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

Melvyn Bragg and guests discuss the voyage of HMS Challenger which set out from Portsmouth in 1872 with a mission a to explore the ocean depths around the world and search for new life. The scale of the enterprise was breath taking and, for its ambition, it has since been compared to the Apollo missions. The team onboard found thousands of new species, proved there was life on the deepest seabeds and plumbed the Mariana Trench five miles below the surface. Thanks to telegraphy and mailboats, its vast discoveries were shared around the world even while Challenger was at sea, and they are still being studied today, offering insights into the ever-changing oceans that cover so much of the globe and into the health of our planet. The image above is from the journal of Pelham Aldrich R.N. who served on the Challenger Surveying Expedition from 1872-5. With Erika Jones Curator of Navigation and Oceanography at Royal Museums Greenwich Sam Robinson Southampton Marine and Maritime Institute Research Fellow at the University of Southampton And Giles Miller Principal Curator of Micropalaeontology at the Natural History Museum London Producer: Simon Tillotson

Melvyn Bragg and guests discuss one of the greatest changes in the history of life on Earth. Around 400 million years ago some of our ancestors, the fish, started to become a little more like humans. At the swampy margins between land and water, some fish were turning their fins into limbs, their swim bladders into lungs and developed necks and eventually they became tetrapods, the group to which we and all animals with backbones and limbs belong. After millions of years of this transition, these tetrapod descendants of fish were now ready to leave the water for a new life of walking on land, and with that came an explosion in the diversity of life on Earth. The image above is a representation of Tiktaalik Roseae, a fish with some features of a tetrapod but not one yet, based on a fossil collected in the Canadian Arctic. With Emily Rayfield Professor of Palaeobiology at the University of Bristol Michael Coates Chair and Professor of Organismal Biology and Anatomy at the University of Chicago And Steve Brusatte Professor of Palaeontology and Evolution at the University of Edinburgh Producer: Simon Tillotson

Melvyn Bragg and guests discuss an atomic particle that's become inseparable from modernity. JJ Thomson discovered the electron 125 years ago, so revealing that atoms, supposedly the smallest things, were made of even smaller things. He pictured them inside an atomic ball like a plum pudding, with others later identifying their place outside the nucleus - and it is their location on the outer limit that has helped scientists learn so much about electrons and with electrons. We can use electrons to reveal the secrets of other particles and, while electricity exists whether we understand electrons or not, the applications of electricity and electrons grow as our knowledge grows. Many questions, though, remain unanswered. With Victoria Martin Professor of Collider Physics at the University of Edinburgh Harry Cliff Research Fellow in Particle Physics at the University of Cambridge And Frank Close Professor Emeritus of Theoretical Physics and Fellow Emeritus at Exeter College at the University of Oxford Producer: Simon Tillotson

Melvyn Bragg and guests discuss the abrupt transformation of stars after shining brightly for millions or billions of years, once they lack the fuel to counter the force of gravity. Those like our own star, the Sun, become red giants, expanding outwards and consuming nearby planets, only to collapse into dense white dwarves. The massive stars, up to fifty times the mass of the Sun, burst into supernovas, visible from Earth in daytime, and become incredibly dense neutron stars or black holes. In these moments of collapse, the intense heat and pressure can create all the known elements to form gases and dust which may eventually combine to form new stars, new planets and, as on Earth, new life. The image above is of the supernova remnant Cassiopeia A, approximately 10,000 light years away, from a once massive star that died in a supernova explosion that was first seen from Earth in 1690 With Martin Rees Astronomer Royal, Fellow of Trinity College, Cambridge Carolin Crawford Emeritus Member of the Institute of Astronomy and Emeritus Fellow of Emmanuel College, University of Cambridge And Mark Sullivan Professor of Astrophysics at the University of Southampton Producer: Simon Tillotson

Melvyn Bragg and guests discuss one of our ancestors, Homo erectus, who thrived on Earth for around two million years whereas we, Homo sapiens, emerged only in the last three hundred thousand years. Homo erectus, or Upright Man, spread from Africa to Asia and it was on the Island of Java that fossilised remains were found in 1891 in an expedition led by Dutch scientist Eugène Dubois. Homo erectus people adapted to different habitats, ate varied food, lived in groups, had stamina to outrun their prey; and discoveries have prompted many theories on the relationship between their diet and the size of their brains, on their ability as seafarers, on their creativity and on their ability to speak and otherwise communicate. The image above is from a diorama at the Moesgaard Museum in Denmark, depicting the Turkana Boy referred to in the programme. With Peter Kjærgaard Director of the Natural History Museum of Denmark and Professor of Evolutionary History at the University of Copenhagen José Joordens Senior Researcher in Human Evolution at Naturalis Biodiversity Centre and Professor of Human Evolution at Maastricht University And Mark Maslin Professor of Earth System Science at University College London Producer: Simon Tillotson

Melvyn Bragg and guests discuss the study of earthquakes. A massive earthquake in 1755 devastated Lisbon, and this disaster helped inspire a new science of seismology which intensified after San Francisco in 1906 and advanced even further with the need to monitor nuclear tests around the world from 1945 onwards. While we now know so much more about what lies beneath the surface of the Earth, and how rocks move and crack, it remains impossible to predict when earthquakes will happen. Thanks to seismology, though, we have a clearer idea of where earthquakes will happen and how to make some of them less hazardous to lives and homes. With Rebecca Bell Senior lecturer in Geology and Geophysics at Imperial College London Zoe Mildon Lecturer in Earth Sciences and Future Leaders Fellow at the University of Plymouth And James Hammond Reader in Geophysics at Birkbeck, University of London Producer: Simon Tillotson

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Melvyn Bragg and guests discuss William Herschel (1738 – 1822) and his sister Caroline Herschel (1750 – 1848) who were born in Hanover and made their reputation in Britain. William was one of the most eminent astronomers in British history. Although he started life as a musician, as a young man he became interested in studying the night sky. With an extraordinary talent, he constructed telescopes that were able to see further and more clearly than any others at the time. He is most celebrated today for discovering the planet Uranus and detecting what came to be known as infrared radiation. Caroline also became a distinguished astronomer, discovering several comets and collaborating with her brother. With Monica Grady Professor of Planetary and Space Sciences at the Open University Carolin Crawford Institute of Astronomy, Cambridge and an Emeritus Fellow of Emmanuel College, University of Cambridge And Jim Bennett Keeper Emeritus at the Science Museum in London. Studio producer: John Goudie

Melvyn Bragg and guests discuss the simple animals which informed Charles Darwin's first book, The Structure and Distribution of Coral Reefs, published in 1842. From corals, Darwin concluded that the Earth changed very slowly and was not fashioned by God. Now coral reefs, which some liken to undersea rainforests, are threatened by human activity, including fishing, pollution and climate change. With Steve Jones Senior Research Fellow in Genetics at University College London Nicola Foster Lecturer in Marine Biology at the University of Plymouth And Gareth Williams Associate Professor in Marine Biology at Bangor University School of Ocean Sciences Producer Simon Tilllotson.

Melvyn Bragg and guests discuss the race to build an atom bomb in the USA during World War Two. Before the war, scientists in Germany had discovered the potential of nuclear fission and scientists in Britain soon argued that this could be used to make an atom bomb, against which there could be no defence other than to own one. The fear among the Allies was that, with its head start, Germany might develop the bomb first and, unmatched, use it on its enemies. The USA took up the challenge in a huge engineering project led by General Groves and Robert Oppenheimer and, once the first bomb had been exploded at Los Alamos in July 1945, it appeared inevitable that the next ones would be used against Japan with devastating results. The image above is of Robert Oppenheimer and General Groves examining the remains of one the bases of the steel test tower, at the atomic bomb Trinity Test site, in September 1945. With Bruce Cameron Reed The Charles A. Dana Professor of Physics Emeritus at Alma College, Michigan Cynthia Kelly Founder and President of the Atomic Heritage Foundation And Frank Close Emeritus Professor of Theoretical Physics at the University of Oxford and a Fellow of Exeter College, Oxford Producer: Simon Tillotson

Melvyn Bragg and guests discuss the remarkable diversity of the animals that dominated life on land in the Triassic, before the rise of the dinosaurs in the Jurassic, and whose descendants are often described wrongly as 'living fossils'. For tens of millions of years, the ancestors of alligators and Nile crocodiles included some as large as a bus, some running on two legs like a T Rex and some that lived like whales. They survived and rebounded from a series of extinction events but, while the range of habitats of the dinosaur descendants such as birds covers much of the globe, those of the crocodiles have contracted, even if the animals themselves continue to evolve today as quickly as they ever have. With Anjali Goswami Research Leader in Life Sciences and Dean of Postgraduate Education at the Natural History Museum Philip Mannion Lecturer in the Department of Earth Sciences at University College London And Steve Brusatte Professor of Palaeontology and Evolution at the University of Edinburgh Producer Simon Tillotson

Melvyn Bragg and guests discuss the search for Longitude while at sea. Following efforts by other maritime nations, the British Government passed the Longitude Act in 1714 to reward anyone who devised reliable means for ships to determine their longitude at sea. Mariners could already calculate how far they were north or south, the Latitude, using the Pole Star, but voyaging across the Atlantic to the Caribbean was much less predictable as navigators could not be sure how far east or west they were, a particular problem when heading for islands. It took fifty years of individual genius and collaboration in Britain and across Europe, among astronomers, clock makers, mathematicians and sailors, for the problem to be resolved. With Rebekah Higgitt Principal Curator of Science at National Museums Scotland Jim Bennett Keeper Emeritus at the Science Museum And Simon Schaffer Professor of History and Philosophy of Science at the University of Cambridge Producer: Simon Tillotson

