Kirsty Wark celebrates the artistry of numbers with three mathematicians Eugenia Cheng, Sarah Hart and Emily Howard.

Eugenia Cheng asks Is Maths Real? in her new book, which offers a new way to look at the subject by focusing on the questions, rather than the answers. She explores how asking the simplest of questions – ‘why does 1 + 1 = 2?’ – can get to the very heart of the search for mathematical truth.

Sarah Hart wants to break down the perceived barriers between mathematics and the creative arts. In Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature she reveals the geometry lurking in Moby-Dick, George Eliot’s obsession with statistics, and Jurassic Park’s fractal patterns.

Emily Howard has a dual passion for maths and music. In her compositions she plays with mathematical shapes and processes. Her new record Torus, released on NMC Recordings in April, brings together works including sphere and Compass.

Producer: Katy Hickman

Just how safe is the online world? Yale Professor of Law and Philosophy Scott Shapiro delves into cybersecurity in his book, Fancy Bear Goes Phishing. The book’s title derives from the exploits of ‘Fancy Bear’, an elite unit of the Russian military intelligence that hacked the US Democratic National Committee in 2016. From a bored graduate student who accidentally crashed the nascent internet, to cyber criminals and bot farms, Shapiro looks at the dark history of the information age.

Dr Alice Hutchings first began researching cybercrime in the late 1990s, while working in industry, and is now Director of the Cambridge Cybercrime Centre. She argues that the romanticised image of the underground hacker as an anti-authoritarian ‘lone wolf’ who possesses technological wizardry is outdated. Hacking has become industrialised with criminals able to buy ‘off-the-shelf’ tools to infect computers.

While hackers constantly look to exploit vulnerabilities within the technology, one of the major weak points are users themselves. Jenny Radcliffe’s job is to expose the flaws and weaknesses in security operations. In People Hacker she explains how she uses a blend of psychology, stagecraft and charm to gain access to computer systems, and reveals how people can boost their security and make her job more difficult.

Producer: Katy Hickman

Billions of people worldwide suffer from some kind of allergy and this is the focus of Theresa MacPhail’s book, Allergic. As a medical anthropologist and allergy sufferer herself she looks back at the history of diagnosis and treatment and investigates the worrying increase in numbers. It's thought by 2030 half the population will be sufferers.

James Kinross is a colorectal surgeon and suggests that some of the answer as to why there’s been a rise in allergies lies in the imbalance of our microbiome - our inner ecosystem of viruses, bacteria and other microbes. In his book, Dark Matter, he argues that the microbiome is under threat from our modern lifestyles, the food we consume, and the air we breathe.

Fermented foods are now thought to be integral to a healthy gut because they provide a vast amount of natural probiotics which can boost immunity and soothe the digestive tract. Johnny Drain is a materials scientist and a chef who believes in the benefits of fermentation, and has looked worldwide for innovations in techniques and flavours.

Producer: Natalia Fernandez

In front of an audience at the Hay Festival Tom Sutcliffe asks what Dickens would say about the world today. The prize-winning Barbara Kingsolver discusses her retelling of David Copperfield, in which her eponymous hero, Demon Copperfield, must struggle to survive amid rural poverty and America’s opioid crisis.

Michael Rosen has imagined his own modern Oliver Twist (An Unexpected Twist) and A Christmas Carol (Bah! Humbug!) and reflects on the unspoken grief and trauma of recent years, retold in his memoir, Getting Better.

And while Natalie Haynes’s favourite Dickens adaptation is The Muppet Christmas Carol, she explores how the telling and retelling of stories and ancient myths shines a light on our contemporary world. Her latest work, Stone Blind, looks again at the tragedy of Medusa.

Producer: Katy Hickman

The exhibition Animals: Art, Science and Sound at the British Library (until 28 August 2023) reveals how animals have been documented across the world through history. Cheryl Tipp, Curator of Wildlife and Environmental Sound, explores how people have tried to capture bird song – from using musical notation in the 17th century to the first commercial recording three centuries later, and the recording of the last Kauaʻi ʻōʻō songbird in Haiwaii.

Swifts are summer migrants, flying thousands of miles, only pausing to breed in Europe. Their screeching cries and darting flight might be the sight and sound of summer evenings, and yet we know relatively little about their lives. In One Midsummer’s Day the naturalist Mark Cocker goes in search of the elusive swift, and finds a whole natural world of connections.

The ecologist Tim Blackburn also discovers the hidden rules and interconnectedness of nature in his study of moths. His book, The Jewel Box, celebrates the diversity he finds within the moth trap on the roof of his flat. But also exposes a glimpse of a larger landscape, beyond the world of lepidoptera.

