Try and imagine a world without numbers. Telling people how many siblings you have, counting your wages or organising to meet a friend at a certain time would all be much more difficult. If you’re reading this on a digital screen, even these words are produced through a series of zero and one symbols. We take them so much for granted yet some cultures don’t count and some languages don’t have the words or symbols for numbers. This programme looks at when and why humans first started start to count, where the symbols many of us use today originate from and when concepts like zero and infinity came about.Joining Bridget Kendall to explore the history of numbers and counting are anthropological linguist Caleb Everett from the University of Miami, writer and historian of mathematics Tomoko Kitagawa, and Emeritus Professor of Mathematics at Warwick University in the UK, Ian Stewart.Photo: An abacus on a table.(CaoChunhai//Getty Images)

The Dutch post-Impressionist painter Vincent van Gogh is one of the most influential painters in western art. His series of still life sunflowers are known around the world today but during his lifetime in the 1800s he lived in poverty, selling very little of his work, some say just one painting, and suffered several serious breakdowns. One of his most famous works, The Starry Night, is said to be the view from his room in a French psychiatric hospital where he’d admitted himself shortly after severing his own left ear. This programme looks at the man behind these iconic paintings, explores how and why he became a painter and picks apart the various theories around his death from a gunshot wound at the age of just 37. Joining Bridget Kendall to discuss van Gogh’s life and work are Louis van Tilborgh, Senior Researcher at the Van Gogh Museum in Amsterdam and Professor of Art History at the University of Amsterdam; van Gogh biographer and co-author of Van Gogh: The Life, Steven Naifeh; and British art historian Lucrezia Walker.(Image: Self-Portrait by Vincent van Gogh. Credit:Getty Images)

A proud Hungarian by birth, Franz Liszt was a pioneer both in his piano playing and in his compositions. He was also the nearest thing to a rock star that classical music had in the 19th century. Fans would reportedly swarm over him, try and grab his gloves, even smoke his discarded cigars! Liszt lived up to his public image in his private life, with hectic touring schedules and colourful relationships with numerous women. But he was also generous to a fault – for example, frequently teaching for free - and he was a great champion of other composers.Rajan Datar is joined by three people for whom Liszt and his music occupy a central position in their professional lives: Dr. Rena Mueller, a musicologist emerita at New York University who is working on a complete thematic catalogue of Liszt's music; Dr. Éva Polgár who teaches at Azusa Pacific University in California and is a pianist noted for her championing of not just Liszt's works but all the music from her native Hungary; and professor Kenneth Hamilton, Head of School of Music at Cardiff University, who is not just a distinguished pianist but also an author and broadcaster.Examples from Liszt’s works used in the programme: Mazeppa (S.138) played by Leslie Howard Totentanz performed by Krystian Zimerman , Boston Symphony Orchestra, Seiji Ozawa La Campanella (Études d'exécution transcendente d'après Paganini, S.140) played by Leslie Howard Apparition No. 2 played by Ashley Wass Sonetto 123 del Petrarca (Années de pèlerinage II) played by Wilhelm Kempff Chase Neige (12 Études d'exécution transcendante, S.139) played by Boris Berezovsky Wilde Jagd (Études d'exécution transcendante, S.139 ) played by Daniil Trifonov Mazeppa (orchestral version, S. 100) performed by Wiener Philharmoniker, Giuseppe Sinopoli Ballade No. 2 played by Kenneth Hamilton Hungarian Rhapsody No. 2 played by Arcadi Volodos Csardas Obstinée played by Éva Polgár Les jeux d'eaux à la Villa d'Este (Années de pèlerinage III) played by Egon Petri(Image: Detail from a 19th-century caricature of Franz Liszt, Bibliothèque-Musée De L'Opéra National De Paris-Garnier. Credit: DeAgostini/Getty Images)

"That’s some Catch, that Catch 22". It’s a novel that gave rise to a new term in the English language and gave voice to American soldiers serving in Vietnam in the 1960s. Since its publication in 1961, Catch-22, Joseph Heller’s best-selling novel, has not only come to symbolise the cynical self-serving aspect of war run as a business, but also the way an ordinary person can be trapped and controlled by bureaucracy and social rules, in whatever area of life. It’s a novel that’s sold tens of millions of copies, and it continues to engage new readers. So, what is the secret of its success? Bridget Kendall is joined by the American novelist and friend of Joseph Heller, Christopher Buckley; Dr Beci Carver, lecturer in 20th century literature at Exeter University, whose forthcoming book is Modernism’s Whims; and Tracy Daugherty, author of Just One Catch: A Biography of Joseph Heller, and Emeritus Professor at Oregon State University in the US. With the contribution of Patricia Chapman Meder, the author of The True Story of Catch-22, whose father was the inspiration for Colonel Cathcart, Heller’s commander who kept increasing the number of flight missions. Produced by Anne Khazam for the BBC World Service. (Photo: An early edition of Joseph Heller’s novel Catch 22. Credit: Nicholas Kamm/AFP via Getty Images)