Melvyn Bragg and guests discuss Laplace (1749-1827) who was a giant in the world of mathematics both before and after the French Revolution. He addressed one of the great questions of his age, raised but side-stepped by Newton: was the Solar System stable, or would the planets crash into the Sun, as it appeared Jupiter might, or even spin away like Saturn threatened to do? He advanced ideas on probability, long the preserve of card players, and expanded them out across science; he hypothesised why the planets rotate in the same direction; and he asked if the Universe was deterministic, so that if you knew everything about all the particles then you could predict the future. He also devised the metric system and reputedly came up with the name 'metre'. With Marcus du Sautoy Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford Timothy Gowers Professor of Mathematics at the College de France And Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews Producer: Simon Tillotson

Melvyn Bragg and guests discuss the devastating mass extinctions of the Late Devonian Period, roughly 370 million years ago, when around 70 percent of species disappeared. Scientists are still trying to establish exactly what happened, when and why, but this was not as sudden as when an asteroid hits Earth. The Devonian Period had seen the first trees and soils and it had such a diversity of sea life that it’s known as the Age of Fishes, some of them massive and armoured, and, in one of the iconic stages in evolution, some of them moving onto land for the first time. One of the most important theories for the first stage of this extinction is that the new soils washed into oceans, leading to algal blooms that left the waters without oxygen and suffocated the marine life. The image above is an abstract group of the huge, armoured Dunkleosteus fish, lost in the Late Devonian Extinction With Jessica Whiteside Associate Professor of Geochemistry in the Department of Ocean and Earth Science at the University of Southampton David Bond Professor of Geology at the University of Hull And Mike Benton Professor of Vertebrate Paleontology at the School of Life Sciences, University of Bristol.

Melvyn Bragg and guests discuss one of the outstanding French mathematicians and natural philosophers of the 18th Century, celebrated across Europe. Emilie du Châtelet, 1706-49, created a translation of Newton’s Principia from Latin into French that helped spread the light of mathematics on the emerging science, and her own book Institutions de Physique, with its lessons on physics, was welcomed as profound. She had the privileges of wealth and aristocracy, yet had to fight to be taken seriously as an intellectual in a world of ideas that was almost exclusively male. With Patricia Fara Emeritus Fellow of Clare College, Cambridge David Wootton Anniversary Professor of History at the University of York And Judith Zinsser Professor Emerita of History at Miami University of Ohio and biographer of Emilie du Châtelet. Producer: Simon Tillotson

Melvyn Bragg and guests discuss solar eclipses, some of life’s most extraordinary moments, when day becomes night and the stars come out before day returns either all too soon or not soon enough, depending on what you understand to be happening. In ancient China, for example, there was a story that a dragon was eating the sun and it had to be scared away by banging pots and pans if the sun were to return. Total lunar eclipses are more frequent and last longer, with a blood moon coloured red like a sunrise or sunset. Both events have created the chance for scientists to learn something remarkable, from the speed of light, to the width of the Atlantic, to the roundness of Earth, to discovering helium and proving Einstein’s Theory of General Relativity. With Carolin Crawford Public Astronomer based at the Institute of Astronomy, University of Cambridge and a fellow of Emmanuel College Frank Close Emeritus Professor of Physics at the University of Oxford And Lucie Green Professor of Physics and a Royal Society University Research Fellow at Mullard Space Science Laboratory at University College London Producers: Simon Tillotson and Julia Johnson

Melvyn Bragg and guests discuss Alan Turing (1912-1954) whose 1936 paper On Computable Numbers effectively founded computer science. Immediately recognised by his peers, his wider reputation has grown as our reliance on computers has grown. He was a leading figure at Bletchley Park in the Second World War, using his ideas for cracking enemy codes, work said to have shortened the war by two years and saved millions of lives. That vital work was still secret when Turing was convicted in 1952 for having a sexual relationship with another man for which he was given oestrogen for a year, or chemically castrated. Turing was to kill himself two years later. The immensity of his contribution to computing was recognised in the 1960s by the creation of the Turing Award, known as the Nobel of computer science, and he is to be the new face on the £50 note. With Leslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford Simon Schaffer Professor of the History of Science at the University of Cambridge and Fellow of Darwin College And Andrew Hodges Biographer of Turing and Emeritus Fellow of Wadham College, Oxford Producer: Simon Tillotson

In a programme first broadcast on 12 April 2018, Melvyn Bragg and guests discuss the contribution of George Stephenson (1781-1848) and his son Robert (1803-59) to the development of the railways in the 19th Century. George became known as The Father of Railways and yet arguably Robert's contribution was even greater, with his engineering work going far beyond their collaboration. Robert is credited with the main role in the design of their locomotives. George had worked on stationary colliery steam engines and, with Robert, developed the moving steam engine Locomotion No1 for the Stockton and Darlington Railway in 1825. They produced the Rocket for the Rainhill Trials on the Liverpool and Manchester Railway in 1829. From there, the success of their designs and engineering led to the expansion of railways across Britain and around the world. with Dr Michael Bailey Railway historian and editor of the most recent biography of Robert Stephenson Julia Elton Past President of the Newcomen Society for the History of Engineering and Technology and Colin Divall Professor Emeritus of Railway Studies at the University of York Producer: Simon Tillotson This programme is a repeat.

Melvyn Bragg and guests discuss the theoretical physicist Dirac (1902-1984), whose achievements far exceed his general fame. To his peers, he was ranked with Einstein and, when he moved to America in his retirement, he was welcomed as if he were Shakespeare. Born in Bristol, he trained as an engineer before developing theories in his twenties that changed the understanding of quantum mechanics, bringing him a Nobel Prize in 1933 which he shared with Erwin Schrödinger. He continued to make deep contributions, bringing abstract maths to physics, beyond predicting anti-particles as he did in his Dirac Equation. With Graham Farmelo Biographer of Dirac and Fellow at Churchill College, Cambridge Valerie Gibson Professor of High Energy Physics at the University of Cambridge and Fellow of Trinity College And David Berman Professor of Theoretical Physics at Queen Mary University of London Producer: Simon Tillotson

Melvyn Bragg and guests discuss the origins of horses, from their dog sized ancestors to their proliferation in the New World until hunted to extinction, their domestication in Asia and their development since. The genetics of the modern horse are the most studied of any animal, after humans, yet it is still uncertain why they only have one toe on each foot when their wider family had more, or whether speed or stamina has been more important in their evolution. What is clear, though, is that when humans first chose to ride horses, as well as eat them, the future of both species changed immeasurably. With Alan Outram Professor of Archaeological Science at the University of Exeter Christine Janis Honorary Professor in Palaeobiology at the University of Bristol and Professor Emerita in Ecology and Evolutionary Biology at Brown University And John Hutchinson Professor in Evolutionary Biomechanics at the Royal Veterinary College Producer: Simon Tillotson

Melvyn Bragg and guests discuss the flow of particles from the outer region of the Sun which we observe in the Northern and Southern Lights, interacting with Earth's magnetosphere, and in comet tails that stream away from the Sun regardless of their own direction. One way of defining the boundary of the solar system is where the pressure from the solar wind is balanced by that from the region between the stars, the interstellar medium. Its existence was suggested from the C19th and Eugene Parker developed the theory of it in the 1950s and it has been examined and tested by a series of probes in C20th up to today, with more planned. With Andrew Coates Professor of Physics and Deputy Director in charge of the Solar System at the Mullard Space Science Laboratory, University College London Helen Mason OBE Reader in Solar Physics at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Fellow at St Edmund's College And Tim Horbury Professor of Physics at Imperial College London Producer: Simon Tillotson

Melvyn Bragg and guests discuss what happens when parents from different species have offspring, despite their genetic differences. In some cases, such as the zebra/donkey hybrid in the image above, the offspring are usually infertile but in others the genetic change can lead to new species with evolutionary advantages. Hybrids can occur naturally, yet most arise from human manipulation and Darwin's study of plant and animal domestication informed his ideas on natural selection. With Sandra Knapp Tropical Botanist at the Natural History Museum Nicola Nadeau Lecturer in Evolutionary Biology at the University of Sheffield And Steve Jones Senior Research Fellow in Genetics at University College London Producer: Simon Tillotson

Melvyn Bragg and guests discuss the work and ideas of Dorothy Crowfoot Hodgkin (1910-1994), awarded the Nobel Prize in Chemistry in 1964 for revealing the structures of vitamin B12 and penicillin and who later determined the structure of insulin. She was one of the pioneers of X-ray crystallography and described by a colleague as 'a crystallographers' crystallographer'. She remains the only British woman to have won a Nobel in science, yet rejected the idea that she was a role model for other women, or that her career was held back because she was a woman. She was also the first woman since Florence Nightingale to receive the Order of Merit, and was given the Lenin Peace Prize in recognition of her efforts to bring together scientists from the East and West in pursuit of nuclear disarmament. With Georgina Ferry Science writer and biographer of Dorothy Hodgkin Judith Howard Professor of Chemistry at Durham University and Patricia Fara Fellow of Clare College, Cambridge Producer: Simon Tillotson

Melvyn Bragg and guests discuss how scientists sought to understand the properties of gases and the relationship between pressure and volume, and what that search unlocked. Newton theorised that there were static particles in gases that pushed against each other all the harder when volume decreased, hence the increase in pressure. Those who argued that molecules moved, and hit each other, were discredited until James Maxwell and Ludwig Boltzmann used statistics to support this kinetic theory. Ideas about atoms developed in tandem with this, and it came as a surprise to scientists in C20th that the molecules underpinning the theory actually existed and were not simply thought experiments. The image above is of Ludwig Boltzmann from a lithograph by Rudolf Fenzl, 1898 With Steven Bramwell Professor of Physics at University College London Isobel Falconer Reader in History of Mathematics at the University of St Andrews and Ted Forgan Emeritus Professor of Physics at the University of Birmingham Producer: Simon Tillotson

