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.

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.

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.

Meet Tim Raue, the lauded German chef who went from gang life to fine dining. After leaving the streets, he defied all odds with explosive creativity, but also the knack for running several lucrative restaurants. For a high school dropout once told he could only be a house painter, gardener, or cook, it's a culinary story that does seem to be written in the Michelin stars.

Writing itself is 5,000 years old, and for most of that time words were written by hand using a variety of tools. The Romans were able to run an empire thanks to documents written on papyrus. Scroll books could be made quite cheaply and, as a result, ancient Rome had a thriving written culture. With the fall of the Roman Empire, papyrus became more difficult to obtain. Europeans were forced to turn to a much more expensive surface on which to write: Parchment. Medieval handwritten books could cost as much as a house, they also represent a limitation on literacy and scholarship.
No such limitations were felt in China, where paper had been invented in the second century. Paper was the foundation of Chinese culture and power, and for centuries how to make it was kept secret. When the secret was out, paper mills soon sprang up across central Asia. The result was an intellectual flourishing known as the Islamic Golden Age. Muslim scholars made discoveries in biology, geology, astronomy and mathematics. By contrast, Europe was an intellectual backwater.
That changed with Gutenberg’s development of movable type printing. The letters of the Latin alphabet have very simple block-like shapes, which made it relatively simple to turn them into type pieces. When printers tried to use movable type to print Arabic texts, they found themselves hampered by the cursive nature of Arabic writing. The success of movable type printing in Europe led to a thousand-fold increase in the availability of information, which produced an explosion of ideas that led directly to the European Scientific Revolution and the Industrial Revolution that followed.