This ten part history of mathematics reveals the personalities behind the calculations: the passions and rivalries of mathematicians struggling to get their ideas heard. Marcus du Sautoy shows how these masters of abstraction find a role in the real world and proves that mathematics is the driving force behind modern science.

Today, how the mathematics that Leonard Euler invented two hundred years ago has transformed the internet. Euler's solution to an eighteeneth century conundrum paved the way for the search engines most of us use every day

Today, the mathematics of Joseph Fourier. It's thanks to his mathematical insight that you can hear Marcus on the radio and that Brian Eno can create sounds that have never been heard before.

Today how the mathematics of the French revolutionary, Evariste Galois, has proved invaluable to particle physicists working today.The mathematics that Galois began, over two hundred years ago, now absolutely describes the fundamental particles that make up our universe.

The 19th century mathematical celebrity. Professor Marcus du Sautoy describes how a study of asteroids led Gauss to describe the normal distribution.

Today, the pioneering nineteenth century mathematicians who helped Albert Einstien with his maths: Jonas Bolyai, Nicolas Loachevski and Bernhard Riemann. Without the mathematics to describe curved space and multiple dimensions, the theory of relativity doesn't really work.

Today, Georg Cantor, the mathematician who showed us how to carry on counting when the numbers run out. An insight into the nature of infinity that Roger Penrose believes helps to explain why the human brain will always be cleverer than artificial intelligence.

Today Henri Poincare, the man who proved there are certain problems that mathematics will never be able to answer: a mathematical insight that gave rise to chaos theory.

Today, G.H.Hardy, the mathematician who insisted he had never done anything useful. And yet his work on the "diabolical malice" inherent in prime numbers inspired the millions of codes that now help to keep the internet safe.

Today, the mathematician that never was, Nicolas Bourbaki. A group of French mathematicians, working between the two world wars and writing under the pseudonym Nicolas Bourbaki transformed their discipline and paved the way for several mathematical breakthroughs in the 21st century.

The universe will die. The sun and other stars like it will throw out heat until they have no more energy to burn. The big bang threw everything outwards at a massive rate. As it gets bigger, so the gaps between matter get bigger and are filled with "dark energy". Instead of gravity pulling everything back down to a "big crunch" the dark energy accelerates the expansion process, pushing everything further apart faster and faster. In the end everything will be a cold, sad, blackness as the stars all go out, or are too far apart for us to see anything - but "us" will be long gone.

A strange subatomic particle produced in an atom-smashing experiment here on earth could, theoretically, tumble to the centre of the planet and start eating the planet from the inside out - death by industrial accident. Or a random quantum fluctuation in distant space could switch off the machinery that makes matter big, and this would send a bubble of destruction moving at the speed of light and shutting down all creation in its path. All of the ideas explored in this series suggest that the future is not rosy - that the universe is going to end and that we will end along with it...or can we escape?

A series exploring how our ideas about the end of the universe have been shaped by religion, belief, and the contemporary state of scientific thinking and observation. The series is presented by Vatican Astronomer, Brother Guy Consolmagno. He is a Jesuit astro-physicist who came to religion via science and his wonder at the universe. At the Vatican Observatory in Castel Gandolfo, Italy, he compares cutting edge cosmology with Chinese, Ancient Greek, Buddhist, Medieval and Victorian ideas about the end of everything.

It will die. Like a ball thrown into the air, no matter how fast the acceleration to begin with, gravity always wins. The universe will reach a critical mass, then start to fall back in on itself. This is the big crunch theory. The power of gravity wins out over the accelerating power throwing everything outwards. Microseconds from the end, black holes begin to merge with each other, little different from the collapsing state of the surrounding universe. The implosion becomes increasingly powerful, crushing all matter and every physical thing out of existence. Space and time end - there is eternal nothingness beyond this point, unless...

Yes the universe will end, but at the crunch the process starts all over again, and could go on forever (cf. Hindu and Buddhist ideas of re-birth). Another possibility is "multiverses" - there are lots of different universes, all in different states of existence, some at moment of big bang, but will never become a universe as we know it, so grow to the size of a grape and shrink back, or expand outwards and never turn into frothy, lumpy matter - just a thin soup with no life in them. Our universe is perfect…not too fast to become a soup and not too slow so it falls back in on itself to destruct - just lumpy enough for galaxies to form and the whole thing hold together - a balancing act between gravity and acceleration, for the time being.

The Medici are synonymous with the Renaissance, but why did these bankers act as patrons to artists like Michelangelo and Donatello - was it a love of art or something more sinister?

Classicist Bettany Hughes continues her journey through the beauty and the blood-letting of Renaissance Florence. Could it be that the Renaissance as we know it wasn't a renaissance at all? Could Donatello's David really be a political statement for the Medici? And what has Liverpool got to do with it? Bettany finds that the Renaissance is more than it's cracked up to be.

Historian Bettany Hughes concludes her journey through the beauty and the blood of renaissance Florence. This week she finds that, contrary to popular belief, it was smart women, gay men and false gods who made the corner stones of western civilisation