the final episode deals with plants that live in hostile environments. Attenborough visits Ellesmere Island, north of the Arctic Circle, to demonstrate that even in a place that is unconducive to life, it can be found. Algae and lichens grow in or on rock, and during summer, when the ice melts, flowers are much more apparent. However, they must remain close to the ground to stay out of the chilling wind. In the Tasmanian mountains, plants conserve heat by growing into 'cushions' that act as solar panels, with as many as a million individual shoots grouped together as one. Others, such as the lobelia in Mount Kenya, have a 'fur coat' of dense hairs on their leaves. The saguaro cactus in the Sonoran Desert flourishes because of its ability to retain vast amounts of water, which can't be lost through leaves because it has none. Many desert dwellers benefit from an accelerated life cycle, blooming rapidly within weeks after rainfall. Conversely, Mount Roraima is one of the wettest places on Earth. It is a huge sandstone plateau with high waterfalls and nutrients are continuously washed away, so plants have to adapt their diet if they are to survive. A bladderwort is shown invading a bromeliad. Inhabitants of lakes have other problems to contend with: those that dominate the surface will proliferate, and the Amazon water lily provides an apt illustration. Attenborough ends the series with an entreaty for the conservation of plant species.

The film reveals the secret story behind one of the greatest intellectual feats of World War II, a feat that gave birth to the digital age.
In 1943 Bill Tutte, a 24-year-old maths student and a GPO engineer called Tommy Flowers combined to hack into Hitler's personal super code machine - not Enigma but an even tougher system, which he called his 'secrets writer'. Their break turned the Battle of Kursk, powered the D-day landings and orchestrated the end of the conflict in Europe. But it was also to be used during the Cold War - which meant both men's achievements were hushed up and never officially recognised.

We can survive for weeks without food, but only days without water: it is the essential element of life. Yet many millions of us live in parched deserts around the world. In the second episode of Human Planet, we discover how the eternal quest for water brings huge challenges - and ingenious solutions - in the driest places on Earth. Battling through a sand storm in Mali, Mamadou must get his cows to a remote lake but desert elephants have arrived first. Can he find a safe way through the elephant blockade? Alone for weeks on end, Tubu women and children navigate the endless dunes of the Sahara. How does young Shede know where to find the last oasis, three days walk across the sea of sand? At the height of the drought we witness a spectacular frenzy: two thousand men rushing into Antogo Lake to catch the fish trapped by the evaporating water. When the rain finally arrives in the desert it's a time for flowering and jubilation - and love. The Wodaabe men of Niger put on make-up for an intoxicating courtship dance and beauty contest.

Go with us on a mathematical mystery tour, a provocative exploration of math's astonishing power across the centuries. We discover math's signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the successful landing of rovers on Mars. But where does math get its power?" Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, all leading to the ultimate riddle: Is math an invention or a discovery? Humankind's clever trick, or the language of the universe? Whether we think we're good with numbers or not, we all use math in our daily lives. The Great Math Mystery sheds fascinating light on how math works in our brains and ponders the ultimate mystery of why it works so well when decoding the universe.

In the second episode, Professor Iain Stewart discovers how flowers have transformed our planet. He journeys to the remote islands of the South Pacific to track down the earliest flowers. In the deserts of Africa and rainforests of Vietnam, he sees how they brought brilliant colour to the most barren landscapes and sculpted the earth itself. And he learns how they drove the evolution of all animals - kick-starting our human story.

The fifth programme explores the alliances formed between the animal and plant worlds. Attenborough dives into Australia's Great Barrier Reef and contrasts the nocturnal feeding of coral, on microscopic creatures, with its daytime diet of algae. Some acacias are protected by ants, which will defend their refuge from any predator. Besides accommodation, the guards are rewarded with nectar and, from certain species, protein for their larvae as well. Fungi feed on plants but can also provide essential nutriment to saplings (Mycorrhiza). The connection is never broken throughout a tree's life and a quarter of the sugars and starches produced in its leaves is channelled back to its fungal partners. Meanwhile, fungi that feed on dead wood leave a hollow trunk, which also benefits the tree. Orchids enjoy a similar affiliation. Lichens are the product of a relationship between fungi and a photosynthetic associate, usually algae. They are extremely slow-growing, and a graveyard is the perfect location to discover their exact longevity. Mistletoe is a hemiparasite that obtains its moisture from a host tree, while using own leaves to manufacture food. Its seeds are deposited on another by the mistletoe tyrannulet, following digestion of the fruit. The dodder (Cuscuta) is also parasitic, generally favouring nettles, and siphons its nourishment through periodic 'plugs' along its stem. The rafflesia has no stem or leaves and only emerges from its host in order to bloom — and it produces the largest single flower: one metre across.