Behind every line on a graph, there lies an extraordinary human story. Mathematician Hannah Fry is here to tell us ten of them.

There is a bizarre number in maths referred to simply as ‘i’. It appears to break the rules of arithmetic - but turns out to be utterly essential for applications across engineering and physics. We’re talking about the square root of -1. WHICH MAKES NO SENSE. Professor Fry waxes lyrical about the beauty and power of this so-called ‘imaginary’ number to a sceptical Dr Rutherford. Dr Michael Brooks tells the surprising story of the duelling Italian mathematicians who gave birth to this strange idea, and shares how Silicon Valley turned it into cold hard cash. It's all about oscillations, Professor Jeff O’Connell demonstrates. And finally, Dr Eleanor Knox reveals that imaginary numbers are indispensable for the most fundamental physics of all: quantum mechanics. Imaginary, impossible…but essential! Contributors: Professor Jeff O’Connell, Ohlone College California, Dr Michael Brooks, Author of 'The Maths That Made Us', and Dr Eleanor Knox, Philosopher of Physics at KCL and a Senior Visiting Fellow at the University of Pittsburgh. Producer: Ilan Goodman

This episode will render you oblivious, conked out and blissfully unaware. It’s about anaesthetics: those potent potions that send you into a deep, deathly sleep. Listener Alicia wants to know how they work, so our sleuths call on the expertise of consultant anaesthetist Dr Fiona Donald. Fiona shares her experience from the clinical frontline, and explains what we do and don’t know about how these chemicals work their mind-numbing magic. We hear about ground-breaking research led by Professor Irene Tracey, which reveals how a pattern of slow brain waves can be used to determine the optimum dosage of these dangerous drugs. And finally, Drs Rutherford and Fry wonder: what does all this tell us about normal consciousness? Professor Anil Seth shares how we can use brain tech to measure different levels of conscious awareness – from sleepy to psychedelic. Presenters: Hannah Fry and Adam Rutherford Producer: Ilan Goodman

‘Can we bring back extinct species?’ wonders listener Mikko Campbell. Well, Professor Fry is pretty excited by the prospect of woolly mammoths roaming the Siberian tundra once more. And everyone is impressed with the science that might make it happen. But Dr Rutherford comes out STRONGLY against the whole thing. Can our expert guests win him over? Dr Helen Pilcher shares the tale of Celia the lonely mountain goat, and makes the case for cloning to help protect species at risk of extinction. Professor Beth Shapiro sets out how biotech company ‘Colossal’ plans to engineer Asian elephants’ DNA to make a new group of mammoth-like creatures. And we hear how genetic technologies are being used in conservation efforts around the world. BUT WHAT ABOUT T-REXES? Not gonna happen. Sorry. Contributors: Dr Helen Pilcher, author of ‘Bring Back the King: The New Science of De-Extinction’, Professor Beth Shapiro from the University of California Santa Cruz, Dr Ben Novak of Revive and Restore and Tullis Matson from Nature’s SAFE. Presenters: Hannah Fry and Adam Rutherford Producer: Ilan Goodman

The Great Pyramids of Giza are awesome feats of engineering and precision. So who built them - and how? Was it a mysteriously super-advanced civilization now oddly extinct? Was it even aliens? Nah, course not! Rutherford and Fry investigate how these inspiring monuments were really constructed, and learn about the complex civilisation and efficient bureaucracy that made them possible. Professor Sarah Parcak busts the myth that they were built by slaves. In fact, she reveals, it was gangs of well-paid blokes fuelled by the ancient Egyptian equivalent of burgers and beer. And Dr Chris Naunton explains how it was not some mysterious tech, but incredible organisation and teamwork which made it possible to transport massive stone blocks over long distances several thousand years before trucks arrived. Dr Heba Abd El Gawad points out how racism led to bizarre assumptions in the history of archaeology, and how those assumptions linger in contemporary conspiracy theories which refuse to accept that Egyptians could have built the pyramids themselves! Presenters: Hannah Fry and Adam Rutherford Contributors: Professor Sarah Parcak, University of Alabama, Dr Chris Naunton, Egyptologist and broadcaster, Dr Heba Abd El Gawad, University College London Producers: Ilan Goodman & Emily Bird

