This four-part British television series outlines aspects of the history of mathematics. Written and presented by University of Oxford professor Marcus du Sautoy, it is a co-production between the Open University and the BBC. In the first episode, Marcus du Sautoy in Egypt uncovers use of a decimal system based on ten fingers of the hand and discovers that the way we tell the time is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a counting tool into the analytical subject of today. A controversial figure, Pythagoras’ teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers. As well as his work on the properties of right angled triangles, Pythagoras developed another important theory after observing musical instruments. He discovered that the intervals between harmonious musical notes are always in whole number intervals.

Intelligence and adaptability allow primates to tackle the many challenges of life, and this is what makes our closest relatives so successful. This resourcefulness has enabled primates to conquer an incredible diversity of habitat. Hamadryas baboons live on the open plains of Ethiopia in groups up to 400 strong. Strength in numbers gives them some protection from potential predators. But, should their path cross with other baboon troops, it can lead to all-out battle, as males try to steal females from one another, and even settle old scores. Japanese macaques are the most northerly-dwelling primates and they experience completely different challenges. Some beat the freezing conditions by having access to a thermal spa in the middle of winter. But this privilege is only for those born of the right female bloodline. For western lowland gorillas, it's the male silverback that leads his family group in the rich forests of the Congo basin. He advertises his status to all with a powerful chest-beating display. Most primates are forest dwellers, and one of the strangest is the tarsier – the only purely carnivorous primate. As it hunts for insects the tarsier leaps from tree to tree in the dead of night, using its huge forward-facing eyes to safely judge each jump. Good communication is essential for success in primate society.

The final episode explores dinosaurs' extraordinary ability to survive. Featured dinosaurs include the bizarre magyarosaurus, which lived in the shadow of the biggest flying animal - hatzegopteryx - and showed an amazing adaptation to island life; and the weird nothronychus, a carnivore that gave up meat eating. This astonishing capacity to evolve into ever more diverse and bizarre forms meant that dinosaurs not only spread throughout the world, but also dominated life upon it for more than 160 million years. It was only an unprecedented extraterrestrial event that finally saw the end of planet dinosaur.

Sagan discusses comets and asteroids as planetary impactors, giving recent examples of the Tunguska event and a lunar impact described by Canterbury monks in 1178. It moves to a description of the environment of Venus, from the previous fantastic theories of people such as Immanuel Velikovsky to the information gained by the Venera landers and its implications for Earth's greenhouse effect. The Cosmos Update highlights the connection to global warming.

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.

There is an extraordinary range of temperatures in the universe. This program examines the extreme lower temperature range, the temperature we live in and below, explaining how cold is essential for the formation of habitats suitable for life. Explore icy planets and moons, discover the role of cold in the Universe, and learn about the importance of ice to the development of habitable worlds.