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