Melvyn Bragg and guests discuss theories about the origins of teeth in vertebrates, and what we can learn from sharks in particular and their ancestors. Great white sharks can produce up to 100,000 teeth in their lifetimes. For humans, it is closer to a mere 50 and most of those have to last from childhood. Looking back half a billion years, though, the ancestors of sharks and humans had no teeth in their mouths at all, nor jaws. They were armoured fish, sucking in their food. The theory is that either their tooth-like scales began to appear in mouths as teeth, or some of their taste buds became harder. If we knew more about that, and why sharks can regenerate their teeth, then we might learn how humans could grow new teeth in later lives. With Gareth Fraser Assistant Professor in Biology at the University of Florida Zerina Johanson Merit Researcher in the Department of Earth Sciences at the Natural History Museum and Philip Donoghue Professor of Palaeobiology at the University of Bristol Producer: Simon Tillotson

Melvyn Bragg and guests discuss how members of the same species send each other invisible chemical signals to influence the way they behave. Pheromones are used by species across the animal kingdom in a variety of ways, such as laying trails to be followed, to raise the alarm, to scatter from predators, to signal dominance and to enhance attractiveness and, in honey bees, even direct development into queen or worker. The image above is of male and female ladybirds that have clustered together in response to pheromones. With Tristram Wyatt Senior Research Fellow at the Department of Zoology at the University of Oxford Jane Hurst William Prescott Professor of Animal Science at the University of Liverpool and Francis Ratnieks Professor of Apiculture and Head of the Laboratory of Apiculture and Social Insects at the University of Sussex Producer: Simon Tillotson

Melvyn Bragg and guests discuss the remarkable achievement of Aristotle (384-322BC) in the realm of biological investigation, for which he has been called the originator of the scientific study of life. Known mainly as a philosopher and the tutor for Alexander the Great, who reportedly sent him animal specimens from his conquests, Aristotle examined a wide range of life forms while by the Sea of Marmara and then on the island of Lesbos. Some ideas, such as the the spontaneous generation of flies, did not survive later scrutiny, yet his influence was extraordinary and his work was unequalled until the early modern period. The image above is of the egg and embryo of a dogfish, one of the animals Aristotle described accurately as he recorded their development. With Armand Leroi Professor of Evolutionary Development Biology at Imperial College London Myrto Hatzimichali Lecturer in Classics at the University of Cambridge And Sophia Connell Lecturer in Philosophy at Birkbeck, University of London Producer: Simon Tillotson

Melvyn Bragg and guests discuss the ideas and life of one of the greatest mathematicians of the 20th century, Emmy Noether. Noether’s Theorem is regarded as one of the most important mathematical theorems, influencing the evolution of modern physics. Born in 1882 in Bavaria, Noether studied mathematics at a time when women were generally denied the chance to pursue academic careers and, to get round objections, she spent four years lecturing under a male colleague’s name. In the 1930s she faced further objections to her teaching, as she was Jewish, and she left for the USA when the Nazis came to power. Her innovative ideas were to become widely recognised and she is now considered to be one of the founders of modern algebra. With Colva Roney Dougal Professor of Pure Mathematics at the University of St Andrews David Berman Professor in Theoretical Physics at Queen Mary, University of London Elizabeth Mansfield Professor of Mathematics at the University of Kent Producer: Simon Tillotson

Melvyn Bragg and guests discuss the planet Venus which is both the morning star and the evening star, rotates backwards at walking speed and has a day which is longer than its year. It has long been called Earth’s twin, yet the differences are more striking than the similarities. Once imagined covered with steaming jungles and oceans, we now know the surface of Venus is 450 degrees celsius, and the pressure there is 90 times greater than on Earth, enough to crush an astronaut. The more we learn of it, though, the more we learn of our own planet, such as whether Earth could become more like Venus in some ways, over time. With Carolin Crawford Public Astronomer at the Institute of Astronomy and Fellow of Emmanuel College, University of Cambridge Colin Wilson Senior Research Fellow in Planetary Science at the University of Oxford And Andrew Coates Professor of Physics at Mullard Space Science Laboratory, University College London Produced by: Simon Tillotson and Julia Johnson

Melvyn Bragg and guests discuss the properties of atoms or molecules with a single unpaired electron, which tend to be more reactive, keen to seize an electron to make it a pair. In the atmosphere, they are linked to reactions such as rusting. Free radicals came to prominence in the 1950s with the discovery that radiation poisoning operates through free radicals, as it splits water molecules and produces a very reactive hydroxyl radical which damages DNA and other molecules in the cell. There is also an argument that free radicals are a byproduct of normal respiration and over time they cause an accumulation of damage that is effectively the process of ageing. For all their negative associations, free radicals play an important role in signalling and are also linked with driving cell division, both cancer and normal cell division, even if they tend to become damaging when there are too many of them. With Nick Lane Professor of Evolutionary Biochemistry at University College London Anna Croft Associate Professor at the Department of Chemical and Environmental Engineering at the University of Nottingham And Mike Murphy Professor of Mitochondrial Redox Biology at Cambridge University Producer: Simon Tillotson

Melvyn Bragg and guests discuss the history of real and imagined machines that appear to be living, and the questions they raise about life and creation. Even in myth they are made by humans, not born. The classical Greeks built some and designed others, but the knowledge of how to make automata and the principles behind them was lost in the Latin Christian West, remaining in the Greek-speaking and Arabic-speaking world. Western travellers to those regions struggled to explain what they saw, attributing magical powers. The advance of clockwork raised further questions about what was distinctly human, prompting Hobbes to argue that humans were sophisticated machines, an argument explored in the Enlightenment and beyond. The image above is Jacques de Vaucanson's mechanical duck (1739), which picked up grain, digested and expelled it. If it looks like a duck... with Simon Schaffer Professor of History of Science at Cambridge University Elly Truitt Associate Professor of Medieval History at Bryn Mawr College And Franziska Kohlt Doctoral Researcher in English Literature and the History of Science at the University of Oxford Producer: Simon Tillotson

Melvyn Bragg and guests discuss how some bats, dolphins and other animals emit sounds at high frequencies to explore their environments, rather than sight. This was such an unlikely possibility, to natural historians from C18th onwards, that discoveries were met with disbelief even into the C20th; it was assumed that bats found their way in the dark by touch. Not all bats use echolocation, but those that do have a range of frequencies for different purposes and techniques for preventing themselves becoming deafened by their own sounds. Some prey have evolved ways of detecting when bats are emitting high frequencies in their direction, and some fish have adapted to detect the sounds dolphins use to find them. With Kate Jones Professor of Ecology and Biodiversity at University College London Gareth Jones Professor of Biological Sciences at the University of Bristol And Dean Waters Lecturer in the Environment Department at the University of York Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the discovery and growing understanding of the Proton, formed from three quarks close to the Big Bang and found in the nuclei of all elements. The positive charges they emit means they attract the fundamental particles of negatively charged electrons, an attraction that leads to the creation of atoms which in turn leads to chemistry, biology and life itself. The Sun (in common with other stars) is a fusion engine that turn protons by a series of processes into helium, emitting energy in the process, with about half of the Sun's protons captured so far. Hydrogen atoms, stripped of electrons, are single protons which can be accelerated to smash other nuclei and have applications in proton therapy. Many questions remain, such as why are electrical charges for protons and electrons so perfectly balanced? With Frank Close Professor Emeritus of Physics at the University of Oxford Helen Heath Reader in Physics at the University of Bristol And Simon Jolly Lecturer in High Energy Physics at University College London Producer: Simon Tillotson.

In a programme first broadcast on April 12th 2018, Melvyn Bragg and guests discuss the contribution of George Stephenson (1781-1848) and his son Robert (1803-59) to the development of the railways in C19th. George became known as The Father of Railways and yet arguably Robert's contribution was even greater, with his engineering work going far beyond their collaboration. Robert is credited with the main role in the design of their locomotives. George had worked on stationary colliery steam engines and, with Robert, developed the moving steam engine Locomotion No1 for the Stockton and Darlington Railway in 1825. They produced the Rocket for the Rainhill Trials on the Liverpool and Manchester Railway in 1829. From there, the success of their designs and engineering led to the expansion of railways across Britain and around the world. with Dr Michael Bailey Railway historian and editor of the most recent biography of Robert Stephenson Julia Elton Past President of the Newcomen Society for the History of Engineering and Technology and Colin Divall Professor Emeritus of Railway Studies at the University of York Producer: Simon Tillotson. This programme is a repeat

Melvyn Bragg and guests discuss the pioneering scientist Rosalind Franklin (1920 - 1958). During her distinguished career, Franklin carried out ground-breaking research into coal and viruses but she is perhaps best remembered for her investigations in the field of DNA. In 1952 her research generated a famous image that became known as Photograph 51. When the Cambridge scientists Francis Crick and James Watson saw this image, it enabled them the following year to work out that DNA has a double-helix structure, one of the most important discoveries of modern science. Watson, Crick and Franklin's colleague Maurice Wilkins received a Nobel Prize in 1962 for this achievement but Franklin did not and today many people believe that Franklin has not received enough recognition for her work. With: Patricia Fara President of the British Society for the History of Science Jim Naismith Interim lead of the Rosalind Franklin Institute, Director of the Research Complex at Harwell and Professor at the University of Oxford Judith Howard Professor of Chemistry at Durham University Producer: Victoria Brignell.

