When does a crowd of people become unsafe? How well will Aston Villa do next season? When is it cost-effective to replace a kitchen?

The answers may seem arbitrary but, to Nira Chamberlain, they lie in mathematics. You can use maths to model virtually anything.

Dr Nira Chamberlain is President of the Institute of Mathematics and its Applications, and Principal Mathematical Modeller for the multinational engineering company SNC-Lavalin Atkins.

He specialises in complex engineering and industrial problems, creating mathematical models to describe a particular feature or process, and then running simulations to better understand it, and predict its behaviour.

Nira is one of just a handful of esteemed mathematicians, and the first black mathematician. to be featured in ‘Who’s Who’, Britain’s book of prominent people.

Since 2018, he’s made the Black Power List, which celebrates the UK’s top 100 most influential people of African or African-Caribbean heritage, ranking higher than Stormzy and Lewis Hamilton when he was first listed. Proof, he says, that maths really is for everyone.

PRODUCER: Beth Eastwood

Luminescent bone-eating worms, giant squid and a sea cucumber commonly known as the headless chicken monster: some extraordinary creatures live at the bottom of the sea. For a long time almost everyone agreed the pressure was too intense for any life to exist. Now, it seems, the more we look the more new species we find. But, many fear, marine life would be threatened if plans to extract precious metals from the potato-sized metallic nodules that grow on the seabed are allowed to go ahead.

Metals such as copper, manganese and cobalt are in high demand in the manufacture of mobile phones and renewable energy technologies, such as batteries for electric cars, wind turbines and solar panels. Deep sea mining companies argue that we will need these metals to create a carbon Net Zero economy. Meantime, the World Wildlife Fund is pushing for a moratorium on deep sea mining. And several companies agree: including Google, BMW, Volvo and Samsung. Do we need to choose between green and blue? Or is there a third way that protects both the planet and all the riches in our oceans?

Marine biologist, Helen Scales talks to Jim Al-Khalili about her life and work: fish watching off an atoll in the South China Sea to assess the extinction risks to the Humphead Wrasse and a research expedition to explore the brilliant abyss. And she warns of the environmental devastation that could be caused if plans to mine the metals on the bottom of the ocean were to be allowed to go ahead.

Producer: Anna Buckley

Throbbing head, nausea, dizziness, disturbed vision – just some of the disabling symptoms that can strike during a migraine attack. This neurological condition is far more common than you might think, affecting more people than diabetes, epilepsy and asthma combined.

While medications, to help relieve the symptoms of migraine, have been around for some time, they haven’t worked for everyone. And what happens in the brain during a migraine attack was, until recently, poorly understood.

Peter Goadsby is Professor of Neurology at King's College London’s Institute of Psychiatry, Psychology & Neuroscience and is a true pioneer in the field of migraine.

Over the course of his career, he has unravelled what happens in the brain during a migraine attack and his insights are already benefiting patients - in the form of new medications that can not only treat a migraine, but also prevent it from occurring.

Peter shares this year’s Brain Prize, the world's largest prize for brain research, with three other internationally renowned scientists in the field.

Producer: Beth Eastwood

Professor Jane Clarke has had a fascinating double career. Having been a science teacher for many years, she didn’t start her research career until she was 40. Today she is a world-leading expert in molecular biophysics and, in particular, in how protein molecules in the body fold up into elaborate 3D structures, that only then enables them to carry out their roles. How they do this has been one of the fundamental questions in biology and the key to combating some of our most challenging diseases, caused by the misfolding of proteins.

Jane talks about her journey, from Tottenham schoolteacher to Cambridge Professor and Fellow of the Royal Society, and how, despite the obstacles she’s encountered along the way, she’s always been driven by her passion to understand the mystery of the machinery of life.

Producer: Adrian Washbourne

When Martin Sweeting was a student, he thought it would be fun to try to build a satellite using electronic components found in some of the earliest personal computers. An amateur radio ham and space enthusiast, he wanted to create a communications satellite that could be used to talk to people on the other side of the world. It was a team effort, he insists, with friends and family pitching in and a lot of the work being done on his kitchen table. Somehow he managed to persuade Nasa to let his microsatellite hitch a ride into space and, after the first message was received, spent more than a decade trying to get a good picture of planet earth. The technology that Martin pioneered underpins modern life with thousands of reprogrammable microsatellites now in orbit around the earth and thousands more due to launch in the next few years to bring internet connections to remote parts of the world. The university spin-off company, Surrey Satellite Technologies Limited (SSTL) that Martin set up in the 1980s with an initial investment of £100 sold for £50 million a quarter of a century later. If his company had been bought by venture capitalists, he says he would probably have ended up making TVs. Instead he developed the satellite technology on which so much of modern life depends.

Producer: Anna Buckley

Photo Credit: SSTL

We all know how to be more healthy. And yet we are also remarkably good at NOT doing what we know is good for us. We keep meaning to get fit, but the sofa seems so much more appealing than a run. We know we shouldn’t have another slice of cake, but we do.

Inside the mind of a forensic botanist, Mark Spencer tells Jim Al-Khalili how he uses plant evidence to help solve crimes. By studying the vegetation at crime scenes, Mark can tell how long a dead body has been laying in the ground. Brambles can be particularly informative, he says. And by looking at tiny traces of plants under the microscope, he can link suspects to victims, or particular locations.

What would happen to our carbon emissions if we all went vegan? Astrophysicist, Sarah Bridle tells Jim Al-Khalili why she switched her attention from galaxies to food. A rising star in the study of extra-galactic astronomy, Sarah was a driving force behind one of the most ambitious astronomy projects of recent times, the Dark Energy Survey of the universe. A few years ago, she started trying to calculate the carbon emissions from different foods so that she could make more informed choices about what she was eating in terms of the impact they were having on climate change. Before long, she was adapting the statistical tools and techniques she had developed to study dark matter and dark energy, to quantify the carbon cost of different foods and lobby government to make food labels indicating carbon cost of foods compulsory.

For a long time people who heard voices or suffered paranoid delusions were thought to be too crazy to benefit from talking therapies. As a young man working on a prison psychiatric ward, Richard Bentall thought otherwise. Together with a small group of clinical psychologists, he pioneered the use of the talking therapy CBT for psychosis and conducted rigorous randomized controlled trials to find out if and why it worked. Turns out, having a good relationship with your the therapist is at the heart of why therapy succeeds, regardless of the type of therapy practised.

Richard talks to Jim Al-Khalili about his quest to understand psychosis and how his own mental health has suffered at times. He's interested in how adverse life events affect our mental health and has shown that people who suffer abuse, bullying and victimization as children are three times more likely to have a psychotic episode later in life. A large survey of our mental health, launched by Richard and colleagues on day one of the first lockdown has revealed that lockdown and Covid-19 has not led to a tsunami of mental illness that many feared. 10% of the population has seen their mental health improve.

Mice, like humans, prefer to be treated with a little dignity, and that extends to how they are handled.

Pick a mouse up by its tail, as was the norm in laboratories for decades, and it gets anxious. Make a mouse anxious and it can skew the results of the research it’s being used for.

What mice like, and how they behave, is the focus of Professor Jane Hurst’s research. Much of that behaviour, she’s discovered, can be revealed by following what they do with their noses - where they take them and what’s contained in the scent marks they sniff.

Now William Prescott Professor of Animal Science at the University of Liverpool, Jane has unravelled a complex array of scent signals that underpin the way mice communicate, and how each selects a mate.

Within this heady mix of male scent, she’s identified one particular pheromone that is so alluring to females that she named it Darcin, after Mr Darcy in Pride and Prejudice.

Producer: Beth Eastwood