Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

From a 2,400-year-old corpse in remarkable condition to how shrunken heads are made, these 15 ancient secrets will have you completely riveted. The Vesuvius eruption may have been a gradual process. It took a storm to lift the cover on this ancient Roman city. The people of Pompeii often resorted to vigilante justice. How the wealthy of Pompeii protected their valuables? Was this pre-Viking gathering a prelude to a massacre? The valuable commodity behind King Solomon's wealth. This valuable Viking grave is missing something important. Is this where humanity decided to settle down? This mysterious stone structure is older than Stonehenge. This 2,400 year old corpse is in remarkable condition. Here's exactly how shrunken heads are made. DNA analysis reveals troubling news about shrunken heads. This mass grave discovery could alter Roman history. Gladiator teeth reveal signs of infant malnourishment. Evidence suggests Stonehenge was an elite cemetery.

This is the story of a book that could have changed the history of the World. To the untrained eye, it is nothing more than a small and unassuming Byzantine prayer book. For faintly visible beneath the prayers on its pages are other, unique, writings - words that have been lost for nearly two thousand years. The text is the only record of work by one of the world's greatest minds - the ancient Greek, Archimedes - a mathematical genius centuries ahead of his time. Hidden for a millennium in a middle eastern library, it has been written over, broken up, painted on, cut up and re-glued. But in the nick of time scientists have saved the precious, fragile document, and for the first time it is revealing just how revolutionary Archimedes' ideas were. If it had been available to scholars during the Renaissance, we might have reached the Moon over a hundred years ago.

Our icy adventure begins with host Dr. Iain Stewart in the Alps, where he goes down an ice crevasse to show viewers how snowfall develops into expansive masses. Then, we see how ice can shape the earth's topography giving rise to features like Yosemite National Park and Manhattan Island, in NY. Finally, journey to Greenland and see how ice sheets and glaciers are melting at a phenomenal rate that is likely to accelerate over the coming years, changing the world as we know it.

The BBC has made an extraordinary new documentary, presented by Sir David Attenborough, which will reveal the discovery of a fossilised skeleton that may be a vital ‘missing link’ in human evolution. The centrepiece of the programme is the unveiling of the first-ever complete skeleton of an extinct animal called an adapid

The Bronze Age covers 2,000 years of history in the Aegean/Mediterranean, Egypt and Near East from roughly 3000 BC to 1000 BC. New animations produced by Pixeldust include the reconstruction of four ancient capitals, including the Egyptian city of Thebes and the early Greek capital of Mycenae. What singled out this period and the new societies and cities that emerged? The development of formal writing is one among several important factors.