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Sir Roger Penrose was jointly awarded the Nobel Prize in physics this year for his ground-breaking work on black holes and their relationship with the general theory of relativity. He looks back at his extraordinary career with Andrew Marr – from his early interest in mathematical patterns and the ‘impossible’ works of Escher, to his revolutionary use of mathematics in cosmology and his continued fascination with the beginning and end of time. Carlo Rovelli is a theoretical physicist who researches quantum gravity, as well as a best-selling author. In his latest collection of essays, There are Places in the World Where Rules are Less Important than Kindness, he demonstrates a curiosity that crosses the boundaries from the sciences to the arts. He reflects on everything from Newton’s alchemy to Einstein’s mistakes, and from Dante’s cosmology to Nabokov's butterflies. The world underwater is the physicist Helen Czerski’s playground. The focus of much of her research has been the physics of breaking waves and bubbles on the ocean surface. As one of this year’s Royal Institution Christmas Lecturers, Czerski will reveal the vital role oceans play in the Earth’s heating and plumbing systems, and the impact of human activity on the planet.Producer: Katy Hickman

The Latin scholar Shadi Bartsch has written a new translation of Virgil’s The Aeneid. She tells Kirsty Wark how this timeless epic about the legendary ancestor of a Roman emperor has been constantly invoked and reinterpreted over its two thousand year history. She argues that this poem still has much to say to contemporary readers about gender, politics, religion, morality, nationalism and love.It was while arguing about the merits of the Aeneid’s tragic queen, Dido of Carthage, that the classicist Natalie Haynes decided it was time to rescue the women in ancient myths. Centuries of male interpretations, she argues, has led to the demonization and dismissal of the likes of Medusa, Phaedra and Medea. In Pandora’s Jar: Women in Greek Myths she goes back to the original stories, reinstating the more complex roles given to these women in antiquity.In the 17th-century the Italian painter Artemisia Gentileschi drew inspiration from the women in ancient myths, allegories and the Bible, as seen in a new exhibition of her work at the National Gallery in London. The curator, Letizia Treves, says that Gentileschi challenged conventions and defied expectations, painting subjects that were traditionally the preserve of male artists, and transforming the meek into warriors.Producer: Katy Hickman(Picture credit: the National Gallery)

The pandemic has exposed serious weaknesses in Western governments, according to John Micklethwait, editor-in-chief of Bloomberg and former editor of The Economist. In The Wake-Up Call he argues that the Covid crisis has accelerated a shift in balance of power from the West to East. Micklethwait tells Andrew Marr that unless the West can respond more creatively to what is happening, the prospect of a new Eastern-dominated world order, with China at the centre, will be inevitable.But the historian Rana Mitter argues that China is increasingly presenting itself as the creator and protector of the international order, rather than its threat. In China’s Good War he explores how the country is revisiting its role as an Allied Force in World War II, to assert newfound confidence abroad and to shape a new nationalism at home.And Katya Adler, the BBC's Europe Editor, looks at the problems facing the EU, including the relationship of China and the impact of coronavirus. She assesses how Macron, Merkel, Ursula von der Leyen and other leaders have handled this year's challenges.Producer: Hannah Sander