Melvyn Bragg and guests discuss fungi. These organisms are not plants or animals but a kingdom of their own. Millions of species of fungi live on the Earth and they play a crucial role in ecosystems, enabling plants to obtain nutrients and causing material to decay. Without fungi, life as we know it simply would not exist. They are also a significant part of our daily life, making possible the production of bread, wine and certain antibiotics. Although fungi brought about the colonisation of the planet by plants about 450 million years ago, some species can kill humans and devastate trees. With: Lynne Boddy Professor of Fungal Ecology at Cardiff University Sarah Gurr Professor of Food Security in the Biosciences Department at the University of Exeter David Johnson N8 Chair in Microbial Ecology at the University of Manchester Producer: Victoria Brignell.

The octopus, the squid, the nautilus and the cuttlefish are some of the most extraordinary creatures on this planet, intelligent and yet apparently unlike other life forms. They are cephalopods and are part of the mollusc family like snails and clams, and they have some characteristics in common with those. What sets them apart is the way members of their group can change colour, camouflage themselves, recognise people, solve problems, squirt ink, power themselves with jet propulsion and survive both on land, briefly, and in the deepest, coldest oceans. And, without bones or shells, they grow so rapidly they can outstrip their rivals when habitats change, making them the great survivors and adaptors of the animal world. With Louise Allcock Lecturer in Zoology at the National University of Ireland, Galway Paul Rodhouse Emeritus Fellow of the British Antarctic Survey and Jonathan Ablett Senior Curator of Molluscs at the Natural History Museum Producer: Simon Tillotson.

In a programme first broadcast in 2017, Melvyn Bragg and guests discuss Gauss (1777-1855), widely viewed as one of the greatest mathematicians of all time. He was a child prodigy, correcting his father's accounts before he was 3, dumbfounding his teachers with the speed of his mental arithmetic, and gaining a wealthy patron who supported his education. He wrote on number theory when he was 21, with his Disquisitiones Arithmeticae, which has influenced developments since. Among his achievements, he was the first to work out how to make a 17-sided polygon, he predicted the orbit of the minor planet Ceres, rediscovering it, he found a way of sending signals along a wire, using electromagnetism, the first electromagnetic telegraph, and he advanced the understanding of parallel lines on curved surfaces. With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews And Nick Evans Professor of Theoretical Physics at the University of Southampton Producer: Simon Tillotson.

In a programme first broadcast in 2017, Melvyn Bragg and guests discuss the development of theories about dinosaur feathers, following discoveries of fossils which show evidence of feathers. All dinosaurs were originally thought to be related to lizards - the word 'dinosaur' was created from the Greek for 'terrible lizard' - but that now appears false. In the last century, discoveries of fossils with feathers established that at least some dinosaurs were feathered and that some of those survived the great extinctions and evolved into the birds we see today. There are still many outstanding areas for study, such as what sorts of feathers they were, where on the body they were found, what their purpose was and which dinosaurs had them. With Mike Benton Professor of Vertebrate Palaeontology at the University of Bristol Steve Brusatte Reader and Chancellor's Fellow in Vertebrate Palaeontology at the University of Edinburgh and Maria McNamara Senior Lecturer in Geology at University College, Cork Producer: Simon Tillotson.

In a programme first broadcast in 2017, Melvyn Bragg and guests discuss why some birds migrate and others do not, how they select their destinations and how they navigate the great distances, often over oceans. For millennia, humans set their calendars to birds' annual arrivals, and speculated about what happened when they departed, perhaps moving deep under water, or turning into fish or shellfish, or hibernating while clinging to trees upside down. Ideas about migration developed in C19th when, in Germany, a stork was noticed with an African spear in its neck, indicating where it had been over the winter and how far it had flown. Today there are many ideas about how birds use their senses of sight and smell, and magnetic fields, to find their way, and about why and how birds choose their destinations and many questions. Why do some scatter and some flock together, how much is instinctive and how much is learned, and how far do the benefits the migrating birds gain outweigh the risks they face? With Barbara Helm Reader at the Institute of Biodiversity, Animal Health and Comparative Medicine at the University of Glasgow Tim Guilford Professor of Animal Behaviour and Tutorial Fellow of Zoology at Merton College, Oxford and Richard Holland Senior Lecturer in Animal Cognition at Bangor University Producer: Simon Tillotson.

Melvyn Bragg and guests discuss enzymes, the proteins that control the speed of chemical reactions in living organisms. Without enzymes, these reactions would take place too slowly to keep organisms alive: with their actions as catalysts, changes which might otherwise take millions of years can happen hundreds of times a second. Some enzymes break down large molecules into smaller ones, like the ones in human intestines, while others use small molecules to build up larger, complex ones, such as those that make DNA. Enzymes also help keep cell growth under control, by regulating the time for cells to live and their time to die, and provide a way for cells to communicate with each other. With Nigel Richards Professor of Biological Chemistry at Cardiff University Sarah Barry Lecturer in Chemical Biology at King's College London And Jim Naismith Director of the Research Complex at Harwell Bishop Wardlaw Professor of Chemical Biology at the University of St Andrews Professor of Structural Biology at the University of Oxford Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the life and work of Louis Pasteur (1822-1895) and his extraordinary contribution to medicine and science. It is said few people have saved more lives than Pasteur. A chemist, he showed that otherwise identical molecules could exist as 'left' and 'right-handed' versions and that molecules produced by living things were always left-handed. He proposed a germ theory to replace the idea of spontaneous generation. He discovered that microorganisms cause fermentation and disease. He began the process named after him, pasteurisation, heating liquids to 50-60 C to kill microbes. He saved the beer and wine industries in France when they were struggling with microbial contamination. He saved the French silk industry when he found a way of protecting healthy silkworm eggs from disease. He developed vaccines against anthrax and rabies and helped establish immunology. Many of his ideas were developed further after his lifetime, but one of his legacies was a charitable body, the Pasteur Institute, to continue research into infectious disease. With Andrew Mendelsohn Reader in the School of History at Queen Mary, University of London Anne Hardy Honorary Professor at the Centre for History in Public Health at the London School of Hygiene and Tropical Medicine and Michael Worboys Emeritus Professor in the History of Science, Technology and Medicine at the University of Manchester Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the life and ideas of Wolfgang Pauli (1900-1958), whose Exclusion Principle is one of the key ideas in quantum mechanics. A brilliant physicist, at 21 Pauli wrote a review of Einstein's theory of general relativity and that review is still a standard work of reference today. The Pauli Exclusion Principle proposes that no two electrons in an atom can be at the same time in the same state or configuration, and it helps explain a wide range of phenomena such as the electron shell structure of atoms. Pauli went on to postulate the existence of the neutrino, which was confirmed in his lifetime. Following further development of his exclusion principle, Pauli was awarded the Nobel Prize in Physics in 1945 for his 'decisive contribution through his discovery of a new law of Nature'. He also had a long correspondence with Jung, and a reputation for accidentally breaking experimental equipment which was dubbed The Pauli Effect. With Frank Close Fellow Emeritus at Exeter College, University of Oxford Michela Massimi Professor of Philosophy of Science at the University of Edinburgh and Graham Farmelo Bye-Fellow of Churchill College, University of Cambridge Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the high temperatures that marked the end of the Paleocene and start of the Eocene periods, about 50m years ago. Over c1000 years, global temperatures rose more than 5 C on average and stayed that way for c100,000 years more, with the surface of seas in the Arctic being as warm as those in the subtropics. There were widespread extinctions, changes in ocean currents, and there was much less oxygen in the sea depths. The rise has been attributed to an increase of carbon dioxide and methane in the atmosphere, though it is not yet known conclusively what the source of those gases was. One theory is that a rise in carbon dioxide, perhaps from volcanoes, warmed up the globe enough for warm water to reach the bottom of the oceans and so release methane from frozen crystals in the sea bed. The higher the temperature rose and the longer the water was warm, the more methane was released. Scientists have been studying a range of sources from this long period, from ice samples to fossils, to try to understand more about possible causes. With Dame Jane Francis Professor of Palaeoclimatology at the British Antarctic Survey Mark Maslin Professor of Palaeoclimatology at University College London And Tracy Aze Lecturer in Marine Micropaleontology at the University of Leeds Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the Kuiper Belt, a vast region of icy objects at the fringes of our Solar System, beyond Neptune, in which we find the dwarf planet Pluto and countless objects left over from the origins of the solar system, some of which we observe as comets. It extends from where Neptune is, which is 30 times further out than the Earth is from the Sun, to about 500 times the Earth-Sun distance. It covers an immense region of space and it is the part of the Solar System that we know the least about, because it is so remote from us and has been barely detectable by Earth-based telescopes until recent decades. Its existence was predicted before it was known, and study of the Kuiper Belt, and how objects move within it, has led to a theory that there may be a 9th planet far beyond Neptune. With Carolin Crawford Public Astronomer at the Institute of Astronomy and Fellow of Emmanuel College, University of Cambridge Monica Grady Professor of Planetary and Space Sciences at the Open University And Stephen Lowry Reader in Planetary and Space Sciences, University of Kent Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the flourishing of maths in the early Islamic world, as thinkers from across the region developed ideas in places such as Baghdad's House of Wisdom. Among them were the Persians Omar Khayyam, who worked on equations, and Al-Khwarizmi, latinised as Algoritmi and pictured above, who is credited as one of the fathers of algebra, and the Jewish scholar Al-Samawal, who converted to Islam and worked on mathematical induction. As well as the new ideas, there were many advances drawing on Indian, Babylonian and Greek work and, thanks to the recording or reworking by mathematicians in the Islamic world, that broad range of earlier maths was passed on to western Europe for further study. With Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews Peter Pormann Professor of Classics & Graeco-Arabic Studies at the University of Manchester And Jim Al-Khalili Professor of Physics at the University of Surrey Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the relationship between parasites and hosts, where one species lives on or in another to the benefit of the parasite but at a cost to the host, potentially leading to disease or death of the host. Typical examples are mistletoe and trees, hookworms and vertebrates, cuckoos and other birds. In many cases the parasite species do so well in or on a particular host that they reproduce much faster and can adapt to changes more efficiently, and it is thought that almost half of all animal species have a parasitic stage in their lifetime. What techniques do hosts have to counter the parasites, and what impact do parasites have on the evolution of their hosts? With Steve Jones Emeritus Professor of Genetics at University College, London Wendy Gibson Professor of Protozoology at the University of Bristol and Kayla King Associate Professor in the Department of Zoology at the University of Oxford Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the German astronomer Johannes Kepler (1571 - 1630). Although he is overshadowed today by Isaac Newton and Galileo, he is considered by many to be one of the greatest scientists in history. The three laws of planetary motion Kepler developed transformed people's understanding of the Solar System and laid the foundations for the revolutionary ideas Isaac Newton produced later. Kepler is also thought to have written one of the first works of science fiction. However, he faced a number of challenges. He had to defend his mother from charges of witchcraft, he had few financial resources and his career suffered as a result of his Lutheran faith. With David Wootton Professor of History at the University of York Ulinka Rublack Professor of Early Modern European History at the University of Cambridge and Fellow of St John's College Adam Mosley Associate Professor in the Department of History at Swansea University Producer: Victoria Brignell.

