Between the middle of the eighteenth century and the early years of the nineteenth, Britain was transformed. This was a revolution, but not a political one: over the course of a few generations industrialisation swept the nation.

All this had profound effects — not all of them positive — as an agrarian and primitive society was turned into an industrial empire, the richest nation on Earth. But the effects were both social and intellectual, as thinkers originated theories to deal with the new realities of urban living, mass production and a consumer society.

John Calvin, a Frenchman exiled to Geneva, became a towering figure of the 16th century Reformation of the Christian Church. He oversaw an austere, theocratic and sometimes brutal regime. But, the zeal he instilled in his followers, and the persecution which dogged them, rapidly spread the faith across Europe, and on to the New World in America.

The Ancient Greek mathematician Pythagoras' ideas, centred on his theory of number, have had a profound impact on Western science and philosophy, from Plato through astronomers like Copernicus to the present day. The central Pythagorean idea was that number had the capacity to explain the truths of the world, and this was as much a mystical belief as a mathematical one.

Francis Bacon was a lawyer and political schemer who climbed the greasy pole of Jacobean politics and then fell down it again. But he is most famous for developing an idea of how science should be done — a method that he hoped would slough off the husk of ancient thinking and usher in a new age. It is called Baconian Method and it has influenced and inspired scientists from Bacon's own time to the present day.

Gambling may be as old as the hills but probability as a mathematical discipline is a relative youngster. It may have started with the toss of a coin but probability now reaches into every area of the modern world, from the analysis of society to the decay of an atom.

Associated with science and atheism, Materialism has influenced many forms of contemporary human thought from the process of history to the diagnosis of disease and boasts a cast list of devotees including Pierre Gassandi, Thomas Hobbes, the Marquis de Sade and Karl Marx. But what does materialism really mean, how has it developed over time and can we still have free will if we are living in a materialist world?

The idea of the social contract — that political authority is held through a contract with those to be ruled — began before Rousseau with the work of John Locke, Hugo Grotius and even Plato. We explore how an idea that burgeoned among the 17th century upheavals of the English civil war and then withered in the face of modern capitalist society still influences our attitude to government today

Poincaré’s ground-breaking work in the 19th and early 20th century has led us to the stars and the consideration of the shape of the universe itself. He is known as the father of topology – the study of the properties of shapes and how they can be deformed. His famous Conjecture in this field has been causing mathematicians sleepless nights ever since. He is also credited as the Father of Chaos Theory. So how did this great polymath change the way we understand the world and indeed the universe? Why did his conjecture remain unproved for almost a century? And has it finally been cracked?

John Stuart Mill was one of the first thinkers to argue that a social theory must engage with ideas of culture and the internal life. He used Wordsworth to inform his social theory, he was a proto feminist and his treatise On Liberty is one of the sacred texts of liberalism.

William James, along with John Dewey and Charles Sanders Peirce, was the founder of an American philosophical movement which flowered during the last thirty years of the nineteenth century and the first twenty years of the 20th century. It purported that knowledge is only meaningful when coupled with action. Nothing is true or false — it either works or it doesn't. In essence, practical application was all.

"Workers of the World Unite! You have nothing to lose but your chains", "Religion is the opium of the people", "From each according to his abilities, to each according to his needs", and "Philosophers have only interpreted the world in various ways, the point, however, is to change it" — which raises the question, is Karl Marx really a philosopher at all?

The infamous September Massacres when Parisian mobs killed thousands of suspected royalists and set the scene for the events to come, when Madame La Guillotine took centre stage and The Terror ruled in France. But how did the French Revolution descend into such extremes of violence? Who or what drove The Terror? And was it really an aberration of the revolutionary cause or the moment when it truly expressed itself?