Mathematics

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.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand. It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here? In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science - how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder? It's a mindbending, counterintuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern. And the best thing is that one doesn't need to be a scientist to understand it. The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans - after watching this film you'll never be able to look at the world in the same way again.

brilliant mathematicians whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death. Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

Do you make your own luck, or does luck make you? Some scientists believe luck is strictly a matter of statistics and probabilities…but others believe unseen forces are at work, and randomness is built into every particle of the universe. We’ll find luck, good and bad, in casinos, basketball courts, genetics labs and the subatomic world. How much does the genetic lottery rule your fate? Are lucky streaks and unfortunate accidents merely our own minds fooling us? It’s a scientific journey that will radically revise your understanding of the laws of nature and the workings of the human brain.

The Pythagorian philosopher Plato hinted enigmatically that there was a golden key that unified all of the mysteries of the universe. It is this golden key that we will return to time and again throughout our exploration. The golden key is the intelligence of the logos, the source of the primordial om. One could say that it is the mind of God. With our limited senses we are observing only the outer manifestation of the hidden mechanics of self similarity. The source of this divine symmetry is the greatest mystery of our existence.