The scientist John Dalton was born in North England in 1766. Although he came from a relatively poor Quaker family, he managed to become one of the most celebrated scientists of his age. Through his work, he helped to establish Manchester as a place where not only products were made but ideas were born. His reputation during his lifetime was so high that unusually a statue was erected to him before he died. Among his interests were meteorology, gasses and colour blindness. However, he is most remembered today for his pioneering thinking in the field of atomic theory. With: Jim Bennett Former Director of the Museum of the History of Science at the University of Oxford and Keeper Emeritus at the Science Museum Aileen Fyfe Reader in British History at the University of St Andrews James Sumner Lecturer in the History of Technology at the Centre for the History of Science, Technology and Medicine at the University of Manchester Producer: Victoria Brignell.

Melvyn Bragg and guests discuss plasma, the fourth state of matter after solid, liquid and gas. As over ninety-nine percent of all observable matter in the Universe is plasma, planets like ours, with so little plasma and so much solid, liquid and gas, appear all the more remarkable. On the grand scale, plasma is what the Sun is made from and, when we look into the night sky, almost everything we can see with the naked eye is made of plasma. On the smallest scale, here on Earth, scientists make plasma to etch the microchips on which we rely for so much. Plasma is in the fluorescent light bulbs above our heads and, in laboratories around the world, it is the subject of tests to create, one day, an inexhaustible and clean source of energy from nuclear fusion. With Justin Wark Professor of Physics and Fellow of Trinity College at the University of Oxford Kate Lancaster Research Fellow for Innovation and Impact at the York Plasma Institute at the University of York and Bill Graham Professor of Physics at Queens University, Belfast Producer: Simon Tillotson.

In a programme first broadcast in 2016, Melvyn Bragg and guests discuss Zeno of Elea, a pre-Socratic philosopher from c490-430 BC whose paradoxes were described by Bertrand Russell as "immeasurably subtle and profound." The best known argue against motion, such as that of an arrow in flight which is at a series of different points but moving at none of them, or that of Achilles who, despite being the faster runner, will never catch up with a tortoise with a head start. Aristotle and Aquinas engaged with these, as did Russell, yet it is still debatable whether Zeno's Paradoxes have been resolved. With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Barbara Sattler Lecturer in Philosophy at the University of St Andrews and James Warren Reader in Ancient Philosophy at the University of Cambridge Producer: Simon Tillotson

Melvyn Bragg and guests discuss the development of photography in the 1830s, when techniques for 'drawing with light' evolved to the stage where, in 1839, both Louis Daguerre and William Henry Fox Talbot made claims for its invention. These followed the development of the camera obscura, and experiments by such as Thomas Wedgwood and Nicéphore Niépce, and led to rapid changes in the 1840s as more people captured images with the daguerreotype and calotype. These new techniques changed the aesthetics of the age and, before long, inspired claims that painting was now dead. With Simon Schaffer Professor of the History of Science at the University of Cambridge Elizabeth Edwards Emeritus Professor of Photographic History at De Montfort University And Alison Morrison-Low, Research Associate at National Museums Scotland Producer: Simon Tillotson.

Melvyn Bragg and guests discuss penicillin, discovered by Alexander Fleming in 1928. It is said he noticed some blue-green penicillium mould on an uncovered petri dish at his hospital laboratory, and that this mould had inhibited bacterial growth around it. After further work, Fleming filtered a broth of the mould and called that penicillin, hoping it would be useful as a disinfectant. Howard Florey and Ernst Chain later shared a Nobel Prize in Medicine with Fleming, for their role in developing a way of mass-producing the life-saving drug. Evolutionary theory predicted the risk of resistance from the start and, almost from the beginning of this 'golden age' of antibacterials, scientists have been looking for ways to extend the lifespan of antibiotics. With Laura Piddock Professor of Microbiology at the University of Birmingham Christoph Tang Professor of Cellular Pathology and Professorial Fellow at Exeter College at the University of Oxford And Steve Jones Emeritus Professor of Genetics at University College, London Producer: Simon Tillotson.

Melvyn Bragg and guests discuss Euclid's Elements, a mathematical text book attributed to Euclid and in use from its appearance in Alexandria, Egypt around 300 BC until modern times, dealing with geometry and number theory. It has been described as the most influential text book ever written. Einstein had a copy as a child, which he treasured, later saying "If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker." With Marcus du Sautoy Professor of Mathematics and Simonyi Professor for the Public Understanding of Science at the University of Oxford Serafina Cuomo Reader in Roman History at Birkbeck University of London And June Barrow-Green Professor of the History of Mathematics at the Open University Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the impact of the eruption of Mt Tambora, in 1815, on the Indonesian island of Sambawa. This was the largest volcanic eruption in recorded history and it had the highest death toll, devastating people living in the immediate area. Tambora has been linked with drastic weather changes in North America and Europe the following year, with frosts in June and heavy rains throughout the summer in many areas. This led to food shortages, which may have prompted westward migration in America and, in a Europe barely recovered from the Napoleonic Wars, led to widespread famine. With Clive Oppenheimer Professor of Volcanology at the University of Cambridge Jane Stabler Professor in Romantic Literature at the University of St Andrews And Lawrence Goldman Director of the Institute of Historical Research at the University of London Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the neutron, one of the particles found in an atom's nucleus. Building on the work of Ernest Rutherford, the British physicist James Chadwick won the Nobel Prize for Physics for his discovery of the neutron in 1932. Neutrons play a fundamental role in the universe and their discovery was at the heart of developments in nuclear physics in the first half of the 20th century. With Val Gibson Professor of High Energy Physics at the University of Cambridge and fellow of Trinity College Andrew Harrison Chief Executive Officer of Diamond Light Source and Professor in Chemistry at the University of Edinburgh And Frank Close Professor Emeritus of Physics at the University of Oxford.

Melvyn Bragg and guests discuss the life and work of Robert Hooke (1635-1703) who worked for Robert Boyle and was curator of experiments at the Royal Society. The engraving of a flea, above, is taken from his Micrographia which caused a sensation when published in 1665. Sometimes remembered for his disputes with Newton, he studied the planets with telescopes and snowflakes with microscopes. He was an early proposer of a theory of evolution, discovered light diffraction with a wave theory to explain it and felt he was rarely given due credit for his discoveries. With David Wootton Anniversary Professor of History at the University of York Patricia Fara President Elect of the British Society for the History of Science And Rob Iliffe Professor of History of Science at Oxford University Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the origins, development and uses of chromatography. In its basic form, it is familiar to generations of schoolchildren who put a spot of ink at the bottom of a strip of paper, dip it in water and then watch the pigments spread upwards, revealing their separate colours. Chemists in the 19th Century started to find new ways to separate mixtures and their work was taken further by Mikhail Tsvet, a Russian-Italian scientist who is often credited with inventing chromatography in 1900. The technique has become so widely used, it is now an integral part of testing the quality of air and water, the levels of drugs in athletes, in forensics and in the preparation of pharmaceuticals. With Andrea Sella Professor of Chemistry at University College London Apryll Stalcup Professor of Chemical Sciences at Dublin City University And Leon Barron Senior Lecturer in Forensic Science at King's College London.

Melvyn Bragg and guests discuss the planet Saturn with its rings of ice and rock and over 60 moons. In 1610, Galileo used an early telescope to observe Saturn, one of the brightest points in the night sky, but could not make sense of what he saw: perhaps two large moons on either side. When he looked a few years later, those supposed moons had disappeared. It was another forty years before Dutch scientist Christiaan Huygens solved the mystery, realizing the moons were really a system of rings. Successive astronomers added more detail, with the greatest leaps forward in the last forty years. The Pioneer 11 spacecraft and two Voyager missions have flown by, sending back the first close-up images, and Cassini is still there, in orbit, confirming Saturn, with its rings and many moons, as one of the most intriguing and beautiful planets in our Solar System. With Carolin Crawford Public Astronomer at the Institute of Astronomy and Fellow of Emmanuel College, University of Cambridge Michele Dougherty Professor of Space Physics at Imperial College London And Andrew Coates Deputy Director in charge of the Solar System at the Mullard Space Science Laboratory at UCL.

