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This episode explores the nature of the greenhouse effect (discovered by Joseph Fourier and Svante Arrhenius), and the evidence demonstrating the existence of global warming from humanity's influence. Tyson begins by describing the long-term history of the planet Venus; based on readings from the Venera series of probes to the planet, the planet had once had an ocean and an atmosphere, but due to the release of carbon dioxide from volcanic eruptions, the runaway greenhouse effect on Venus caused the surface temperatures to increase and boiled away the oceans. Tyson then notes the delicate nature of the amount of carbon dioxide in the atmosphere can influence Earth's climate due to the greenhouse effect, and that levels of carbon dioxide have been increasing since the start of the 20th century. Evidence has shown this to be from mankind's consumption of oil, coal, and gas instead of from volcanic eruptions due to the isotopic signature of the carbon dioxide. The increase in carbon dioxide has led to an increase in temperatures, in turn leading to positive feedback loops of the melting polar ice caps and dethawing of the permafrost to increase carbon dioxide levels. Tyson then notes that humans have discovered means of harvesting solar power, such as Augustin Mouchot's solar-driven motor in the 19th century, and Frank Shuman's solar-based steam generator in the 1910's. Tyson points out that in both cases, the economics and ease of using cheap coal and oil caused these inventions to be overlooked at the time. Today, solar and wind-power systems would be able to collect enough solar energy from the sun easily. Tyson then compares the motivation for switching to these cleaner forms of energy to the efforts of the Space race and emphasizes that it is not too late for humanity to correct its course.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

Dr Michael Scott looks at the dramatic decline of Athens and the remarkable triumph and transformation of theatre. During the 4th century BC Athens would lose its Empire, its influence and even its democracy. But theatre, that most Athenian of inventions, would thrive, spreading throughout the Greek world and beyond and giving rise to a new kind of comedy, one so popular and prevalent that it is still at the heart of our comedy today.

The story of Nikola Tesla, the great scientist, visionary, and inventor who gave the world alternating current electricity, as well as being the father of radio. The film tells the story of this man's astonishing genius, his visions and inventions. Tesla's own scientific and autobiographical writings, as well as archival photographs and re-enactments are used to tell the story. A native of Austro-Hungary, Tesla came to America in 1884. Working first with Edison, the two inventors fell out over Edison's insistence on using direct current. Tesla took his alternating current vision to Westinghouse. Tesla worked to unlock the secrets of energy and electricity. The film follows Tesla's exploits and eccentricities, which made him a darling of the press. Largely forgotten today in spite of the great debt the modern world owes him, the film pays tribute to this overlooked genius

In this episode, Michael demonstrates how our society is built on our search to find the answer to what makes up everything in the material world. This is a story that moves from the secret labs of the alchemists and their search for gold by the stone of the philosophers to the creation of the world's first synthetic dye - Purple - and onto the invention of the transistor. This quest may seem abstract and highly theoretical. Yet it has delivered the greatest impact on humanity. By trying to answer this question, scientists have created theories from elements to atoms, and the strange concepts of quantum physics that underpin our modern, technological world.

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.