The Sky at Night looks back at the last ten years of astronomy and ponders the most significant milestones and revelations. With the help of six distinguished astronomers, Chris and Maggie consider the state of astronomy in 2020 and wonder what new, exciting discoveries await us across the rest of the decade, as a host of new ground and space telescopes come online. Astronomer Royal Lord Martin Rees is among the guests to walk along the Astronomical Wall of Discovery in this one-hour special.

In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Professor Brian Cox journeys across the vastness of time and space revealing epic moments of sheer drama that changed the universe forever.
The series begins this epic exploration of the cosmos with a hymn to the great luminous bodies that bring light and warmth to the universe: the stars. It is estimated that there are two hundred trillion stars in the universe, each playing their part in an epic story of creation- a great saga that stretches from the dawn of time, with the arrival of the first star, through diverse generations until the arrival of our own star, the sun, and a civilization that has grown up in its light.

In 2014, the International Space Station had to move three times to avoid lethal chunks of space debris and there is an increasing problem of satellites mysteriously breaking down. With first-hand accounts from astronauts and experts, know the scale of the problem of space junk. Our planet is surrounded by hundreds of millions of pieces of junk moving at 17,000 miles per hour. Now the US government is investing a billion dollars to track them, and companies around the world are developing ways to clear up their mess - from robot arms to nets and harpoons. Learn the science behind the hit film Gravity and discovers the reality is far more worrying than the Hollywood fiction.

Perhaps the most mysterious structure on Earth, Stonehenge has stood on a plain in Southern England for 5000 years. Its foundations predate the Great Pyramids. It is one of mankind's most ancient mysteries. Why is it here? Is it a temple? A burial ground? A place for sacrifice? Or could the mystery of Stonehenge be revealed in its builders' desire to explore the unknown heavens and touch the universe? Using the cutting-edge computer-generated imagery that takes us into deep space, we'll also go inside a virtual Stonehenge to see what the ancients saw and push this prehistoric marvel to give up its age-old secrets.
In this episode we explore the possibility that this was a prehistoric astronomical observatory. Here ancient astronomer priests may have divined the complex movements of the Sun and Moon, recognizing patterns that would not be discovered elsewhere for thousands of years. The primitive Shamans may have also been the first astronomers to predict eclipses.

Dan Snow uncovers the lost Vikings in America with space archaeologist Dr Sarah Parcak. Sarah uses satellites 383 miles above the earth to spot ruins as small as 30cm buried beneath the surface. As Sarah searches for Viking sites from Britain to America, Dan explores how they voyaged thousands of miles when most ships never left the shoreline. He also tracks their expansion west, first as raiders and then as settlers and traders throughout Britain and beyond to Iceland and Greenland. In North America they excavate what could be the most westerly Viking settlement ever discovered.