Melvyn Bragg and guests discuss the eminent 19th-century scientist Michael Faraday. Born into a poor working-class family, he received little formal schooling but became interested in science while working as a bookbinder's apprentice. He is celebrated today for carrying out pioneering research into the relationship between electricity and magnetism. Faraday showed that if a wire was turned in the presence of a magnet or a magnet was turned in relation to a wire, an electric current was generated. This ground-breaking discovery led to the development of the electric generator and ultimately to modern power stations. During his life he became the most famous scientist in Britain and he played a key role in founding the Royal Institution's Christmas lectures which continue today. With: Geoffrey Cantor Professor Emeritus of the History of Science at the University of Leeds Laura Herz Professor of Physics at the University of Oxford Frank James Professor of the History of Science at the Royal Institution Producer: Victoria Brignell.

Melvyn Bragg and his guests discuss the evolution and role of Circadian Rhythms, the so-called body clock that influences an organism's daily cycle of physical, behavioural and mental changes. The rhythms are generated within organisms and also in response to external stimuli, mainly light and darkness. They are found throughout the living world, from bacteria to plants, fungi to animals and, in humans, are noticed most clearly in sleep patterns. With Russell Foster Professor of Circadian Neuroscience at the University of Oxford Debra Skene Professor of Neuroendocrinology at the University of Surrey And Steve Jones Emeritus Professor of Genetics at University College London.

Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it's impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments. With Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews Timothy Gowers Royal Society Research Professor in Mathematics at the University of Cambridge And Leslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford Producer: Simon Tillotson.

Melvyn Bragg and guests discuss the rise of the idea of perpetual motion and its decline, in the 19th Century, with the Laws of Thermodynamics. For hundreds of years, some of the greatest names in science thought there might be machines that could power themselves endlessly. Leonardo Da Vinci tested the idea of a constantly-spinning wheel and Robert Boyle tried to recirculate water from a draining flask. Gottfried Leibniz supported a friend, Orffyreus, who claimed he had built an ever-rotating wheel. An increasing number of scientists voiced their doubts about perpetual motion, from the time of Galileo, but none could prove it was impossible. For scientists, the designs were a way of exploring the laws of nature. Others claimed their inventions actually worked, and promised a limitless supply of energy. It was not until the 19th Century that the picture became clearer, with the experiments of James Joule and Robert Mayer on the links between heat and work, and the establishment of the First and Second Laws of Thermodynamics. With Ruth Gregory Professor of Mathematics and Physics at Durham University Frank Close Professor Emeritus of Physics at the University of Oxford and Steven Bramwell Professor of Physics and former Professor of Chemistry at University College London Producer: Simon Tillotson.

In 1977, scientists in the submersible "Alvin" were exploring the deep ocean bed off the Galapagos Islands. In the dark, they discovered hydrothermal vents, like chimneys, from which superheated water flowed. Around the vents there was an extraordinary variety of life, feeding on microbes which were thriving in the acidity and extreme temperature of the vents. While it was already known that some microbes are extremophiles, thriving in extreme conditions, such as the springs and geysers of Yellowstone Park (pictured), that had not prepared scientists for what they now found. Since the "Alvin" discovery, the increased study of extremophile microbes has revealed much about what is and is not needed to sustain life on Earth and given rise to new theories about how and where life began. It has also suggested forms and places in which life might be found elsewhere in the Universe. With Monica Grady Professor of Planetary and Space Sciences at the Open University Ian Crawford Professor of Planetary Science and Astrobiology at Birkbeck University of London And Nick Lane Reader in Evolutionary Biochemistry at University College London Producer: Simon Tillotson.

While glass items have been made for at least 5,000 years, scientists are yet to explain, conclusively, what happens when the substance it's made from moves from a molten state to its hard, transparent phase. It is said to be one of the great unsolved problems in physics. While apparently solid, the glass retains certain properties of a liquid. At times, ways of making glass have been highly confidential; in Venice in the Middle Ages, disclosure of manufacturing techniques was a capital offence. Despite the complexity and mystery of the science of glass, glass technology has continued to advance from sheet glass to crystal glass, optical glass and prisms, to float glasses, chemical glassware, fibre optics and metal glasses. With: Dame Athene Donald Professor of Experimental Physics at the University of Cambridge and Master of Churchill College, Cambridge Jim Bennett Former Director of the Museum of the History of Science at the University of Oxford and Keeper Emeritus at the Science Museum Paul McMillan Professor of Chemistry at University College London Producer: Simon Tillotson.

Melvyn Bragg and his guests discuss the Earth's Core. The inner core is an extremely dense, solid ball of iron and nickel, the size of the Moon, while the outer core is a flowing liquid, the size of Mars. Thanks to the magnetic fields produced within the core, life on Earth is possible. The magnetosphere protects the Earth from much of the Sun's radiation and the flow of particles which would otherwise strip away the atmosphere. The precise structure of the core and its properties have been fascinating scientists from the Renaissance. Recent seismographs show the picture is even more complex than we might have imagined, with suggestions that the core is spinning at a different speed and on a different axis from the surface. With Stephen Blundell Professor of Physics and Fellow of Mansfield College at the University of Oxford Arwen Deuss Associate Professor in Seismology at Utrecht University and Simon Redfern Professor of Mineral Physics at the University of Cambridge Producer: Simon Tillotson.

Melvyn Bragg and his guests discuss the scientific achievements of the Curie family. In 1903 Marie and Pierre Curie shared a Nobel Prize in Physics with Henri Becquerel for their work on radioactivity, a term which Marie coined. Marie went on to win a Nobel in Chemistry eight years later; remarkably, her daughter Irène Joliot-Curie would later share a Nobel with her husband Frédéric Joliot-Curie for their discovery that it was possible to create radioactive materials in the laboratory. The work of the Curies added immensely to our knowledge of fundamental physics and paved the way for modern treatments for cancer and other illnesses. With: Patricia Fara Senior Tutor of Clare College, University of Cambridge Robert Fox Emeritus Professor of the History of Science at the University of Oxford Steven T Bramwell Professor of Physics and former Professor of Chemistry at University College London Producer: Simon Tillotson.

Melvyn Bragg and his guests discuss dark matter, the mysterious and invisible substance which is believed to make up most of the Universe. In 1932 the Dutch astronomer Jan Oort noticed that the speed at which galaxies moved was at odds with the amount of material they appeared to contain. He hypothesized that much of this 'missing' matter was simply invisible to telescopes. Today astronomers and particle physicists are still fascinated by the search for dark matter and the question of what it is. With Carolin Crawford Public Astronomer at the Institute of Astronomy, University of Cambridge and Gresham Professor of Astronomy Carlos Frenk Ogden Professor of Fundamental Physics and Director of the Institute for Computational Cosmology at the University of Durham Anne Green Reader in Physics at the University of Nottingham Producer: Simon Tillotson.

Melvyn Bragg and his guests discuss the photon, one of the most enigmatic objects in the Universe. Generations of scientists have struggled to understand the nature of light. In the late nineteenth century it seemed clear that light was an electromagnetic wave. But the work of physicists including Planck and Einstein shed doubt on this theory. Today scientists accept that light can behave both as a wave and a particle, the latter known as the photon. Understanding light in terms of photons has enabled the development of some of the most important technology of the last fifty years. With: Frank Close Professor Emeritus of Physics at the University of Oxford Wendy Flavell Professor of Surface Physics at the University of Manchester Susan Cartwright Senior Lecturer in Physics and Astronomy at the University of Sheffield. Producer: Thomas Morris.

Melvyn Bragg and guests discuss Behavioural Ecology, the scientific study of animal behaviour. What factors influence where and what an animal chooses to eat? Why do some animals mate for life whilst others are promiscuous? Behavioural ecologists approach questions like these using Darwin's theory of natural selection, along with ideas drawn from game theory and the economics of consumer choice. Scientists had always been interested in why animals behave as they do, but before behavioural ecology this area of zoology never got much beyond a collection of interesting anecdotes. Behavioural ecology gave researchers techniques for constructing rigorous mathematical models of how animals act under different circumstances, and for predicting how they will react if circumstances change. Behavioural ecology emerged as a branch of zoology in the second half of the 20th century and proponents say it revolutionized our understanding of animals in their environments. GUESTS Steve Jones, Emeritus Professor of Genetics at University College London Rebecca Kilner, Professor of Evolutionary Biology at the University of Cambridge John Krebs, Principal of Jesus College at the University of Oxford Producer: Luke Mulhall.

Melvyn Bragg and guests discuss Isambard Kingdom Brunel, the Victorian engineer responsible for bridges, tunnels and railways still in use today more than 150 years after they were built. Brunel represented the cutting edge of technological innovation in Victorian Britain, and his life gives us a window onto the social changes that accompanied the Industrial Revolution. Yet his work was not always successful, and his innovative approach to engineering projects was often greeted with suspicion from investors. Guests: Julia Elton, former President of the Newcomen Society for the History of Engineering and Technology Ben Marsden, Senior Lecturer in the School of Divinity, History and Philosophy at the University of Aberdeen Crosbie Smith, Professor of the History of Science at the University of Kent Producer: Luke Mulhall.

