock.The properties of gases like nitrous oxide or “laughing gas” held out hope. The chemist Humphrey Davy in the 1790s described it as “highly pleasurable, thrilling”. He also noticed his toothache disappeared. But he failed to apply his observations and it wasn't until the 1840s that there was a major breakthrough in anaesthetics, when an enterprising dentist in Boston managed to anaesthetize a patient with ether. It became known as the “Yankee Dodge”. Ether had its drawbacks and the search for a suitable alternative continued until chloroform was tried in 1847, winning many admirers including Queen Victoria, the first English royal to use it. So why did it take so long for inhaled gases to advance from providing merely recreational highs to providing an essential tool of humane surgery? What role did the development of the atomic bomb play in the development of anaesthetics? And how have society's changing attitudes to pain informed the debate?With David Wilkinson, Consultant Anaesthetist at St Bartholomew’s Hospital in London and President of the History of Anaesthesia Society; Stephanie Snow, Research Associate at the Centre for the History of Science, Technology & Medicine at the University of Manchester; Anne Hardy, Professor in the History of Modern Medicine at University College London

Melvyn Bragg and guests discuss the history of microbiology. We have more microbes in our bodies than we have human cells. We fear them as the cause of disease, yet are reliant on them for processes as diverse as water purification, pharmaceuticals, bread-making and brewing. In the future, we may look to them to save the planet from environmental hazards as scientists exploit their ability to clean up pollution. For microbes are the great recyclers on the earth, processing everything – plants, animals and us. Without microbes life would grind to a halt. How did we first discover these invisible masters of the universe? The development of microscopes in the 17th Century played a key part, but for a while science seemed stuck in this purely observational role. It is only when Louis Pasteur and Robert Koch began to manipulate microbes in the lab two hundred years later that stunning advances were made. These breakthroughs led to an understanding of how microbes transform matter, spread disease and also prevent it with the development of antibiotics and vaccines.With John Dupré, Professor of Philosophy of Science at Exeter University; Anne Glover, Professor of Molecular and Cell Biology at Aberdeen University; and Andrew Mendelsohn, Senior Lecturer in the History of Science and Medicine at Imperial College, University of London

Melvyn Bragg and guests discuss the history of optics. From telescopes to microscopes, from star-gazing to the intimacies of a magnified flea. As Galileo turned his telescope to the heavens in the early 1600s, Kepler began to formulate a theory of optics. The new and improving instruments went hand in hand with radical new ideas about how we see and what we see. Spectacles allowed scholars to study long into the evening (and into old age), while giant telescopes, up to 100 feet long, led to the discovery of planets and attempts to map the universe. The craze for optical trickery swept Europe with enthusiastic amateurs often providing valuable discoveries. But this new view of the world through a lens raised questions too – how much can you rely on the senses, on what you see? The further into space you can spy, the larger and more unmanageable the universe becomes. At the same time, the microscope was utterly transforming the world close at hand.So how did these developments inform ideas of knowledge? If new methods of scientific observation support an empirical approach, what does this mean for divine, innate reason?With Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge; Jim Bennett, Director of the Museum of the History of Science and Fellow of Linacre College at the University of Oxford; Emily Winterburn, Curator of Astronomy at the National Maritime Museum

Melvyn Bragg and guests discuss one of the most important philosophers of the 20th century, Karl Popper whose ideas about science and politics robustly challenged the accepted ideas of the day. He strongly resisted the prevailing empiricist consensus that scientists' theories could be proved true.Popper wrote: “The more we learn about the world and the deeper our learning, the more conscious, specific and articulate will be our knowledge of what we do not know, our knowledge of our ignorance”. He believed that even when a scientific principle had been successfully and repeatedly tested, it was not necessarily true. Instead it had simply not proved false, yet! This became known as the theory of falsification.He called for a clear demarcation between good science, in which theories are constantly challenged, and what he called “pseudo sciences” which couldn't be tested. His debunking of such ideologies led some to describe him as the “murderer of Freud and Marx”. He went on to apply his ideas to politics, advocating an Open Society. His ideas influenced a wide range of politicians, from those close to Margaret Thatcher, to thinkers in the Eastern Communist bloc and South America.So how did Karl Popper change our approach to the philosophy of science? How have scientists and philosophers made use of his ideas? And how are his theories viewed today? Are we any closer to proving scientific principles are “true”?With John Worrall, Professor of Philosophy of Science at the London School of Economics; Anthony O'Hear, Weston Professor of Philosophy at Buckingham University; Nancy Cartwright, Professor of Philosophy at the LSE and the University of California