If you were a woman in the mid-19th century, some universities might let you attend public lectures on science, but very few would enrol women as regular students. The number of women allowed to sit exams and get academic degrees was vanishingly small. In mathematics it was almost unheard of. But the Russian mathematician Sofya Kovalevskaya changed all that. She was one of the first women in modern Europe both to gain a doctorate in mathematics and become a tenured professor. She was also the first woman to be part of the editorial committee of a leading mathematics journal and the publicity around her achievements helped pave the way for women to play a greater role in university life. Above all, she was an outstanding mathematician with at least one theorem bearing her name still used to this day.So how did Kovalevskaya do it? How much was talent? How much luck and opportunity? And how much just sheer force of character?To guide us through Sofya Kovalevskaya’s eventful life - and her equations – Bridget Kendall is joined by three experts: Ann Hibner Koblitz, professor emerita at Arizona State University and the author of A Convergence of Lives: Sofya Kovalevskaya - Scientist, Writer, Revolutionary; June Barrow-Green, professor of the history of mathematics at the Open University in the UK and chair of the International Commission on the History of Mathematics; and Elena Arsenyeva, associate professor at St. Petersburg State University in Russia and the coordinator of the Leonhard Euler International Mathematical Institute.(Photo: Sofya Kovalevskaya Credit: Fine Art Images/Heritage Images/Getty Images)

The ancient Inca town Machu Picchu is now the most visited tourist attraction in Peru – and yet it lay nearly forgotten for over three centuries until American and Peruvian explorers drew the world's attention to it in the 1910s. And despite a century of excavations at the site, there are still many unanswered questions about Machu Picchu: why was it built in the first place, who were the immigrants that made up a large proportion of the town’s population, and why was it abandoned so quickly.To find out more about Machu Picchu, Bridget Kendall is joined by leading archaeologists of the Inca civilisation Lucy Salazar and Michael Malpass, the celebrated mountaineer and explorer Johan Reinhard and by writer Mark Adams who retraced the steps of the 1911 expedition led by Hiram Bingham that put Machu Picchu back on the map.(Photo: Machu Picchu, Peru. Credit: Eitan Abramovich/Getty Images)

How do you approach the decisions you make in life? Do you think about them in terms of the maximum pleasure and minimum pain that any choice would lead to for yourself and others around you? If so, you are beginning to think along similar lines to the influential British philosopher and reformer Jeremy Bentham with his concept of Utilitarianism. This was not Bentham’s only contribution to radical thought. With the prison and judicial systems, with education, women’s suffrage, animal rights and the monarchy, throughout his life he came up with a huge body of work that challenged the status quo and still feels relevant today. Rajan Datar is joined by three expert guests to guide us through the life and work of this remarkable thinker: professor Philip Schofield from University College London who is both the director of the Bentham Project and the general editor of the Collected Works of Jeremy Bentham; Emmanuelle de Champs who is professor of British history and civilisation at CY Cergy Paris University, and Jeffrey Kaplan who is assistant professor of philosophy at the University of North Carolina, Greensboro.(Image: Coloured engraving of Jeremy Bentham, early 19th century. Credit: Stock Montage/Getty Images)

Copper is a metal that has been with us since the dawn of civilisation. The Romans used it to build their empire, and its high thermal and electrical conductivity led to the 19th century discovery of how to generate electricity and a revolution in telecommunications. Copper was even used to build the Statue of Liberty in New York, and it’s because of copper’s tendency to oxidise that the statue is no longer shiny brown but green. Today we still depend on this 'eternal metal', so called because it doesn’t decay or rust, and it has become a staple and necessary component in new green technologies like solar power and electric cars. But extracting copper has always been very damaging to human health and the environment - so how has our relationship with copper changed over the centuries? Joining Rajan Datar to find out more about copper past and present is Nikita Sud, Professor of Development studies at Oxford University and the author of The Making of Land and The Making of India; the archaeologist Dr William Parkinson, who is a curator at the Field Museum, and Professor of Anthropology at the University of Illinois at Chicago; and Andrea Sella, Professor of Chemistry at University College, London. Produced by Anne Khazam for the BBC World Service. (Image: Stripped copper cables. Credit: Christoph Burgstedt/Science Photo Library via Getty Images)

Agatha Christie put her decision to become a writer down to a lack of education and a capacity for day-dreaming. Her murder mysteries, full of ingenious plot twists, are still regarded by many as the finest examples of crime fiction and have sold in their billions in the English language and in translation.Although the world she depicts is considered by some to be cosy and genteel, and her plots formulaic, a new generation of screenwriters is bringing out the darker side of Christie’s imagination. So what accounts for her continuing global success, when today’s crime fiction tends to be grittier and more realist?Bridget Kendall is joined by Dr Michelle Kazmer, Professor in the School of Information at Florida State University, who’s combined a lifelong passion for crime fiction with study into how we use information – such as clues or evidence; Dr Mark Aldridge, Associate Professor of Film and Television at Solent University and the author of Agatha Christie on Screen and Poirot: The Greatest Detective in the World; and James Prichard, Agatha Christie’s great-grandson. Award-winning crime writer Ragnar Jónasson also explains how Agatha Christie's novels influenced his own work.Produced by Fiona Clampin for BBC World Service.

Boudica, also known as Boadicea, was a member of Iron Age aristocracy in Roman occupied England and her husband was the ruler of the Iceni people. When he died in around 60AD, Boudica, driven by Roman brutality, led a rebellion against the Roman army and marched on London. It was a ferocious attack that nearly drove the Romans out of Britain before Boudica was finally defeated. Today, she is an iconic and sometimes controversial figure. To explore Boudica, Bridget Kendall is joined by professors Richard Hingley and Miranda Aldhouse-Green and Dr. Jane Webster.(Image: Detail from Boadicea Haranguing the Britons by William Sharp, after John Opie, line engraving, published 1793. Credit: by Hulton Archive/Getty Images)