The second programme deals with the mechanics of flight. Getting into the air is by far the most exhausting of a bird's activities, and Sir Attenborough observes shearwaters in Japan that have taken to climbing trees to give them a good jumping-off point. The albatross is so large that it can only launch itself after a run-up to create a flow of air over its wings. A combination of aerodynamics and upward air currents (or thermals), together with the act of flapping or gliding is what keeps a bird aloft. Landing requires less energy but a greater degree of skill, particularly for a big bird, such as a swan. Weight is kept to a minimum by having a beak made of keratin instead of bone, a light frame, and a coat of feathers, which is maintained fastidiously. The peregrine falcon holds the record for being fastest in the air, diving at speeds of over 300 km/h. Conversely, the barn owl owes its predatory success to flying slowly, while the kestrel spots its quarry by hovering. However, the true specialists in this regard are the hummingbirds, whose wings beat at the rate of 25 times a second. The habits of migratory birds are explored. After stocking up with food during the brief summer of the north, such species will set off on huge journeys southwards. Some, such as snow geese, travel continuously, using both the stars and the sun for navigation. They are contrasted with hawks and vultures, which glide overland on warm air, and therefore have to stop overnight.

In the 1960s and 1970s a generation of Mexican Americans, frustrated by persistent discrimination and poverty, find a new way forward, through social action and the building of a new "Chicano" identity. The movement is ignited when farm workers in the fields of California, led by Cesar Chavez and Dolores Huerta, march on Sacramento for equal pay and humane working conditions. Through plays, poetry and film, Luis Valdez and activist Corky Gonzalez create a new appreciation of the long history of Mexicans in the South West and the Mestizo roots of Mexican Americans. In Los Angeles, Sal Castro, a schoolteacher, leads the largest high school student walkout in American history, demanding that Chicano students be given the same educational opportunities as Anglos. In Texas, activists such as Jose Angel Gutierrez, create a new political party and change the rules of the electoral game. By the end of the 1970s Chicanos activism and identity have transformed what it means to be an American. Chicano and Latino studies are incorporated into school curriculum; Latinos are included in the political process.

In late Cretaceous Canada, in what will be known as Dinosaur Provincial Park, a Daspletosaurus stalks a Chasmosaurus in a forest, but loses the element of surprise and is forced to retreat. The Chasmosaurus comes across a younger Daspletosaurus, before being ambushed by a group of the tyrannosaurids. The episode then cuts to the high Arctic, where Edmontosaurus are hunted by a large species of Troodon. The theropods attack at night, separating a juvenile from the herd and severely wounding it, only to be driven away by an adult. In the morning, they return to eat the carcass of the juvenile, which died during the night. The episode returns to the Daspletosaurus, who chase and bring down the Chasmosaurus. The larger adults bully the youngsters off the carcass, forcing them to wait until they have finished. The episode then cuts to Madagascar, where a mother Majungasaurus (an Abelisaurid) and her two offspring chase a group of Rahonavis off a carcass. However, they are temporarily driven off themselves by a male Majungasaurus. But, after he steals some food from one of the young, the female attacks him, before she and her young cannibalise his body. The episode returns once again to North America, where the Daspletosaurus are waiting for the annual migration of Centrosaurus. They attack during a rainstorm, killing some of the ceratopsians. The Centrosaurus make it to a flooded river and begin to swim across, and although many make it to the other side, some are caught by giant crocodilians or are severely wounded by floating debris and thus drown, or drown for unseen reasons. In the morning, the carcasses attract scavengers, including the Daspletosaurus. A montage is then shown of Daspletosaurus and Majungasaurus, the narrator saying that together, the tyrannosaurids and abelisaurids were the last of the killer dinosaurs.

The magnificent ancient city of pyramids at Caral in Peru is a thousand years older than the earliest known civilisation in the Americas and, at 2,627 BC, is as old as the pyramids of Egypt. Many now believe it is the fabled missing link of archaeology - a 'mother city'. If so, then these extraordinary findings could finally answer one of the great questions of archaeology: why did humans become civilised?" For over a century, archaeologists have been searching for what they call a mother city. Civilisation began in only six areas of the world: Egypt, Mesopotamia, India, China, Peru and Central America. In each of these regions people moved from small family units to build cities of thousands of people. They crossed the historic divide, one of the great moments in human history. Why? To find the answer archaeologists needed to find a mother city - the first stage of city-building. Caral, is so much older than anything else in South America that it is a clear candidate to be the mother city. It also is in pristine condition. Nothing has been built on it at all. Instead laid out before the world is an elaborate complex of pyramids, temples, an amphitheatre and ordinary houses. Scientists developed a number of theories. Some said it was because of the development of trade, others that it was irrigation. Some even today believe it was all because of aliens. Gradually an uneasy consensus emerged. The key force common to all civilisations was warfare. Crucially, there is not the faintest trace of warfare at Caral; no battlements, no weapons, no mutilated bodies. Instead, Ruth's findings suggest it was a gentle society, built on commerce and pleasure. In one of the pyramids they uncovered beautiful flutes made from condor and pelican bones. They have also found evidence of a culture that took drugs and perhaps aphrodisiacs. Most stunning of all, they have found the remains of a baby, lovingly wrapped and buried with a precious necklace made of stone beads.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

The Pythagorean Theorem is simple: x2 + y2 = z2. In this form, the equation can be solved. But what if the 2 is replaced with any positive integer greater than 2? Would the equation still be solvable? More than 300 years ago, amateur mathematician Pierre de Fermat said no, and claimed he could prove it. Unfortunately, the book margin in which he left this prophecy was too small to contain his thinking. Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. Andrew Wiles methodically worked in near isolation to determine the proof for this seemingly simple equation.