Producer: Katy Hickman

The economic historian and former trader Anne Murphy looks back at the Bank of England in the 18th century. In Virtuous Bankers she shows how a private institution became ‘a great engine of state’ and central to Britain’s economic and geopolitical power. Anne Murphy tells Adam Rutherford that both its inner workings and outer structure had to command the respect of the general public.

Interest was a fact of life long before the involvement of central banks and goes back as far as ancient Mesopotamia. In Price of Time the financial historian and Reuters’ commentator Edward Chancellor explores its long history and warns of the financial instability caused by years of low interest rates. Far from benefitting the majority of individuals, the ultra-low rates following the banking crash in 2008 have proved a boon for bankers, financiers and corporate stakeholders.

After the crash, the businessman David Fishwick was concerned that few people or small businesses in his home town of Burnley could get access to credit. His challenge to the traditional high street banks was to set up his own banking enterprise which became Burnley Savings and Loans – a story told in a Channel 4 series and the film Bank of Dave (on Netflix). He argues for a return to banking as a means to serve and grow the local economy.

Producer: Katy Hickman

What to do with the art of monstrous men? That’s the question Claire Dederer grapples with in Monsters: A Fan’s Dilemma. She wonders whether she can or should continue to love the work of Roman Polanski and Michael Jackson, Hemingway and Picasso? And if it’s possible to divorce the art from the artist.

How do we now view the glorious, technicolour paintings of Paul Gauguin’s works from Tahiti? The writer Devika Ponnambalam has imagined the life of one of his muses Teha’amana in her latest novel, I Am Not Your Eve. Gauguin was 43 when he first arrived on the island in 1891 and made numerous teenage girls his ‘unofficial wives’.

The science writer Michael Bond is interested in the psychology behind fandom. In his book Fans he looks at the pleasure of tribalism and sense of belonging, but also what happens when one’s hero falls short, and the cognitive dissonance needed to continue to stay true to a monstrous genius.

Producer: Katy Hickman

Adam Rutherford asks what ordinary life was like in the Soviet Union and how far its collapse helps to explain Russia today.

The historian Katja Hoyer presents a more nuanced picture of life in East Germany, far from the caricature often painted in the West. In Beyond the Wall: East Germany, 1949-1990 she acknowledges the oppression and hardship often faced by ordinary people, but argues that this now-vanished society was also home to its own distinctive and rich social and cultural landscape.

But what did it feel like to live through the fall of communism and then democracy? These are the questions Adam Curtis looked to reveal in his 7-part television series, Russia 1985-1999 TraumaZone (available on BBC iPlayer). The archive footage from thousands of hours of tapes filmed by BBC crews across the country records the lives of Russians at every level of society as their world collapsed around them.

Producer: Katy Hickman

Trees have the remarkable ability to pass knowledge down to succeeding generations and to survive the ravages of climate change, if only we’d let them alone, according to the German forester Peter Wohlleben. In The Power of Trees (translated by Jane Billinghurst) he explains the significance of leaving ancient forests untouched, and is scathing about the failures in forestry management and the planting of non-native trees for profit.

Jill Butler is an ancient tree specialist and a trustee of the Tree Register of the British Isle which records the nation’s ‘champion trees’ – the tallest and biggest trees of their species. But she’s also keen on getting the public involved in helping to find and care for some of the country’s oldest trees with the citizen science project, Ancient Tree Inventory, run by the Woodland Trust.

The healing powers of ancient trees is celebrated in stories throughout history, including the great Icelandic sagas. In The Norse Myths That Shape the Way We Think Carolyne Larrington, Professor of medieval European Literature explores the renewal that comes from the roots of Yggdrasill, the World Tree.

Producer: Katy Hickman

Why is it so difficult to find a place to call home? By the age of twenty five the journalist Kieran Yates had lived in twenty different houses, from council estates in London to a car showroom in rural Wales. In All The Houses I’ve Ever Lived In she reveals the reality of Britain’s housing crisis, the state’s neglect, and the toll it takes on those forced to move from place to place.

In her memoir Undercurrent the writer and poet Natasha Carthew compares the picture-postcard view of her native Cornwall with the reality of growing up there. She explores the impact of rural poverty, political neglect, and the dominance of second-home owners, but also the sheer beauty of the landscape she calls home.

Christine Whitehead OBE is a specialist in housing economics and evaluates government policies on home ownership and housing supply. She looks at the unintended consequences of implementing policies, like rent caps and controls on buying housing stock in rural areas, and the impact of Covid on the rental market.

The architect Alice Brownfield, Director at Peter Barber Architects, advocates for high density, mixed-use residential schemes for local councils and housing associations. Her practice has been recognised for its work in developing social housing, often on small plots of land, that centres on fostering a sense of community.

Producer: Katy Hickman

Image: Kiln Place, by Peter Barber Architects just after completion. Image credit: Morley von Sternberg