Magnets are inside loads of everyday electronic kit - speakers, motors, phones and more - but listener Lucas is mystified: what, he wonders, is a magnetic field? Our sleuths set out to investigate the mysterious power of magnets, with the help of wizard / physicist Dr Felix Flicker - author of the The Magick of Matter - and materials scientist Dr Anna Ploszajski. They cover the secrets of lodestones - naturally occurring magnetic rocks - and how to levitate crystals, frogs and maybe even people. Matthew Swallow, the Chair of the UK Magnetics Society, explains why magnets make the best brakes for rollercoasters, and Dr Ploszajski explains how magnetically-induced eddy currents are used to sort through our recycling. Finally, Dr Flicker persuades Adam and Hannah that to really understand magnetic fields you have to leave classical physics behind, and go quantum... So our sleuths take a leap into the strange subatomic realm. Contributors: Dr Felix Flicker, Lecturer in Physics at Cardiff University and author of ‘The Magick of Matter’, Dr Anna Ploszajski, materials scientist and author of ‘Handmade’, Matthew Swallow, Chair of the UK Magnetics Society Presented by Hannah Fry and Adam Rutherford Producer: Ilan Goodman

Close your eyes and think of a giraffe. Can you see it? I mean, *really* see it - in rich, vivid detail? If not - you aren’t alone! We’ve had scores of messages from listeners who report having a ‘blind mind’s eye’. They don’t see mental images at all and they want to know why. Jude from Perth wants to know what makes her brain different, and Diane from Scotland wonders whether it affectes her ability to remember family holidays. Our sleuths learn that this is a condition recently termed ‘aphantasia’. They meet the chap who came up with the name, Professor Adam Zeman, a neurologist from the University of Exeter, and quiz him on the brain mechanisms behind this mystery. Professor Julia Simner - a psychologist who, herself, doesn’t see mental images - shares the surprising research into how aphants differ slightly from others in a range of cognitive skills. We also hear about the world class artists and animators who can’t visualise - but can create beautiful, imaginary worlds. Philosophy professor Fiona Macpherson from the University of Glasgow, deepens the mystery: perhaps this largely hidden phenomenon is behind some of the most profound disagreements in the history of psychology. Our mental experiences are all very different - maybe that’s why thinkers have come up with such different theories about how our minds work. Search for the “VVIQ” or Vividness of Visual Imagery questionnaire to take the test yourself. Look for “The Perception Census” to take part in this massive online study of perceptual variation. And look up the 'Aphtantasia Network' if you're curious to find out more. Presenters: Hannah Fry and Adam Rutherford Contributors: Professor Adam Zeman, Professor Julia Simner, Professor Fiona Macpherson Producer: Ilan Goodman

The new series kicks off very soon! As a little aperitif, Hannah and Adam review some surprising studies published in scientific journals. Warning: contains fruity language and grisly medical scenarios…

What do you get if you smash two hydrogen nuclei together? Helium and lots of energy. That’s no joke – it's nuclear fusion! Nuclear fusion is the power source of the sun and the stars. Physicists and engineers here on earth are trying to build reactors than can harness fusion power to provide limitless clean energy. But it’s tricky... Rutherford and Fry are joined by Dr Melanie Windridge, plasma physicist and CEO of Fusion Energy Insights, who explains why the fourth state of matter – plasma – helps get fusion going, and why a Russian doughnut was a key breakthrough on the path to fusion power. Dr Sharon Ann Holgate, author of Nuclear Fusion: The Race to Build a Mini Sun on Earth, helps our sleuths distinguish the more familiar nuclear fission (famous for powerful bombs) from the cleaner and much less radioactive nuclear fusion. And plasma physicist (another one!) Dr Arthur Turrell describes the astonishing amount of investment and innovation going on to try and get fusion power working at a commercial scale. Contributors: Dr Melanie Windridge, Dr Sharon Ann Holgate, Dr Arthur Turrell Producer: Ilan Goodman

