Five mathematical biographies, looking at the histories, uses and idiosyncrasies of some very special numbers: 1, 2, 6, 1729 & G.

Simon Singh investigates five numbers that lie at the heart of some of the trickiest problems in mathematics including four, seven and the largest prime.

Simon Singh takes a quirky look at five of the most important numbers in mathematics: zero, pi, the golden ratio, the imaginary number 'i' and infinity.

Tim Harford explains - and sometimes debunks - the numbers and statistics used in political debate, the news and everyday life.

Mathematician Marcus du Sautoy tours the world to find some of his favourite forms: the cube, the pyramid, the sphere, the bagel and the blob.

Professor of Mathematics Marcus du Sautoy reveals the personalities behind the calculations and argues that mathematics is the driving force behind modern science.

Archimedes Melvyn Bragg and guests discuss Archimedes. How did this Greek mathematician in the third century BC calculate Pi?

Calculus Examining the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented an astonishingly powerful new mathematical tool - calculus.

Fibonacci Sequence In the 19th century the Fibonacci Sequence began to crop up time and again among the structures of the natural world, from the spirals on a pinecone to the petals on a sunflower.

Gödel's Incompleteness Theory Gödel proved that there were some problems in maths that were impossible to solve and the implications of his work take us to the very edge of what we can know.

Imaginary Numbers In the sixteenth century, a group of mathematicians found a solution to a problem that had puzzled generations before them: a completely new kind of number.

Indian Mathematics Mathematics from the Indian subcontinent has provided foundations for much of our modern thinking on the subject.

Mathematics Discussing perceptions mathematics, the nature of mathematical ability, and what mathematics can show us about how life began, and how it might continue.

Negative Numbers In 1759 the British mathematician Francis Maseres wrote that negative numbers 'darken the very whole doctrines of the equations...'

Pi Archimedes calculated Pi to the equivalent of 14 decimal places and today we know its first 1.4 trillion digits.

Prime Numbers For nearly two and a half thousand years, mathematicians have struggled to write a rule to predict the sequence of prime numbers.

Probability Melvyn Bragg and guests discuss the strange mathematics of probability where heads or tails is a simple question with a far from simple answer.

Pythagoras The central Pythagorean idea was that number had the capacity to explain the truths of the world. This was as much a mystical belief as a mathematical one.

Random and Pseudorandom Random numbers have become enormously useful to statisticians, computer scientists and cryptographers. But true randomness is difficult to find.

Renaissance Maths European mathematics went from being an art that would unmask the eternal shapes of geometry to a science that could track the manifold movements and changes of the real world.