On Start the Week Tom Sutcliffe asks if one day we might know everything. The mathematician Marcus du Sautoy and the physicist Roger Penrose explore the far reaches of knowledge, questioning whether certain fields of research will always lie beyond human comprehension. They ask how much fashion and faith shape scientific theories. The experimental physicist Suzie Sheehy attempts to build machines to test the latest theories, while Joanna Kavenna plays with a philosophical Theory of Everything in her latest novel A Field Guide to Reality. Producer: Katy Hickman.

On Start the Week Andrew Marr explores the state of the arts. The English National Opera has lost £5 million of funding and its chorus recently went on strike, but the newly appointed Artistic Director Daniel Kramer, hopes to turn it around. He's directing a new production of Wagner's Tristan and Isolde, and the philosopher Roger Scruton celebrates the mastery of Wagner to express truths about the human condition. The biographer Franny Moyle looks at the life and career of Britain's most famous landscape painter, JMW Turner. Born as the Royal Academy was founded and British art was deemed inferior to its Continental counterpart, his work pushed the boundaries of what was accepted as art at the time. Julia Peyton-Jones looks back at a quarter of a century at the Serpentine Gallery in London, and makes a case for London as the centre of the art world. Producer: Katy Hickman.

On Start the Week Andrew Marr traces the quest to decipher the human genome. The idea of a 'unit of heredity' first emerged at the end of the 19th century: cancer physician Siddhartha Mukherjee recounts the history of the gene and the latest research into genetic heredity and mutation. Giles Yeo looks at what genes can tell us about body weight, while Aarathi Prasad explores how India practises medicine - from cutting-edge science to traditional healing. The historian Emily Mayhew traces the medical breakthroughs that have emerged from the battlefield, from World War I to the conflict in Afghanistan. Producer: Katy Hickman.

Start the Week is at Hay Literary Festival this week discussing war and intelligence. Michael Hayden is a former Air Force four-star general who became director of the US National Security Agency and then the CIA. He talks to Tom Sutcliffe about the decisions made during America's war on terror: from rendition and interrogation to widespread surveillance. Harry Parker was in his twenties when he signed up to join the British Army - he uses the paraphernalia and weaponry of war to tell the story of conflict; while the journalist Janine di Giovanni reports on ordinary people caught up in the fighting in Syria. The human rights lawyer Philippe Sands looks back at his own family's history to make sense of crimes against humanity. Producer: Katy Hickman.

On Start the Week Andrew Marr talks to the artist Cornelia Parker about the secrets revealed in found objects. Parker's latest exhibition at the Foundling Museum is inspired by the 18th Century tokens left with babies by their mothers. Simon Armitage finds a new way of telling the medieval poem Pearl, an allegorical story of grief and lost love. Archaeologist Cyprian Broodbank explains how Must Farm, the first landscape-scale investigation of deep Fenland, is transforming our understanding of Bronze Age life, while British Museum curator Aurelia Masson-Berghoff celebrates the finding of two lost Egyptian cities submerged at the mouth of the Nile for over a thousand years. Producer: Katy Hickman.

World on the Move: on Start the Week Andrew Marr explores how the mass movement of people has changed societies, in a special edition broadcast in front of an audience as part of a day of programmes on BBC Radio 4. The historian Sir Hew Strachan looks back at the largest single influx of people into Britain when 250,000 Belgians arrived during the Great War, while Frank Dikötter explores the biggest forced internal migration as tens of millions of young Chinese were sent to work in the countryside during the Cultural Revolution. The poet Patience Agbabi humanises the mass movement of people with her tale of one refugee's story. And what of those who return? The Bangladeshi author Tahmima Anam looks at what happens when you try to go back home. Producer: Katy Hickman.

On Start the Week Andrew Marr explores the use of technology in education. Professor Sugata Mitra has installed an internet-connected PC in a slum in India and watched how curiosity leads children to learn together. Digital technology is increasingly used in schools but the educationalist Neil Selwyn questions whether this is a positive step. The writer Lynsey Hanley looks at how class is embedded in the education system and the former Headmaster at Eton, Tony Little, on his vision for the future of schooling. Producer: Katy Hickman.

On Start the Week Grayson Perry discusses the concept of masculinity in modern Britain with Mary Ann Sieghart. The new artistic director at the Globe Theatre, Emma Rice, explains how she is playing with gender in Shakespeare's Midsummer Night's Dream, and the celebrated mezzo-soprano Alice Coote talks of her career in 'breeches', singing the male role. The former artists' model, Kelley Swain reveals what it's like being the object of a work of art. Producer: Katy Hickman.

On Start the Week the sculptor Anish Kapoor talks to Andrew Marr about his fascination with voids and black holes, and his excitement at the latest technological advances in deepest black: vantablack. The astrophysicist Martin Ward explains his research into supermassive black holes and why we're finding more of them, while the solar physicist Lucie Green journeys to the centre of the sun where each photon takes hundreds of thousands of years to reach the surface, but just eight minutes to shine as light on the Earth. Writer Ann Wroe walks on the Downs to experience how light affects Nature, and she turns to the artists to meditate on the nature of light. Producer: Katy HickmanPicture credit: Anish Kapoor.

On Start the Week Tom Sutcliffe discusses the writing of war and conflict. The journalist Patrick Cockburn looks back at his years covering crises in the Middle East, especially the rise of the so-called Islamic state. The Turkish writer Ece Temelkuran looks at the difficulty of reporting in a country where press freedoms are severely curtailed and asks whether fiction and poetry are a way of telling a more truthful story. The legendary American investigative reporter Seymour Hersh first gained recognition in the 1960s for exposing the My Lai massacre and its cover-up during the Vietnam War and has spent his career uncovering wrong-doing at the highest level. But reporting is changing and the academic Charlie Beckett celebrates the rise of citizen journalism. Producer: Katy Hickman.