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The mathematician Hannah Fry reveals the hidden numbers, rules and patterns that secretly control our daily lives, in this year’s Royal Institution Christmas lectures. She tells Kirsty Wark how maths and algorithms have the power to reveal the truth - and to obscure it.The economist Tim Harford is in search of the truth as he unravels the events that led to real life disasters. In the podcast series Cautionary Tales, Harford asks what we can learn from catastrophes. He wonders why we are so often susceptible to cons. Science has revolutionised the way we live, and in the field of technology the ingenious invention of blockchain has been heralded as truly radical. As an incorruptible digital ledger of transactions, blockchain has uses far beyond crypto-currencies. The Financial Times journalist Izabella Kaminska looks back over the last decade to consider whether blockchain has lived up to its hype.The latest science promising to transform medicine and biology is nanotechnology. Sonia Contera is a pioneer in the field and believes studying the infinitesimal realm of proteins and DNA will have a profound impact on our health and longevity.Producer: Katy Hickman

Flooding remains a risk in many parts of the country this winter. Andrew Marr explores the impact of water on communities. The engineer David Lerner argues for the extension of the policy of daylighting – opening up rivers covered over by the Victorians. He says Britain’s towns and cities have a lot to learn from Zurich, which was an early pioneer in recovering streams from underground. The social and environmental benefits in Zurich are evident. Torrential rain in November forced many people across the country to leave their homes. The writer Edward Platt looks back at the effect of the record-breaking floods of 2013-14 and the toll it took on those caught up in the deluge. He talks to those responsible for trying to keep the water at bay, and asks what can be done to protect the vulnerable. The artist Tania Kovats’s work is preoccupied with our experience and understanding of water and the landscape. From collecting water from a hundred UK rivers to sculptural forms cast in wetsuits, and to the study of the drawing of water, Kovats places water at the centre of her creativity. The journalist Leaf Arbuthnot looks at the growing evidence for the benefits of wild swimming, even in the cold winter months. For all the danger of living close to water, she asks whether time spent near coastal and river environments is the secret to a happier, healthier life.Producer: Katy Hickman

Corporate rapacity and government collusion are at the centre of William Dalrymple’s history of the East India Company. He tells Amol Rajan how the company moved relentlessly from trade to conquest of India in the 18th century. But Dalrymple warns against the distortion of history both by those in Britain nostalgic for an imperial past, and Hindu nationalists in India.2019 marked the centenary of the Amritsar massacre in which more than a thousand Indians were killed by British soldiers. Although the events leading up to the atrocity are now well documented, Anita Anand has uncovered the extraordinary story of revenge which led to the shooting in London of the man responsible for the massacre. In August this year the Indian government revoked Kashmir’s special status, sparking protests in the Muslim-majority valley. But why has this region - once a princely state, until the end of British rule - become such a flashpoint for violence? Professor Sumantra Bose explores the consequence of the Indian government’s latest actions.Producer: Katy Hickman