Melvyn Bragg and his guests discuss nuclear fusion, the process that powers stars. In the 1920s physicists predicted that it might be possible to generate huge amounts of energy by fusing atomic nuclei together, a reaction requiring enormous temperatures and pressures. Today we know that this complex reaction is what keeps the Sun shining. Scientists have achieved fusion in the laboratory and in nuclear weapons; today it is seen as a likely future source of limitless and clean energy. Guests: Philippa Browning, Professor of Astrophysics at the University of Manchester Steve Cowley, Chief Executive of the United Kingdom Atomic Energy Authority Justin Wark, Professor of Physics and fellow of Trinity College at the University of Oxford Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Euler's number, also known as e. First discovered in the seventeenth century by the Swiss mathematician Jacob Bernoulli when he was studying compound interest, e is now recognised as one of the most important and interesting numbers in mathematics. Roughly equal to 2.718, e is useful in studying many everyday situations, from personal savings to epidemics. It also features in Euler's Identity, sometimes described as the most beautiful equation ever written. With: Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews June Barrow-Green Senior Lecturer in the History of Maths at the Open University Vicky Neale Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the Sun. The object that gives the Earth its light and heat is a massive ball of gas and plasma 93 million miles away. Thanks to the nuclear fusion reactions taking place at its core, the Sun has been shining for four and a half billion years. Its structure, and the processes that keep it burning, have fascinated astronomers for centuries. After the invention of the telescope it became apparent that the Sun is not a placid, steadily shining body but is subject to periodic changes in its appearance and eruptions of dramatic violence, some of which can affect us here on Earth. Recent space missions have revealed fascinating new insights into our nearest star. With: Carolin Crawford Gresham Professor of Astronomy and Fellow of Emmanuel College, Cambridge Yvonne Elsworth Poynting Professor of Physics at the University of Birmingham Louise Harra Professor of Solar Physics at UCL Mullard Space Science Laboratory Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the life and work of Robert Boyle, a pioneering scientist and a founder member of the Royal Society. Born in Ireland in 1627, Boyle was one of the first natural philosophers to conduct rigorous experiments, laid the foundations of modern chemistry and derived Boyle's Law, describing the physical properties of gases. In addition to his experimental work he left a substantial body of writings about philosophy and religion; his piety was one of the most important factors in his intellectual activities, prompting a celebrated dispute with his contemporary Thomas Hobbes. With: Simon Schaffer Professor of the History of Science at the University of Cambridge Michael Hunter Emeritus Professor of History at Birkbeck College, University of London Anna Marie Roos Senior Lecturer in the History of Science and Medicine at the University of Lincoln Producer: Thomas Morris.

Melvyn Bragg and his guests discuss photosynthesis, the process by which green plants and many other organisms use sunlight to synthesise organic molecules. Photosynthesis arose very early in evolutionary history and has been a crucial driver of life on Earth. In addition to providing most of the food consumed by organisms on the planet, it is also responsible for maintaining atmospheric oxygen levels, and is thus almost certainly the most important chemical process ever discovered. With: Nick Lane Reader in Evolutionary Biochemistry at University College London Sandra Knapp Botanist at the Natural History Museum John Allen Professor of Biochemistry at Queen Mary, University of London. Producer: Thomas Morris

Melvyn Bragg and his guests discuss the science of matter and the states in which it can exist. Most people are familiar with the idea that a substance like water can exist in solid, liquid and gaseous forms. But as much as 99% of the matter in the universe is now believed to exist in a fourth state, plasma. Today scientists recognise a number of other exotic states or phases, such as glasses, gels and liquid crystals - many of them with useful properties that can be exploited. With: Andrea Sella Professor of Chemistry at University College London Athene Donald Professor of Experimental Physics at the University of Cambridge Justin Wark Professor of Physics and Fellow of Trinity College at the University of Oxford Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the eye. Humans have been attempting to understand the workings and significance of the organ for at least 2500 years. Some ancient philosophers believed that the eye enabled creatures to see by emitting its own light. The function and structures of the eye became an area of particular interest to doctors in the Islamic Golden Age. In Renaissance Europe the work of thinkers including Kepler and Descartes revolutionised thinking about how the organ worked, but it took several hundred years for the eye to be thoroughly understood. Eyes have long attracted more than purely scientific interest, known even today as the 'windows on the soul'. With: Patricia Fara Senior Tutor of Clare College, University of Cambridge William Ayliffe Gresham Professor of Physic at Gresham College Robert Iliffe Professor of Intellectual History and History of Science at the University of Sussex Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Social Darwinism. After the publication of Charles Darwin's masterpiece On the Origin of Species in 1859, some thinkers argued that Darwin's ideas about evolution could also be applied to human society. One thinker particularly associated with this movement was Darwin's near-contemporary Herbert Spencer, who coined the phrase 'survival of the fittest'. He argued that competition among humans was beneficial, because it ensured that only the healthiest and most intelligent individuals would succeed. Social Darwinism remained influential for several generations, although its association with eugenics and later adoption as an ideological position by Fascist regimes ensured its eventual downfall from intellectual respectability. With: Adam Kuper Centennial Professor of Anthropology at the LSE, University of London Gregory Radick Professor of History and Philosophy of Science at the University of Leeds Charlotte Sleigh Reader in the History of Science at the University of Kent. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Catastrophism, the idea that natural disasters have had a significant influence in moulding the Earth's geological features. In 1822 William Buckland, the first reader of Geology at the University of Oxford, published his famous Reliquae Diluvianae, in which he ascribed most of the fossil record to the effects of Noah's flood. Charles Lyell in his Principles of Geology challenged these writings, arguing that geological change was slow and gradual, and that the processes responsible could still be seen at work today - a school of thought known as Uniformitarianism. But in the 1970s the idea that natural catastrophes were a major factor in the Earth's geology was revived and given new respectability by the discovery of evidence of a gigantic asteroid impact 65 million years ago, believed by many to have resulted in the extinction of the dinosaurs. With: Andrew Scott Leverhulme Emeritus Fellow in the Department of Earth Sciences at Royal Holloway, University of London Jan Zalasiewicz Senior Lecturer in Geology at the University of Leicester Leucha Veneer Visiting Scholar at the Faculty of Life Sciences at the University of Manchester Producer: Thomas Morris.

Melvyn Bragg and his guests discuss complexity and how it can help us understand the world around us. When living beings come together and act in a group, they do so in complicated and unpredictable ways: societies often behave very differently from the individuals within them. Complexity was a phenomenon little understood a generation ago, but research into complex systems now has important applications in many different fields, from biology to political science. Today it is being used to explain how birds flock, to predict traffic flow in cities and to study the spread of diseases. With: Ian Stewart Emeritus Professor of Mathematics at the University of Warwick Jeff Johnson Professor of Complexity Science and Design at the Open University Professor Eve Mitleton-Kelly Director of the Complexity Research Group at the London School of Economics. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the development of the microscope, an instrument which has revolutionised our knowledge of the world and the organisms that inhabit it. In the seventeenth century the pioneering work of two scientists, the Dutchman Antonie van Leeuwenhoek and Robert Hooke in England, revealed the teeming microscopic world that exists at scales beyond the capabilities of the naked eye. The microscope became an essential component of scientific enquiry by the nineteenth century, but in the 1930s a German physicist, Ernst Ruska, discovered that by using a beam of electrons he could view structures much tinier than was possible using visible light. Today light and electron microscopy are among the most powerful tools at the disposal of modern science, and new techniques are still being developed. With: Jim Bennett Visiting Keeper at the Science Museum in London Sir Colin Humphreys Professor of Materials Science and Director of Research at the University of Cambridge Michelle Peckham Professor of Cell Biology at the University of Leeds Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the Roman physician and medical theorist Galen. The most celebrated doctor in the ancient world, Galen was Greek by birth but spent most of his career in Rome, where he was personal physician to three Emperors. He was one of the most prolific authors of his age, and a sixth of all surviving ancient literature in Greek was written by him. Celebrated in his own lifetime, he was regarded as the preeminent medical authority for centuries after his death, both in the Arab world and in medieval Europe. It was only the discoveries of Renaissance science which removed Galen from his dominant position in the pantheon of medicine. With: Vivian Nutton Emeritus Professor of the History of Medicine at University College London Helen King Professor of Classical Studies at the Open University Caroline Petit Wellcome Trust Senior Research Fellow in Classics at the University of Warwick Producer: Thomas Morris.

Melvyn Bragg and his guests discuss exoplanets. Astronomers have speculated about the existence of planets beyond our solar system for centuries. Although strenuous efforts were made to find such planets orbiting distant stars, it was not until the 1990s that instruments became sophisticated enough to detect such remote objects. In 1992 Dale Frail and Aleksander Wolszczan discovered the first confirmed exoplanets: two planets orbiting the pulsar PSR B1257+12. Since then, astronomers have discovered more than 900 exoplanets, and are able to reach increasingly sophisticated conclusions about what they look like - and whether they might be able to support life. Recent data from experiments such as NASA's space telescope Kepler indicates that such planets may be far more common than previously suspected. With: Carolin Crawford Gresham Professor of Astronomy and a member of the Institute of Astronomy at the University of Cambridge Don Pollacco Professor of Astronomy at the University of Warwick Suzanne Aigrain Lecturer in Astrophysics at the University of Oxford and a Fellow of All Souls College. Producer: Thomas Morris.

Melvyn Bragg and his guests begin a new series of the programme with a discussion of the French polymath Blaise Pascal. Born in 1623, Pascal was a brilliant mathematician and scientist, inventing one of the first mechanical calculators and making important discoveries about fluids and vacuums while still a young man. In his thirties he experienced a religious conversion, after which he devoted most of his attention to philosophy and theology. Although he died in his late thirties, Pascal left a formidable legacy as a scientist and pioneer of probability theory, and as one of seventeenth century Europe's greatest writers. With: David Wootton Anniversary Professor of History at the University of York Michael Moriarty Drapers Professor of French at the University of Cambridge Michela Massimi Senior Lecturer in the Philosophy of Science at the University of Edinburgh. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the invention of radio. In the early 1860s the Scottish physicist James Clerk Maxwell derived four equations which together describe the behaviour of electricity and magnetism. They predicted the existence of a previously unknown phenomenon: electromagnetic waves. These waves were first observed in the early 1880s, and over the next two decades a succession of scientists and engineers built increasingly elaborate devices to produce and detect them. Eventually this gave birth to a new technology: radio. The Italian Guglielmo Marconi is commonly described as the father of radio - but many other figures were involved in its development, and it was not him but a Canadian, Reginald Fessenden, who first succeeded in transmitting speech over the airwaves. With: Simon Schaffer Professor of the History of Science at the University of Cambridge Elizabeth Bruton Postdoctoral Researcher at the University of Leeds John Liffen Curator of Communications at the Science Museum, London Producer: Thomas Morris.

