In Our Time: Science

Explore the history of Fermat's Last Theorem and the 350-year delay in proving it. Delve into Pythagoras' theorem and its practical applications. Learn about the lost work of an extraordinary mathematician and the contributions of various mathematicians to the theorem. Discover how a woman mathematician surpassed renowned mathematicians. Uncover the intrigue surrounding Fermat's last theorem and the connection between elliptic curves and modular forms. Finally, dive into Andrew Wiles' proof and its practical applications.

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 LondonNick Lane Senior Lecturer in the Department of Genetics, Evolution and Environment, University College LondonCathie Martin Group Leader at the John Innes Centre and Professor in the School of Biological Sciences at the University of East AngliaProducer: 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.

Melvyn Bragg and his guests discuss the measurement of time. Early civilisations used the movements of heavenly bodies to tell the time, but even in the ancient world more sophisticated timekeeping devices such as waterclocks were known. The development of mechanical clocks in Europe emerged in the medieval period when monks used such devices to sound an alarm to signal it was the hour to pray, although these clocks did not tell them the time. For hundreds of years clocks were inaccurate and it proved hard to remedy the problems, let alone settle on a standard time that the country should follow. It was with the advent of the railways that time finally became standardised in Britain in the mid-19th century and only in 1884 that Greenwich became the prime meridian of the world. Atomic clocks now mark the passing of the days, hours, and minutes and they are capable of keeping time to a second in 15 million years. With:Kristen LippincottFormer Director of the Royal Observatory, GreenwichJim BennettDirector of the Museum of the History of Science at the University of OxfordJonathan BettsSenior Curator of Horology at the Royal Observatory, GreenwichProducer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the physics of electrical conduction. Although electricity has been known for several hundred years, it was only in the early twentieth century that physicists first satisfactorily explained the phenomenon. Electric current is the passage of charged particles through a medium - but a material will only conduct electricity if its atomic structure enables it to do so. In investigating electrical conduction scientists discovered two new classes of material. Semiconductors, first exploited commercially in the 1950s, have given us the transistor, the solar cell and the silicon chip, and have revolutionised telecommunications. And superconductors, remarkable materials first observed in 1911, are used in medical imaging and at the Large Hadron Collider in Geneva. With:Frank CloseProfessor of Physics at the University of OxfordJenny NelsonProfessor of Physics at Imperial College LondonLesley CohenProfessor of Solid State Physics at Imperial College LondonProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the evolution of the Scientific Method, the systematic and analytical approach to scientific thought. In 1620 the great philosopher and scientist Francis Bacon published the Novum Organum, a work outlining a new system of thought which he believed should inform all enquiry into the laws of nature. Philosophers before him had given their attention to the reasoning that underlies scientific enquiry; but Bacon's emphasis on observation and experience is often seen today as giving rise to a new phenomenon: the scientific method.The scientific method, and the logical processes on which it is based, became a topic of intense debate in the seventeenth century, and thinkers including Isaac Newton, Thomas Huxley and Karl Popper all made important contributions. Some of the greatest discoveries of the modern age were informed by their work, although even today the term 'scientific method' remains difficult to define.With: Simon SchafferProfessor of the History of Science at the University of CambridgeJohn WorrallProfessor of the Philosophy of Science at the London School of Economics and Political ScienceMichela MassimiSenior Lecturer in the Philosophy of Science at University College London.Producer: Thomas Morris.

Melvyn Bragg and guests discuss the giant molecules that form the basis of all life. Macromolecules, also known as polymers, are long chains of atoms. They form the proteins that make up our bodies, as well as many of the materials of modern life. Man's ability to mimic the structure of macromolecules has led to the invention of plastics such as nylon, paints and adhesives. Most of our clothes are made of macromolecules, and our food is macromolecular. The medical sciences are making increasingly sophisticated use of macromolecules, from growing replacement skin and bone to their increasing use in drug delivery. One of the most famous macromolecules is DNA, an infinitely more complex polymer than man has ever managed to produce. We've only known about macromolecules for just over a century, so what is the story behind them and how might they change our lives in the future?With:Tony RyanPro-Vice Chancellor for the Faculty of Science at the University of SheffieldAthene DonaldProfessor of Experimental Physics at the University of Cambridge and a Fellow of Robinson CollegeCharlotte WilliamsReader in Polymer Chemistry and Catalysis at Imperial College, London Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss the Hippocratic Oath. The Greek physician Hippocrates, active in the fifth century BC, has been described as the father of medicine, although little is known about his life and some scholars even argue that he was not one person but several. A large body of work originally attributed to him, the Hippocratic Corpus, was disseminated widely in the ancient world, and contains treatises on a wide variety of subjects, from fractures to medical ethics.Today we know that the Hippocratic Corpus cannot have been written by a single author. But many of its texts shaped Western medicine for centuries. The best known is the Hippocratic Oath, an ethical code for doctors. Celebrated in the ancient world, and later referred to by Arabic scholars, it offers medics guidance on how they should behave. Although it has often been revised and adapted, the Hippocratic Oath remains one of the most significant and best known documents of medical science - but there is little evidence that it was routinely sworn by doctors until modern times. With:Vivian NuttonEmeritus Professor of the History of Medicine at University College LondonHelen KingProfessor of Classical Studies at the Open UniversityPeter PormannWellcome Trust Associate Professor in Classics and Ancient History at the University of WarwickProducer: Thomas Morris.

Melvyn Bragg and his guests discuss the origins of infectious disease. Infectious disease has been with us for millennia. There are reports of ancient outbreaks of plague in the Bible, and in numerous historical sources from China, the Middle East and Europe. Other infections, including smallpox, tuberculosis and measles, have also been known for centuries. But some diseases made their first appearances only recently: HIV emerged around a century ago, while the Ebola virus was first recorded in the 1970s.But where do the agents of disease come from, and what determines where and when new viruses and bacteria appear? Modern techniques allow scientists to trace the histories of infective agents through their genomes; the story of disease provides a fascinating microcosm of the machinery of evolution.With:Steve JonesProfessor of Genetics at University College LondonSir Roy AndersonProfessor of Infectious Disease Epidemiology at Imperial College LondonMark PallenProfessor of Microbial Genomics at the University of Birmingham.Producer: Thomas Morris.