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Hello calculus is a mathematical technique created in the 17th century, which made it possible for the first time in history to measure varying rates of change.

This was an astoundingly powerful innovation, which didn't just have a profound impact on mathematics itself, but eventually enabled us to do everything from predicting the pressure building up behind a dam to tracking the position of a space shuttle.

The potential power of calculus was recognized from the start, but the question of who invented it provoked one of the most bitter and lasting feuds in scientific history.

The antagonists were an English natural philosopher, Sir Isaac Newton, and a German philosopher and political adviser, God-freed Leibniz.

It was a fight set against the backdrop of the Hanoverian succession to the English throne, the formation of the raw society, which pitted England against Europe, and geometric notation against algebra, and the nature of God.

To discuss calculus and the battle between Leibniz and Newton over who conceived it, I'm joined by Simon Schaffer, professor of the history of science at the University of Cambridge, Patricia Farrer, senior tutor of Claire College, University of Cambridge, and Jack is the old department lecturer in the history of mathematics at the University of Oxford.

Simon Schaffer, can we start with God-freed Leibniz and why was he such an important figure?

Leibniz is a fascinating figure, and I imagine less familiar to a British audience than his great antagonist, Isaac Newton.

Both of them have biscuits, named after them, fig newtons on the one hand, and Leibniz, which is a very fashionable form of snack in Germany even today.

Leibniz was born in 1646 in Leipzig, so he's what, four years younger than Newton, brilliant young lawyer, diplomat, administrator.

Already in his early twenties, he drafted a series of radical and remarkably far-sighted political and legal documents, including the fascinating proposal that the greatest military power in Europe at the time.

That of Louis XIV's France should be persuaded to stop crossing the Rhine and invading the German lands and instead divert all its military energies to Egypt.

In order to pursue this program, Leibniz traveled to Paris in the early 1670s and then to London, and it was in that period when he's in his twenties and early thirties,

that he began his remarkable rapid and in a very interesting way autodidactic project in mathematics and the sciences.

Like Newton, he was a classicist. These extraordinary mathematics, such contribution to maths, read classics.

There was no such thing as reading mathematics.

So when did he go for, and why did he become so very important, so very quick?

Well, let's assume he's very brilliant. That's why I began so much. But what did he go for? What took him to calculus?

I think two factors that mattered most to him were in play in the 1670s. On the one hand, we have to remember what the intellectual milieu in which he was working amounted to.

Leibniz was born towards the end of one of the most devastating European wars, what we now call the 30 years war.

Almost a third of the German population, it's been estimated, died during that period.

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