On Start the Week Tom Sutcliffe looks at how science has shaped our civilisation. Mark Miodownik explores how the discovery of new materials has transformed the way we live, from the Stone Age to the Silicon Age. While the mathematician Ian Stewart argues that calculations made centuries ago have led to untold innovations, and that mathematical equations really have changed our world. The natural world is the starting point for the sculptor, Peter Randall-Page and his abstract geometric form carved in stone. And Jane Rapley from Central Saint Martins College of Art and Design considers how far fashion designers are influenced by modern materials and techniques, and inspired by the natural world. Producer: Katy Hickman.

On Start the Week Andrew Marr considers the 'great man' view of history, and how far an age can be represented by its leaders and innovators. Mary Beard looks back to ancient times when history and biography were considered two distinct genres. While John Guy returns to the reign of Elizabeth I, Max Hastings and Lola Young give an overview of the modern Elizabethan age. Producer: Katy Hickman.

On Start the Week Andrew Marr looks at the state of conservatism. Thomas Frank chronicles the rebirth of right-wing populism in the United States, with the resurgent Tea Party. It's a movement driven by ideology with a vision of utopian capitalism. At home right-wing commentators bemoan the lack of ideology at the heart of the government. Peter Hitchens argues for a political philosophy that stresses a sense of place and history, and decries the Tory Party's shift to the 'centre ground'. The neoconservative Douglas Murray goes further in asserting that military might is vital to defend freedom and justice. But the new MP Margot James follows her party's model of caring capitalism, and its move away from its reputation as the unelectable "Nasty Party".Producer: Katy Hickman.

On Start the Week Andrew Marr talks revolution. Wael Ghonim explains how social networks played a vital role in the Arab Spring. His Facebook page,'We Are All Khaled Said', which featured the death of a young Egyptian, inspired a new generation to fight oppression. Mary King, Professor of Peace and Conflict Studies looks back to earlier struggles in eastern Europe, and the journalist Paul Mason explores how far the worldwide economic crisis and growing inequality lie behind the new revolutions. Producer: Katy Hickman.

Andrew Marr explores the idea of Justice on Start the Week. In a satire on the International Criminal Tribunal, the playwright Simon Stephens, asks how far such a court can deal with perpetrators of terrible crimes, when the accused neither recognises its authority, or shares its morality. Closer to home John Podmore looks back at 25 years as a prison governor and inspector, in a damning indictment on Britain's prison service. The criminologist Mike Hough asks why people obey the law, and questions whether the threat of punishment is ever a deterrent. And the director of Liberty Shami Chakrabarti defends the right to civil liberties and freedom of speech, even of those many may consider to be unpalatable.Producer: Natalia Fernandez.

Andrew Marr looks for solutions to the current global crisis. Detlev Schlichter dismisses the practice of printing more money in times of recession, arguing that in the next decade our reliance on paper money will collapse, and he proposes a return to hard commodities, like gold. The historian Philip Coggan pits creditors against debtors, tax payers against public sector workers, and believes it's time for a new monetary system to emerge. The Labour peer, Lord Glasman thinks we need to change the relationship between parliament and the market. And Angela Knight sticks up for the bankers, insisting they hold the key to the crisis, so deserve both a bonus and a bit of respect. Producer: Katy Hickman.

On Start the Week, Andrew Marr begins the new year with a look at austerity. Anna Coote argues that it's time to embrace a new set of values that are not dependent on high rolling consumerism and, as unemployment rises, to share out the working hours more evenly. The great chronicler of Austerity Britain of the fifties, David Kynaston, explores whether there are any lessons to be learnt from earlier decades of thrift and dissent. The artist Antony Gormley discusses a new collaboration in which he explores the idea of survival in a world in which we are bombarded with information but have very little direct control. And Fintan O'Toole, Irish Times columnist, looks at at how Ireland is dealing with its 5th austerity budget and asks if there are lessons we can learn from the fate of the Celtic Tiger. Producer: Katy Hickman.

On Start the Week Andrew Marr visits the painter David Hockney to find out why he has swapped LA for East Yorkshire. Hockney takes him on a tour of the farm tracks and woods he has been painting near his home in Bridlington, and talks of his fascination at the changes of the season. In his vast studio hang pictures of increasing size and vibrant colour, many painted using his iPad. He might be in his seventies, but Hockney tells Andrew Marr that he's on a roll, busier than ever; excited by the new technology and full of ideas for his next works of art. Producer: Katy Hickman.

Andrew Marr discusses the idea of Christmas with Canon Giles Fraser who argues that the Christian Christmas was invented by the Emperor Constantine for political, not religious, reasons, 300 years after the birth of Christ. Canon Fraser will be discussing the idea that the legacy of Constantine's December feast distorts the message of Christ and casts a long shadow on modern believers. Clare Tomalin will be talking about Dickens and how the Victorian imagination shaped our understanding of what Christmas is and should be, and Susan Hill will be exploring the Christmas ghost story - one of the tenacious Victorian traditions still being reinvented in the 21st century.Producer: Eleanor Garland.

On Start the Week Andrew Marr asks if sport still embodies a notion of fair play and Corinthian spirit, or whether it has become mired in corruption, money and celebrity. Mihir Bose argues that sport is no longer just a game, but has become one of the most powerful political tools in the world. The social historian Janie Hampton looks back to a time when amateur wasn't a dirty word, while Brian Moore the 'pitbull' of the scrum, looks back at a disastrous year for the professionalism of English rugby. The philosopher Julian Savulescu believes the nostalgia for the age of the amateur is blinding people to the reality of today, and that far from penalising those who take performance enhancing drugs, we should merely set a safe limit and allow free rein. Producer: Katy Hickman.