Volcanoes are one of nature’s most awesome and destructive forces, but they are also the life force and architect of our planet. They can raise up great mountains and create new land, or they can level cities and destroy entire civilizations. They provide a glimpse of the power of Earth’s internal heat source, without which it would have become a dead planet millions of years ago. In this episode, Iain takes us on a journey to some of the most dramatic places on Earth, starting in Ethiopia.

Beneath Yellowstone National Park, lies the biggest volcano on Earth. An eruption in the past was so big it plunged the earth into a volcanic winter that lasted years. A super-eruption would be more than millions of Hiroshima bombs going off all at once. It would be even worse than an asteroid impact: Entire cities lost beneath ash, people and animals crushed alive, power networks destroyed, sun dimmed across the globe, harvests failed, widespread famine. Could this nightmare really happen? We will use the latest scientific data to uncover the danger beneath us, as we see our planet like never before.

The film intends to illustrate the birth and death of an undiscovered universe, with powerful images, from the Big Bang to the Mesozoic era and through the present and beyond. Based on a project conceived decades ago, the documentary is highly experimental and perhaps Terrence Malick's most ambitious film, described by the director himself as 'one of my greatest dreams.'

'Blood Brothers' follows the lives of two species, Paranthropus boisei and Homo habilis who embody two alternative ways of ape-man life. Although heavyset, with distinctive gorilla-like faces, the boisei are gentle characters. They live within a strict social structure and are led by a dominant male whose strength and power holds the group together. The habilis have taken a different approach to survival. They don't have the specialisms of the boisei but instead have developed into the archetypal jack-of-all-trades, inquisitive scavengers prepared to try almost anything to survive. Tough, active, gregarious and noisy, they are always on the move and always alert to the possibility of a meal. But in the near drought of the dry season the habilis are struggling. It seems as if their way of life cannot help them when conditions are tough.

Nearly half a million years ago, the most advanced human yet roams Europe. Strong and powerful, Homo heidelbergensis are fierce hunters, use sophisticated tools and live in close-knit family groups. Over 200,000 years they become split into two populations by extremes of weather and environment and evolve separately into two very different species. In the North are the Neanderthals, whose physical power and resilience is the key to surviving in ice age Northern Europe. About 140,000 years ago, Africa is in the grip of a devastating drought, and something remarkable has happened to the descendants of heidelbergensis who live there. The combination of environment and chance has bred in them a unique ability that will change the course of human history. It will be this small band of southern survivors, perhaps numbering just a few tens of thousands, who will come to dominate the world and be known as Homo sapiens.

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.