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.

An unsettling yet visually fascinating documentary presenting the history of nuclear weapons development and testing between 1945 until 1963. Narrated by William Shatner, features extremely rare film segments from top secret government archives and startling footage of nuclear bomb tests conducted by Great Britain and China, plus the largest atomic explosion ever created by Russia, and de-classified U.S. footage released to the public as recent as May, 2006. Whether being exploded under the ocean, suspended by a balloon, shot from a cannon or even detonated in space, these weapons are capable of devastating destruction - the quality of these images is as startling as are remarkable.

Fourth episode examines how plants either share environments harmoniously or compete for dominance within them. Attenborough highlights the 1987 hurricane and the devastation it caused. However, for some species, it was that opportunity for which they had lain dormant for many years. The space left by uprooted trees is soon filled by others who move relatively swiftly towards the light. The oak is one of the strongest and longest-lived, and other, lesser plants nearby must wait until the spring to flourish before the light above is extinguished by leaves. Tropical forests are green throughout the year, so brute force is needed for a successful climb to the top of the canopy: the rattan is an example that has the longest stem of any plant. As its name suggests, the strangler fig 'throttles' its host by growing around it and cutting off essential water and light. Some can take advantage of a fallen tree by setting down roots on the now horizontal trunk and getting nutriment from the surrounding moss and the fungi on the dead bark. The mountain ash (eucalyptus regnans) grows so tall, that regeneration becomes a considerable problem. It is easily flammable, so its solution is to shed its seeds during a forest fire and sacrifice itself. It therefore relies on the periodic near-destruction of its surroundings in order to survive. Attenborough observes that catastrophes such as fire and drought, while initially detrimental to wildlife, eventually allow for deserted habitats to be reborn.

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.

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.

Sir David Attenborough reveals plants as they have never been seen before - on the move and dangerously devious. About the major problems of life - growing, finding food, reproduction - and the varied ways plants have evolved to solve it. Filmed from the plant's point of view, using computer animations, fibre-optics and unique time-lapse photography. The first episode looks at how plants are able to move". The bramble is an aggressive example: it advances forcefully from side to side and, once settled on its course, there is little that can stand in its way. An altogether faster species is the birdcage plant, which inhabits Californian sand dunes. When its location becomes exposed, it shifts at great speed to another one with the assistance of wind — and it is this that allows many forms of vegetation to distribute their seeds. While not strictly a plant, the spores of fungi are also spread in a similar fashion. One of the most successful (and intricate) flowers to use the wind is the dandelion, whose seeds travel with the aid of 'parachutes'. They are needed to travel miles away from their parents, who are too densely packed to allow any new arrivals. Trees have the advantage of height to send their seeds further, and the cottonwood is shown as a specialist in this regard. The humidity of the tropical rainforest creates transportation problems, and the liana-species Alsomitra macrocarpa is one plant whose seeds are aerodynamic 'gliders'. Some, such as those of the sycamore, take the form of 'helicopters', while others, such as the squirting cucumber release their seeds by 'exploding'. Water is also a widely used method of propulsion. The tropical sea bean Entada gigas has one of the biggest fruits of all plants and is dispersed by water streams. However, most plants use living couriers, whether they be dogs, humans and other primates, ants or birds, etc., and to that end, they use colour and smell to signify when they are ripe for picking.