Sneezes, wheezes, runny noses and red eyes - this episode is all about allergies. An allergic reaction is when your immune system reacts to something harmless – like peanuts or pollen – as if it was a parasitic invader. It’s a case of biological mistaken identity. Professor Judith Holloway from the University of Southampton guides our sleuths through the complex immune pathways that make allergies happen and tells the scary story of when she went into anaphylactic shock from a rogue chocolate bar. Professor Adam Fox, a paediatric allergist at Evelina Children’s Hospital, helps the Drs distinguish intolerances or sensitivities – substantial swelling from a bee sting, for example - from genuine allergies. Hannah’s orange juice ‘allergy’ is exposed as a probable fraud! Hannah and Adam explore why allergies are on the increase, and Professor Rick Maizels from the University of Glasgow shares his surprising research using parasitic worms to develop anti-allergy drugs! Producer: Ilan Goodman Contributors: Professor Judith Holloway, Professor Adam Fox, Professor Rick Maizels

Hungry for pi? Chow down on this! Pi is the ratio between a circle’s diameter and its circumference. Sounds dull – but pi turns out to have astonishing properties and crop up in places you would never expect. For a start, it goes on forever and never repeats, meaning it probably contains your name, date of birth, and the complete works of Shakespeare written in its digits. Maths comedian Matt Parker stuns Adam with his ‘pie-endulum’ experiment, in which a chicken and mushroom pie is dangled 2.45m to form a pendulum which takes *exactly* 3.14 seconds per swing. Mathematician Dr Vicky Neale explains how we can be sure that the number pi continues forever and never repeats - despite the fact we can never write down all its digits to check! She also makes the case that aliens would probably measure angles using pi because it’s a fundamental constant of the universe. NASA mission director Dr Marc Rayman drops in to explain how pi is used to navigate spacecraft around the solar system. And philosopher of physics Dr Eleanor Knox serves up some philoso-pi, revealing why some thinkers have found pi’s ubiquity so deeply mysterious. Hannah grins with delight for most of show. It’s all maths! Producer: Ilan Goodman Contributors: Matt Parker, Dr Vicky Neale, Dr Marc Rayman, Dr Eleanor Knox

Why are some smells so nasty and others so pleasant? Rutherford and Fry inhale the science of scent in this stinker of an episode. Our sleuths kick off with a guided tour of the airborne molecules and chemical receptors that power the sense of smell. Armed with a stack of pungent mini-flasks, Professor Matthew Cobb from the University of Manchester shows Hannah and Adam just how sensitive olfaction can be, and how our experience of some odours depends on our individual genetic make-up. Dr Ann-Sophie Barwich from Indiana University reveals how most everyday smells are complex combinations of hundreds of odorants, and how the poo-scented molecule of indole turns up in some extremely surprising places. With the help of a flavoured jellybean and some nose clips, Hannah experiences how smell is crucial to flavour, adding complexity and detail to the crude dimensions of taste. Speaking of food, listener Brychan Davies is curious about garlic and asparagus: why do they make us whiff? Professor Barry Smith from the Centre for the Study of the Senses reveals it's down to sulphur-containing compounds, and tells the story of how a cunning scientist managed to figure out the puzzle of asparagus-scented urine. Finally, another listener Lorena Busto Hurtado wants to know whether a person’s natural odour influences how much we like them. Barry Smith says yes - we may sniff each other out a bit like dogs - and cognitive neuroscientist Dr Rachel Herz points to evidence that bodily bouquet can even influence sexual attraction! Producer: Ilan Goodman Contributors: Professor Matthew Cobb, Professor Barry Smith, Dr Ann-Sophie Barwich, Dr Rachel Herz

