According to the popular notion of science history, the period between the ninth and thirteenth centuries was what has come to be called the Dark Ages.
Scientific advances ground to a halt and the world languished in an intellectual backwater and then the Renaissance happened. The world woke up and great science got going again, picking up where the ancient Greeks and Romans had left off.
But, as Professor Jim Al-Khalili will show in this series, that simply is not true.
In part two Dr Jackie Stedall and Professor Ian Stewart tell us the story of Al-Khwarismi, the mathematician who introduced the world to the radical system of Hindu numerals - the numbers zero to nine - and how the word algebra comes from the Arabic title of one of his books.
In his book he revolutionised maths by focussing on the relationships between numbers rather than simply using maths to find the answer to particular problems. For mathematicians today, this was a vital development in our understanding. Another legacy was his name which gives us the modern word algorithm, a process that lies at the heart of how all computers work.
Professor Nader el-Bizri tells also of the great Ibn al-Haytham, who first realised how it is that vision works.
His work with light and optics was so revolutionary that he could be seen as the father of physics, rivaling Isaac Newton for the title.
Perhaps more importantly, he was also the instigator of what we now call the scientific method. Some people have thought that such a precise approach to scientific study began in Europe, hundreds of years later.
First broadcast on 22 April 2009.