Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

An informative and ambitious journey exploring how the evolution of scientific understanding is intimately interwoven with society's historical path. The Story Of Science tells the forces that came together to create scientific knowledge; the practical business of making instruments and machines; the great forces of history – revolutions, voyages of discovery and artistic movements – and the dogged determination of scientists and experimenters. This is the story of how scientific ideas shaped the modern world and how science made history. Michael Mosley begins the first episode with the story of one of the great upheavals in human history - how we came to understand that our planet was not at the centre of everything in the cosmos, but just one of billions of bodies in a vast and expanding universe. He reveals the critical role of medieval astrologers in changing our view of the heavens, and the surprising connections to the upheavals of the Renaissance, the growth of coffee shops and Californian oil and railway barons. Michael shows how important the practical skills of craftsmen have been to this story and finds out how Galileo made his telescope to peer at the heavens and by doing so helped change our view of the universe forever.

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.

Andrew Graham-Dixon examines early Christian art and the reasons for its evolution during the Renaissance. He also reveals just how far modern artists have been influenced by the pre-perspective view of the world.

The episode begins with Tyson describing how pattern recognition manifested in early civilization as using astronomy and astrology to predict the passing of the seasons, including how the passage of a comet was often taken as an omen. Tyson continues to explain that the origin of comets only became known in the 20th century due to the work of Jan Oort and his hypothesis of the Oort cloud. Tyson then continues to relate the collaboration between Edmond Halley and Isaac Newton in the last part of the 17th century in Cambridge. The collaboration would result in the publication of Philosophiæ Naturalis Principia Mathematica, the first major work to describe the laws of physics in mathematical terms, despite objections and claims of plagiarism from Robert Hooke and financial difficulties of the Royal Society of London. Tyson explains how this work challenged the prevailing notion that God had planned out the heavens, but would end up influencing many factors of modern life, including space flight. Tyson further describes Halley's contributions including determining Earth's distance to the sun, the motion of stars and predicting the orbit of then-unnamed Halley's Comet using Newton's laws. Tyson contrasts these scientific approaches to understanding the galaxy compared to what earlier civilizations had done, and considers this advancement as mankind's first steps into exploring the universe. The episode ends with an animation of the Milky Way and Andromeda galaxies' merging based on the principles of Newton's laws.

Zeitgeist Addendum attempts to locate the root causes of this pervasive social corruption, while offering a solution. This solution is not based on politics, morality, laws, or any other 'establishment' notions of human affairs, but rather on a modern, non-superstitious based understanding of what we are and how we align with nature, to which we are a part. The work advocates a new social system which is updated to present day knowledge, highly influenced by the life long work of Jacque Fresco and The Venus Project.