Melvyn Bragg and his guests discuss Einstein's theories of relativity. Between 1905 and 1917 Albert Einstein formulated a theoretical framework which transformed our understanding of the Universe. The twin theories of Special and General Relativity offered insights into the nature of space, time and gravitation which changed the face of modern science. Relativity resolved apparent contradictions in physics and also predicted several new phenomena, including black holes. It's regarded today as one of the greatest intellectual achievements of the twentieth century, and had an impact far beyond the world of science. With: Ruth Gregory Professor of Mathematics and Physics at Durham University Martin Rees Astronomer Royal and Emeritus Professor of Cosmology and Astrophysics at the University of Cambridge Roger Penrose Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss cosmic rays. In 1912 the physicist Victor Hess discovered that the Earth is under constant bombardment from radiation coming from outside our atmosphere. These so-called cosmic rays have been known to cause damage to satellites and electronic devices on Earth, but most are absorbed by our atmosphere. The study of cosmic rays and their effects has led to major breakthroughs in particle physics. But today physicists are still trying to establish where these highly energetic subatomic particles come from. With: Carolin Crawford Gresham Professor of Astronomy and a member of the Institute of Astronomy at the University of Cambridge Alan Watson Emeritus Professor of Physics at the University of Leeds Tim Greenshaw Professor of Physics at the University of Liverpool. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss one of the simplest and most remarkable of all molecules: water. Water is among the most abundant substances on Earth, covering more than two-thirds of the planet. Consisting of just three atoms, the water molecule is superficially simple in its structure but extraordinary in its properties. It is a rare example of a substance that can be found on Earth in gaseous, liquid and solid forms, and thanks to its unique chemical behaviour is the basis of all known life. Scientists are still discovering new things about it, such as the fact that there are at least fifteen different forms of ice. Hasok Chang Hans Rausing Professor of History and Philosophy of Science at the University of Cambridge Andrea Sella Professor of Chemistry at University College London Patricia Hunt Senior Lecturer in Chemistry at Imperial College London. Producer: Thomas Morris.

In a programme first broadcast in 2013, Melvyn Bragg and his guests discuss absolute zero, the lowest conceivable temperature.  In the early eighteenth century the French physicist Guillaume Amontons suggested that temperature had a lower limit.  The subject of low temperature became a fertile field of research in the nineteenth century, and today we know that this limit - known as absolute zero - is approximately minus 273 degrees Celsius.  It is impossible to produce a temperature exactly equal to absolute zero, but today scientists have come to within a billionth of a degree.  At such low temperatures physicists have discovered a number of strange new phenomena including superfluids, liquids capable of climbing a vertical surface. With: Simon Schaffer Professor of the History of Science at the University of Cambridge Stephen Blundell Professor of Physics at the University of Oxford Nicola Wilkin Lecturer in Theoretical Physics at the University of Birmingham Producer: Thomas Morris

Melvyn Bragg and his guests discuss the life and work of the Victorian anthropologist and archaeologist Augustus Pitt-Rivers. Over many years he amassed thousands of ethnographic and archaeological objects, some of which formed the founding collection of the Pitt Rivers Museum at Oxford University. Inspired by the work of Charles Darwin, Pitt-Rivers believed that human technology evolved in the same way as living organisms, and devoted much of his life to exploring this theory. He was also a pioneering archaeologist whose meticulous records of major excavations provided a model for later scholars. With: Adam Kuper Visiting Professor of Anthropology at Boston University Richard Bradley Professor in Archaeology at the University of Reading Dan Hicks University Lecturer & Curator of Archaeology at the Pitt Rivers Museum at the University of Oxford. Producer: Thomas Morris.

Melvyn Bragg and his guests discuss comets, the 'dirty snowballs' of the Solar System. In the early 18th century the Astronomer Royal Sir Edmond Halley compiled a list of appearances of comets, bright objects like stars with long tails which are occasionally visible in the night sky. He concluded that many of these apparitions were in fact the same comet, which returns to our skies around every 75 years, and whose reappearance he correctly predicted. Halley's Comet is today the best known example of a comet, a body of ice and dust which orbits the Sun. Since they contain materials from the time when the Solar System was formed, comets are regarded by scientists as frozen time capsules, with the potential to reveal important information about the early history of our planet and others. With: Monica Grady Professor of Planetary and Space Sciences at the Open University Paul Murdin Senior Fellow at the Institute of Astronomy at the University of Cambridge Don Pollacco Professor of Astronomy at the University of Warwick Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the history of crystallography, the study of crystals and their structure. The discovery in the early 20th century that X-rays could be diffracted by a crystal revolutionised our knowledge of materials. This crystal technology has touched most people's lives, thanks to the vital role it plays in diverse scientific disciplines - from physics and chemistry, to molecular biology and mineralogy. To date, 28 Nobel Prizes have been awarded to scientists working with X-ray crystallography, an indication of its crucial importance. The history of crystallography began with the work of Johannes Kepler in the 17th century, but perhaps the most crucial leap in understanding came with the work of the father-and-son team the Braggs in 1912. They built on the work of the German physicist Max von Laue who had proved that X-rays are a form of light waves and that it was possible to scatter these rays using a crystal. The Braggs undertook seminal experiments which transformed our perception of crystals and their atomic arrangements, and led to some of the most significant scientific findings of the last century - such as revealing the structure of DNA. With: Judith Howard Director of the Biophysical Sciences Institute and Professor of Chemistry at the University of Durham Chris Hammond Life Fellow in Material Science at the University of Leeds Mike Glazer Emeritus Professor of Physics at the University of Oxford and Visiting Professor of Physics at the University of Warwick Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss Fermat's Last Theorem. In 1637 the French mathematician Pierre de Fermat scribbled a note in the margin of one of his books. He claimed to have proved a remarkable property of numbers, but gave no clue as to how he'd gone about it. "I have found a wonderful demonstration of this proposition," he wrote, "which this margin is too narrow to contain". Fermat's theorem became one of the most iconic problems in mathematics and for centuries mathematicians struggled in vain to work out what his proof had been. In the 19th century the French Academy of Sciences twice offered prize money and a gold medal to the person who could discover Fermat's proof; but it was not until 1995 that the puzzle was finally solved by the British mathematician Andrew Wiles. With: Marcus du Sautoy Professor of Mathematics & Simonyi Professor for the Public Understanding of Science at the University of Oxford Vicky Neale Fellow and Director of Studies in Mathematics at Murray Edwards College at the University of Cambridge Samir Siksek Professor at the Mathematics Institute at the University of Warwick. Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the cell, the fundamental building block of life. First observed by Robert Hooke in 1665, cells occur in nature in a bewildering variety of forms. Every organism alive today consists of one or more cells: a single human body contains up to a hundred trillion of them. The first life on Earth was a single-celled organism which is thought to have appeared around three and a half billion years ago. That simple cell resembled today's bacteria. But eventually these microscopic entities evolved into something far more complex, and single-celled life gave rise to much larger, complex multicellular organisms. But how did the first cell appear, and how did that prototype evolve into the sophisticated, highly specialised cells of the human body? With: Steve Jones Professor of Genetics at University College London Nick Lane Senior Lecturer in the Department of Genetics, Evolution and Environment, University College London Cathie Martin Group Leader at the John Innes Centre and Professor in the School of Biological Sciences at the University of East Anglia Producer: Thomas Morris.

Melvyn Bragg and his guests discuss game theory, the mathematical study of decision-making. First formulated in the 1940s, the discipline entails devising 'games' to simulate situations of conflict or cooperation. It allows researchers to unravel decision-making strategies, and even to establish why certain types of behaviour emerge. Some of the games studied in game theory have become well known outside academia - they include the Prisoner's Dilemma, an intriguing scenario popularised in novels and films, and which has inspired television game shows. Today game theory is seen as a vital tool in such diverse fields as evolutionary biology, economics, computing and philosophy. With:Ian StewartEmeritus Professor of Mathematics at the University of WarwickAndrew ColmanProfessor of Psychology at the University of LeicesterRichard BradleyProfessor of Philosophy at the London School of Economics and Political Science.Producer: Thomas Morris.

Melvyn Bragg and his guests discuss the emergence of geology as a scientific discipline. A little over two hundred years ago a small group of friends founded the Geological Society of London. This organisation was the first devoted to furthering the discipline of geology - the study of the Earth, its history and composition. Although geology only emerged as a separate area of study in the late eighteenth century, many earlier thinkers had studied rocks, fossils and the materials from which the Earth is made. Ancient scholars in Egypt and Greece speculated about the Earth and its composition. And in the Renaissance the advent of mining brought further insight into the nature of objects found underground and how they got there. But how did such haphazard study of rocks and fossils develop into a rigorous scientific discipline?With:Stephen PumfreySenior Lecturer in the History of Science at Lancaster UniversityAndrew ScottProfessor of Applied Palaeobotany at Royal Holloway, University of LondonLeucha VeneerResearch Associate at the Centre for the History of Science, Technology and Medicine at the University of Manchester.Producer: Thomas Morris.