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.

In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

An astonishing close encounter with some of the most exotic creatures inhabiting the hidden depths. In the realm of the giant octopus, the rainbow nudibranch (sea slug), and the Scorpion fish, viewers become a fearless undersea explorers, discovering the strange and unusual partnerships these 'star wars' creatures forge to ensure their survival, and learning how this cooperation allows life in this enchanting world to flourish. Filmmaker Howard Hall guides an astonishing adventure. Johnny Depp and Kate Winslet narrate as Green Sea Turtles gather so Surgeonfish can strip harmful algae from their shells. A Humboldt Squid changes color four times per second like a flashing strobe light. A Mantis Shrimp’s claws have the speed of a bullet in battling a hungry octopus. Brace yourself to be submerged in a wondrous new dimension.

The biggest rabbit-hole in history: the search of the smallest thing in the Universe. It is a journey where things don't just become smaller but also a whole lot weirder. Scientists hope to catch a glimpse of miniature black holes, multiple dimensions and even parallel Universes. As they start to explore this wonderland, where nothing is quite what it seems, they may have to rewrite the fundamental laws of time and space.

Beginning with the origins of the universe in the Big Bang, Sagan describes the formation of different types of galaxies and anomalies such as galactic collisions and quasars. The episodes moves further into ideas about the structure of the Universe, such as different dimensions (in the imaginary Flatland and four-dimensional hypercubes), an infinite vs. a finite universe, and the idea of an oscillating Universe (similar to that in Hindu cosmology). The search into other ideas such as dark matter and the multiverse is shown, using tools such as the Very Large Array in New Mexico. Cosmos Update shows new information about the odd, irregular surfaces of galaxies and the Milky Way perhaps being a barred spiral galaxy

They are the most powerful objects in the universe. Nothing, not even light, can escape the gravitational pull of a black hole. Astronomers now think there are billions of them out in the cosmos, swallowing up planets, even entire stars in violent feeding frenzies. New theoretical research into the twisted reality of black holes suggests that three-dimensional space could be an illusion. That reality actually takes place on a two-dimensional hologram at the edge of the universe.