Melvyn Bragg and guests discuss the Greek mathematician Archimedes. Reputed to have shouted “Eureka!” as he leapt from his bath having discovered the principles of floating bodies. Whatever the truth of the myths surrounding the man, he was certainly one of the world’s great mathematicians. The practical application of his work in pulleys and levers created formidable weapons such as catapults and ship tilting systems, allowing his home city in Sicily to defend itself against the Romans. “Give me a place to stand and I will move the earth”, he declared.But despite these triumphs, his true love remained maths for maths sake. Plutarch writes: “He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.” His most important breakthroughs came in the field of geometry with his work on the areas and volumes of curved objects.So how did this Greek mathematician in the third century BC arrive at a calculation of Pi? Did he really create a Death Ray to fight off invading ships? And what does a recently discovered manuscript reveal about his methods?With Jackie Stedall, Junior Research Fellow in the History of Mathematics at Queen's College, Oxford; Serafina Cuomo, Reader in the History of Science at Imperial College London; George Phillips, Honorary Reader in Mathematics at St Andrews University

Melvyn Bragg and guests discuss the Jesuits, a Catholic religious order of priests who became known as “the school masters of Europe”. Founded in the 16th century by the soldier Ignatius Loyola, they became a major force throughout the world, from China to South America. “Give us a boy and we will return you a man, a citizen of his country and a child of God”, they declared. By the 17th century there were more than 500 schools established across Europe. Their ideas about a standardised curriculum and teaching became the basis for many education systems today.They were also among the greatest patrons of art in early modern Europe, using murals and theatre to get their message across. To their enemies they were a sinister collective whose influence reached into the courts of kings. Their wealth and their adaptability to local customs abroad provoked suspicion, prompting their eventual suppression in the late 18th century. They were re-established in 1814 and now have more than twenty thousand members.So why was education so important to the Jesuit movement? How much influence did they really have in the courts and colonies of Europe? And were they really at the heart of conspiracies to murder kings?With Nigel Aston, Reader in Early Modern History at the University of Leicester; Simon Ditchfield, Reader in History at the University of York; Dame Olwen Hufton, Emeritus Fellow of Merton College, Oxford.

Melvyn Bragg and guests discuss the planet Mars. Named after the Roman god of war, Mars has been a source of continual fascination. It is one of our nearest neighbours in space, though it takes about a year to get there. It is very inhospitable with high winds racing across extremely cold deserts. But it is spectacular, with the highest volcano in the solar system and a giant chasm that dwarfs the Grand Canyon.For centuries there has been fierce debate about whether there is life on Mars and from the 19th century it was even thought there might be a system of canals on the planet. This insatiable curiosity has been fuelled by writers like HG Wells and CS Lewis and countless sci-fi films about little green men.So what do we know about Mars – its conditions, now and in the past? What is the evidence that there might be water and thus life on Mars? And when might we expect man to walk on its surface?With John Zarnecki, Professor of Space Science at the Open University and a team leader on the ExoMars mission; Colin Pillinger, Professor of Planetary Sciences at the Open University and leader of the Beagle 2 expedition to Mars; Monica Grady, Professor of Planetary and Space Sciences at the Open University and an expert on Martian meteorites.

Melvyn Bragg and guests discuss the contribution Indian mathematicians have made to our understanding of the subject. Mathematics from the Indian subcontinent has provided foundations for much of our modern thinking on the subject. They were thought to be the first to use zero as a number. Our modern numerals have their roots there too. And mathematicians in the area that is now India, Pakistan and Bangladesh were grappling with concepts such as infinity centuries before Europe got to grips with it. There’s even a suggestion that Indian mathematicians discovered Pythagoras’ theorem before Pythagoras. Some of these advances have their basis in early religious texts which describe the geometry necessary for building falcon-shaped altars of precise dimensions. Astronomical calculations used to decide the dates of religious festivals also encouraged these mathematical developments. So how were these advances passed on to the rest of the world? And why was the contribution of mathematicians from this area ignored by Europe for centuries?With George Gheverghese Joseph, Honorary Reader in Mathematics Education at Manchester University; Colva Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews; Dennis Almeida, Lecturer in Mathematics Education at Exeter University and the Open University.