How do winds start and why do they stop? asks Georgina from the Isle of Wight. What's more, listener Chris Elshaw is suprised we get strong winds at all: why doesn't air just move smoothly between areas of high and low pressure? Why do we get sudden gusts and violent storms? To tackle this breezy mystery, our curious duo don their anoraks and get windy with some weather experts. Dr Simon Clark, a science Youtuber and author of Firmament, convinces Adam that air flow is really about the physics of fluids, which can all be captured by some nifty maths. The idea of pressure turns out to be key, so Hannah makes her own barometer out of a jar, a balloon and some chopsticks, and explains why a bag of crisps will expand as you walk up a mountain. Professor Liz Bentley, Chief Executive of the Royal Meteorological Scoiety, reveals how the dynamics of a simple sea breeze – where air over land is heated more than air over water – illustrates the basic forces driving wind of all kinds. Then everyone gets involved to help Adam understand the tricky Coriolis effect and why the rotation of the Earth makes winds bend and storms spin. And Professor John Turner from the British Antarctic Survey explains why the distinctive features of the coldest continent make its coastline the windiest place on earth. Producer: Ilan Goodman Contributors: Dr Simon Clark, Professor Liz Bentley, Professor John Turner

DO WE HAVE YOUR ATTENTION? Good! But how does that work!? Our intrepid science sleuths explore why some things immediately catch your eye - or ear - while others slip by totally unnoticed. Even, on occasion, basketball bouncing gorillas. Professor Polly Dalton, a psychologist who leads The Attention Lab at Royal Holloway University, shares her surprising research into ‘inattentional blindness’ - when you get so absorbed in a task you can miss striking and unusual things going on right in front of you. Dr Gemma Briggs from the Open University reveals how this can have dangerous everyday consequences: you are four times more likely to have a crash if you talk on the phone while driving - even handsfree. Drs Rutherford and Fry also hear from stroke survivor Thomas Canning, who developed the tendency to ignore everything on the left side of space, despite his vision being totally intact. And Dr Tom Manly, from the University of Cambridge’s Cognition and Brain Sciences Unit, helps our sleuths unpack the neuroscience of this fascinating condition. Producer: Ilan Goodman Contributors: Professor Polly Dalton, Dr Gemma Briggs, Dr Tom Manly

We asked you to send us the boldest, barmiest bits of published research you could find and, dear Curios, you didn't disappoint! It’s time for some silly science.

The world is full of colour! But, wonders listener Maya Crocombe, ‘how do we see colour and why are some people colour blind?’ Dr Rutherford and Professor Fry set out to understand how special light-sensitive cells in our eyes start the process of colour perception, why people sometimes have very different experiences of colour and whether, in the end, colour is really just ‘in our heads’. Dr Gabriele Jordan from Newcastle University explains why lots of men struggle to discriminate between certain colours and why there were lots of complaints from colour-blind viewers when Wales played Ireland at rugby. Professor Anya Hurlbert, also from Newcastle University, tackles the most divisive of internet images: The Dress! Did you see it as blue-black or yellow-gold? Anya explains why people see it so differently, and why our ability to compensate for available light is so useful. Finally, Dr Mazviita Chirimuuta, a philosopher at the University of Edinburgh, gives us her take on what all this means: are colours real, or just in our minds? If you want to see some of the images and activities referenced in the episode read on... To take the colour perception test which Hannah and Adam do in the epsiode, search for the 'Farnsworth Munsell Hue test' - you can do it online for free. To see the Dunstanborough Castle illusion as described in the episode, check out the Gallery section on the Curious Cases BBC website. To learn more about colour blindness, and for support and resources go to colourblindawareness.org Producer: Ilan Goodman First broadcast on BBC Radio 4 in March 2022.

