Discovery

The Six Cornered Snowflake, a booklet written by Johannes Kepler as a New Year's gift, sought to explain the intricate and symmetrical shape of winter's tiny stars of snow. His insightful speculations about minerals and geometry were the beginning of the modern understanding of crystals. Philip Ball tells the story of how Kepler became a key figure in the scientific revolution of the 17th Century. He was a precocious mathematician who became an adviser to Emperor Rudolf II in 1600. Although he contributed to the idea that the sun, not the earth, was the centre of the solar system, his role at the court was to be an astrologer. Philip brings the story of the shape of the snowflakes up to date. It was only 20 years ago with the development of the maths of fractals that we got to understand the formation of the myriad patterns of snowflakes.

2000 years ago Lucretius composed a long poem that theorised about atoms and the natural world. Written in the first century BCE, during a chaotic and frightening time when the Roman Republic was collapsing, Lucretius encouraged people to feel free through contemplating the physics of the Universe. He said that despite living through a time of bloody civil wars and dictatorship people should not believe they were sheep who had to follow those in power. Naomi discovers that the poem is an epic, beautiful and persuasive piece of work. It begins with a discussion of atoms. Lucretius, like Epicurus, followed the Greek tradition in believing that the universe is composed of tiny, indivisible particles. De Rerum Natura asks us to consider that all that really exists in the universe are these atoms and the void between them. Atoms are indestructible, the number of atoms in the universe is infinite and so is the void in which the atoms move. What Lucretius is saying here was revolutionary then – and still has the power to surprise. He’s saying that there are no supernatural forces controlling our lives, no fate pulling the strings, if there are gods they’re made of atoms just like everything else. There is nothing else. Naomi discusses the life of Lucretius and his poem with classicist Dr Emma Woolerton of Durham University. And she talks to particle physicist Professor Jonathan Butterworth of UCL about which of his theories still holds water today. Picture: Gathered sheep, Credit: Chris Strickland, Getty Images

Philip Ball's tale is of a solar eclipse 100 years ago observed by Arthur Eddington, a British astronomer who travelled to the remote island of Principe off the coast of West Africa and saw the stars shift in the heavens. His observations supplied the crucial proof of a theory that transformed our notions of the cosmos and turned a German physicist named Albert Einstein into an international celebrity. But this is also a tale of how a Quaker tried to use science to unite countries. The reparations imposed on Germany after the war extended into science too as many in Great Britain and other Allied nations felt that German science should be ostracised from the international community. As a Quaker, Eddington wanted just the opposite: to see peaceful cooperation restored among nations. Picture: Image of the 1919 Solar eclipse taken by Arthur Eddington (1882-1944), Credit: Science Photo Library Producer: Erika Wright

On Christmas Eve in 1968 Bill Anders was in orbit around the moon in Apollo 8 when he took one of the most iconic photos of the last fifty years: Earthrise. The image got to be seen everywhere, from a stamp issued in 1969 to commemorate the success of Apollo 8, to posters that are still available today. Gaia Vince explores the impact of this image on the environmental movement and our understanding of our place in the universe. “Oh my God. Look at that picture over there. Here’s the earth coming up. Wow, isn’t that pretty.” Bill Anders was on the fourth of the ten orbits of the moon on Apollo 8, along with James Lovell and Frank Borman. Bill had spotted the earth through one of the hatch windows and grabbed his camera to take a black and white photo. But just in time, he picked up another camera with a colour film loaded, and the rest is history. When they returned from space – the first mission to orbit the moon – Nasa used Bill Anders’ image of Earthrise in its publicity. Nasa had understood there was an added value of going into space: taking pictures of our home planet. Stewart Brand was part of both the counterculture and the environmental movement; he’d hung out with Ken Kesey and his merry pranksters and put on happenings. He went on to found the Whole Earth Catalog, which brought together all kinds of alternative thinkers. Stewart Brand put the Earthrise photo on the front cover of one of the editions of the Whole Earth Catalog. Gaia Vince talks to Stewart Brand, and to scientists and artists, about the continuing importance of seeing Earth from above. Picture: Earthrise - The rising Earth is about five degrees above the lunar horizon in this telephoto view taken from the Apollo 8 spacecraft on December 24th 1968, Credit: Nasa Presenter: Gaia Vince Producer: Deborah Cohen

Alex Bellos is brilliant at all things mathematical, but even he can't hold a candle to the amazing mathematical feats of the supercalculators. Alex heads to Wolfsburg in Germany to meet the contestants at this year's Mental Calculation World Cup. These men and women are the fastest human number crunchers on the planet, able to multiply and divide large numbers with no need to reach for a smart phone, computer or calculator. So how do they do it, and is it a skill that any of us can learn? Alex talks to Robert Fountain, the UK's two-time winner of this prestigious prize, about his hopes for this year's competition and the mathematical magicians of the past who have inspired him. He also meets Rachel Riley, Countdown's number queen, to find out what it takes to beat the countdown clock. Picture: The Supercalculators, Credit: Alex Bellos