Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

The next instalment focuses on dietary needs and how different species have evolved beaks to suit their individual requirements. The latter come in a multitude of forms. Blue tits and goldfinches have beaks akin to tweezers, with which to extract seeds, while the hawfinch's razor-like bill can deal with a cherry-stone. However, the crossbill is the only finch that can twist its mandibles in opposite directions. Jays store acorns for winter by burying them in the ground, whereas woodpeckers can keep up to 60,000 of them in one tree trunk. Sap is also desirable, and there are a variety of methods used to obtain it. The hoatzin is the only specialised leaf-eater, and accordingly has a digestive system more akin to that of cattle. Plants recruit birds to aid pollination, and offer nectar as a reward. Hummingbirds eat little else, and the sword-bill's beak is the longest of any bird in relation to its body. Insects are also highly prized, and Galapagos finches are shown to possess some ingenuity as they not only strip bark, but also use 'tools' to reach their prey. Crows are hailed as being among the most intelligent birds, and one is shown using a twig to spear a grub within a fallen log. The robin is an opportunist, and Sir Attenborough observes one seizing morsels as he digs a patch of earth. In South America, a cattle tyrant sits atop an obliging capybara and uses its vantage point to spot passing food that may be dislodged by its grazing partner.

By the time he died in 1931, Thomas Alva Edison was one of the most famous men in the world. The holder of more patents than any other inventor in history, Edison had achieved glory as the genius behind such revolutionary inventions as sound recording, motion pictures, and electric light. Edison's curiosity led him to its cutting edge. With just three months of formal schooling, he took on one seemingly impossible technical challenge after another, and through intuition, persistence, and a unique team approach to innovation, invariably solved it." Driven and intensely competitive, Edison was often neglectful in his private life and could be ruthless in business. Challenged by competition in the industry he'd founded, Edison launched an ugly propaganda campaign against his rivals, and used his credibility as an electrical expert to help ensure that high-voltage electrocution became a form of capital punishment. Edison explores the complex alchemy that accounts for the enduring celebrity of America's most famous inventor, offering new perspectives on the man and his milieu, and illuminating not only the true nature of invention, but its role in turn-of-the-century America's rush into the future.

Inside the world-renowned physics laboratory Fermilab, a team of scientists are constructing an audacious experiment to hunt for a mysterious new ‘ghost’ neutrino. If they find it, this could transform our understanding of the nature and fabric of our universe. The problem is, these tiny particles are almost impossible to detect.
Elsewhere, physicists conduct experiments in some of the most extreme environments on the planet: from deep mine shafts in South Dakota to vast ice fields at the South Pole. In these unlikely places supersized neutrino detectors hope to unlock the universe’s deepest secrets. Could neutrinos overturn the most precise theory of particle physics that humans have ever written down? Could they even be a link to a hidden realm of new particles that permeate the cosmos – so called dark matter? Scientists at Fermilab are edging towards the truth.

This episode examines those birds whose sustenance comes from flesh and their methods of hunting. In New Zealand, Sir Attenborough observes Keas, parrots that do not eat meat exclusively, raiding a shearwater's burrow for a chick. However, it is the dedicated birds of prey, such as owls, buzzards, eagles, falcons and vultures, to which much of the programme is devoted. In order to spot and pursue their victims, senses of sight and hearing are very acute. Vultures are the exception, in that they eat what others have left, and once a carcass is found, so many birds descend on it that the carrion seems submerged beneath them. The Turkey Vulture is an anomaly within its group, as it also has a keen sense of smell. Eagles defend their territory vigorously, and a pair of sea eagles are shown engaging in an aerial battle. The Galápagos Hawk hunts Marine Iguanas, but can only do so when its quarry is vulnerable, during the breeding season. The African Harrier Hawk has adapted to extracting burrowing animals by virtue of an especially long, double-jointed pair of legs. By contrast, a shrike is not equipped with the requisite sharp beak and talons needed for butchery, and so dismembers its kill by impaling it on the thorns of acacias. The Lammergeier eats bones, and will drop them on to rocks from a great height in order to break them down to a digestible size. Also featured are the Eurasian Sparrowhawk, Goshawk and Peregrine Falcon.

In the final challenge of the game of life, raising offspring is the ultimate prize. Continuing the line through the next generation, is the next best thing to immortality. But it’s far from easy... Some parents must risk their own lives for their offspring.