David Attenborough discovers the plants that have evolved to shed their dependency on water enabling them to survive in the driest environments. The story begins at midnight in midsummer as David steps into the Princess of Wales Conservatory to witness the extraordinary nocturnal blooming of a cactus. The queen of the night, with its giant flowers, is the centre piece of a stunning symphony of cacti blooms that burst open in the desert (and at Kew) at night. In a mesmerizing 3D slow motion sequence, we discover the extraordinary connections between cacti and their natural pollinators: bats. As the sun rises, David meets other amazing plants. Species like the century plant, the Agave franzosini, which grows steadily for over 50 years, only to then flower itself to death with one mighty telegraph pole sized bloom which literally bursts out of the roof of Kew’s green house.

Bladderwort utricularia is a pond-dweller that is among the fastest known, its traps snapping shut in less than a millisecond. As the seasons change, David demonstrates how plants operate on a different time scale to us; how they modify their lives according to the time of year. We discover insects’ hidden links with plants, both as pests and pollinators. UV-sensitive 3D cameras reveal the invisible alter-ego of plants and their flowers’ mesmerizing patterns; a parallel-dimension of strange colours and stunning patterns through which plants communicate with them. With the aid of visual effects, David steps among the swirling vortices of plant scent; communication signals with which plants are inextricably plugged in to the natural world. And using a tuning fork, he demonstrates how plants and insects can even communicate with music. As autumn envelopes the Gardens, fungi reveal themselves not as the enemies of plants but their vital allies. In Kew’s atmospheric Fungarium, David discovers a specimen that has the power of mind control and another that lives underground where it has grown to be so big it can be counted as the largest single organism on the planet. It is 6 times bigger than Kew Gardens itself.

The third episode is devoted to the ways in which plants reproduce. Pollen and a stigma are the two components needed for fertilisation. Most plants carry both these within their flowers and rely on animals to transport the pollen from one to the stigma of another. To do this, they attract their couriers with colour, scent and nectar. It isn't just birds that help pollination: some mammals and reptiles also do so. However, it is mostly insects that are recruited to carry out the task. To ensure that pollen is not wasted by being delivered to the wrong flower, some species of plant have developed exclusive relationships with their visitors, and the gentian and its attendant carpenter bees is one example. Since pollen can be expensive to produce in terms of calories, some plants, such as orchids, ration it by means of pollinia and a strategically placed landing platform. Other orchids offer no reward for pollination, but instead mislead their guests by mimicking their markings and aroma, thus enticing males to 'mate' with them (Pseudocopulation). The most extreme fertilisation method is one of imprisonment, and one plant that uses it is the dead horse arum. It is often found near gull colonies, and mimics the appearance and smell of rotting flesh. Blow-flies are attracted to it, and are forced to stay the night before being allowed to depart in the morning, laden with pollen. Finally, Attenborough introduces the world's largest inflorescence: that of the titan arum.

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.

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.

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