'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.

In 1914, Russia entered World War I in response to Austria-Hungary's declaration of war on Russia's ally Serbia. This was fought across multiple fronts while isolated from its allies. The Battle of Tannenberg, where the entire Russian Second Army was annihilated, cast an ominous shadow over the empire's future. The already-existing public distrust of the regime was deepened by the rising costs of the war and rumours of corruption. World War I takes Nicholas to the front. Back home, outrage grows over high casualties and Alexandra and Rasputin's political intrigues.

Washington, D.C. is in many ways a city of extremes. Starland Vocal Band, Marvin Gaye, Duke Ellington, Nils Lofgren, Chuck Brown, Henry Rollins, Fugazi and Trouble Funk all hail from D.C. In the early '70s, the music style go-go originated here, and has remained a local craze ever since. Dave Grohl sits down with Trouble Funk's Big Tony Fisher to talk about go-go, and explores its origins with Chuck Brown, the genre's undisputed godfather.
He also chats with Don Zientara, owner of Inner Ear Studios, which the Virginia-raised Grohl says 'produced the entire soundtrack of my youth,' as well as with members of the harDCore band Bad Brains and Ian MacKaye of Teen Idles, Minor Threat and Fugazi, who all recorded at Inner Ear over the decades. The song 'The Feast and the Famine' is recorded during this episode.

Garrett McNamara and his team return to Nazaré for another season of surfing. The team struggles through a number of accidents and challenges but eventually develop a set of safety procedures that enable them to surf Nazare's wave with less chance of injury or death. The struggles pay off when McNamara catches a nearly 80 foot tall wave that catapults him to international fame and makes him the holder of the world record for largest wave surfed.

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.