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This week, we're investigating the Millennium Prize Problems - a set of mathematical equations that, if solved, will not only nab the lucky winner a million, but also revolutionise the world. Plus, the headlines from the world of science and technology, including why screams are so alarming, how fat fish help the human fight against flab, and what's the future of money?

This week, broadcasting live from the centre of Cambridge, the Naked Scientists delve into the digital age we live in. We look at new, exciting ways to get kids into coding, how big data is changing the world of healthcare, and we take to skies to go drone racing. But what are the problems we face in this technological age? We find out who is using our online data, and explore the dangers of connecting to public Wi-Fi...

Things get a little dangerous as we don our body armour and head out into the battlefield. How do explosives work and what can we do to protect against them? We take a sneak peek at AnUBIS, a device that uses donated human body parts to help to understand the injuries an explosion can cause, and we investigate bomb-proof materials that could also be used in sports. Plus, in the news, why antibiotics at an early age might make you fat, the comet with a cave inside, and why you shouldn't marry your cousin...

It's 60 years since the world's first atomic clock was created. But what is time? When did time begin, and how accurate is timekeeping today? We'll be asking why we need leap seconds, we cook up a Big Bang with lasagne and hear how planet Earth is a terrible time keeper. Plus, in the news, scientists uncover the cause of tinnitus, what do your baby's eyes say about its future behaviour, and one of the earliest life forms goes under the microscope...

Tens of thousands of Londoners developed painful, apple-sized, pus-filled boils before dying from the dreadful disease within days. But just as the ordeal of the Black Death seemed to be subsiding, the Great Fire struck the city. But did the conflagration actually save the lives of thousands? In this scorcher of a show, we go in search of the cause of the plague, explore the origins of the Great Fire, and ask whether history might repeat itself?

What's the point of mosquitoes? Do your eyes pop out if left open when sneezing? Is the Universe infinitely big? Are birds really related to dinosaurs? What is quantum entanglement? If the space station is held in orbit by gravity, why do things float about inside it? Why does hayfever make your eyes itch? Can animals forecast earthquakes? Find out in this week's show where you're in the driving seat asking us the questions...

For World Blood Day we've been delving into the history of blood letting, getting stuck into blood donation and exploring exciting new possibilities for making blood that's safe for everyone. Plus, a new test to reveal every virus infection you've ever had, the LHC fires up again after a two year shut down, and a new weapon in the fight against Ebola...

Are we on the verge of solving one of the longest standing puzzles in physics? Physicists think we're close to discovering the identity of Dark Matter, the mysterious, invisible substance that accounts for nearly a quarter of the mass of Universe. So how will scientists see it, and why does its discovery matter? Plus, genes for pain, how smartphones can save lives, whether babies can feel pain, and how to make tastier cheese...

Colour-switching sticklebacks, geckos with enough adhesive power to hold up a human, bats with built-in sonar and moles with amazing noses - this week we go in search of the world's most incredible animals. Scientists passionate about their species put their cases to our panel. But which animal will be crowned king?

This week, can we colonise Mars? What's causes that smell after it rains? Can genetics inform skin care? And how do astronauts shower in space? Chris Smith, Richard Hollingham and Max Sanderson join Kat Arney to take on your quandaries, and also discuss some of the science news you might have missed this week: the Russian space race fail, hijacking a jet by hacking, and why humans feel pain...