Mathematician Hannah Fry and geneticist Adam Rutherford investigate your everyday science queries. They get stuck into two questions about tides. Lynn Godson wants to know why isn’t high tide at the same time at all points around the coast? Whilst Tim Mosedale asks, could we ever harness tidal power commercially? Did you think tides are caused by the pull of the Moon? And that they come in and out twice a day? Well, yes, that’s true but it turns out there’s so much more to it than that, especially here in the UK, which has the second largest tidal range in the world at the Seven Estuary near Bristol, coming in at an average of 15 metres (50ft in old money). But why should high and low tide times be so different even in places that are relatively close to each other? The answer partly lies in something called bathymetry (which has more to do with baths than you might think – well basins at any rate). As for harnessing sea power, there are some ambitious projects currently in development and predictions that wave and tidal could make up as much as 15 percent of the UK’s energy needs in future. But how realistic is this and how do you ensure that your power generators can survive the rigours of the ocean – storms, saltwater and all those pesky barnacles? To help answer these queries, Hannah and Adam are joined by Physicist and Oceanographer, Helen Czerski and Professor Deborah Greaves OBE, who heads up the COAST lab at the University of Plymouth which studies marine renewable energy technologies. Producers: Rami Tzabar and Jen Whyntie First broadcast on BBC Radio 4 in March 2022.

Why does human hair go grey and is it ever possible for it to go white overnight from shock? Hannah and Adam explore why hair goes grey, how much stressful life events and a lack of sleep can speed up the process. They hear from the pilot whose hair turned white after a flight where all 4 of his engines failed after flying through a volcanic ash cloud - was the shock responsible? They also uncover new research which has shown it's possible for greying hair to return to its natural colour and ask if this finding could be exploited to uncover a cosmetic way to reverse hair greying? Presenters: Hannah Fry and Adam Rutherford Producer: Pamela Rutherford First broadcast on BBC Radio 4 in March 2022.

Two eyes, two arms, two legs - we’re roughly symmetrical on the outside, but inside we’re all over the place! We just have one heart, which is usually on the left, one liver on the right, one spleen and one appendix. Why is that?’ wonders listener Joanne. Our science sleuths discover that being symmetrical down the middle - at least on the outside - is by far the most common body plan across the animal kingdom. Professor Sebastian Shimeld from the University of Oxford takes us on a journey into the deep evolutionary past, to uncover how two-sided body structures first emerged in ancient worm-like creatures, and why this layout eventually proved so useful for swimming, walking and flying. Garden snails turn out to be a surprising exception – their shells coil in one direction and on just one side of their body. Professor Angus Davison from the University of Nottingham tells the tale of his international quest to find a romantic partner for Jeremy – a rare left-coiling snail who could only mate with another left-coiling snail! Dr Daniel Grimes from the University of Oregon unfolds the delicate mechanisms by which an initally symmetrical embryo starts to develop differently down one side, and everyone puzzles over the mystery of the left-handed 'mirror molecules' - so called L-amino acids - which turn out to be the building blocks of every living organism. A curious case indeed! Presenters: Hannah Fry and Adam Rutherford Producer: Ilan Goodman First broadcast on BBC Radio 4 in March 2022.

We use Wi-Fi every day, but do you know how it works? “Is it waves and science or just some mystical magical force?” wonders listener Abby. Well, our science sleuths are on the case. To help them navigate the strange realm of electromagnetic waves they are joined by Andrew Nix, Professor of Wireless Communication Systems from the University of Bristol. He explains why your wi-fi router won’t heat up your baked beans, but your microwave will. Andrea Goldsmith, Professor of Electrical and Computer Engineering at Princeton University, also joins to reveal how these waves are crammed full of 0s and 1s- whether that's a pic of your pets or a video chat with pals. And finally, how do you get the best Wi-Fi at home? Dr Rutherford, it turns out, has made some rookie errors... Listen out for our top tips so you don't make them too! Presenters: Hannah Fry and Adam Rutherford Producer: Ilan Goodman First broadcast on BBC Radio 4 in 2022.