The Greek Legacy

How the Ancient Greeks shaped modern mathematics

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To Ancient Greece and back again

Often called the "birthplace of civilisation", Ancient Greece heralded numerous advances in philosophy, science, sport and also mathematics. Over six centuries from 600 BC a group of revolutionary thinkers – from Thales, Pythagoras, Democritus and Aristotle to Euclid, Archimedes and Hypatia of Alexandria – formalised the rules and language of modern mathematics.

This animated adventure brings to life some of these key figures to demonstrate the crucial role played by the Ancient Greeks in the story of maths.

For Greek thinkers, maths wasn't simply a means of calculating amounts but a way of testing reality and understanding the true nature of the world around them. Indeed, Pythagoras is believed to have coined both the words "philosophy" ("love of wisdom") and "mathematics" ("that which is learned"). In turn, Euclid came to be known as the "father of geometry".

At the heart of this new understanding, was the concept of "the proof", developed by Euclid in what is commonly regarded as the most important and successful mathematical textbook of all time – the "Stoicheion" or "Elements". Built upon the axiomatic method, mathematical proofs were a way of testing assumptions by building up a mathematical argument using self-evident or assumed statements (or, "axioms").

It is this methodology that formed the foundational language and logic of modern mathematics throughout the world.  Indeed, Euclid's Elements was widely used as the seminal maths textbook right up until the start of the twentieth century.


Many thanks to James Grime for his expert help on the script and recording the voice-over. Follow him @jamesgrime or find out more at

Thanks also to the wonderful 12foot6 and Phoebe Halstead for bringing our ideas to life in animated form. 

Music by Bedřich Smetana: Má Vlast Moldau

This video was created as part of the Greek Legacy Masterclass project, generously supported by the Stavros Niarchos Foundation:




Stavros Niarchos Foundation
Dr James Grime

Phoebe Halstead / 12foot6

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Around 2,500 years ago, a group of revolutionary thinkers changed the way we think about mathematics. Through the idea of proof, the ancient Greeks showed that maths isn't just about performing calculations, but a way of understanding and testing the reality of the world around us.

The sign above Plato's Academy was said to have read: let no one ignorant of geometry enter here.

And the great Archimedes was even killed by a soldier because he refused to leave a proof unfinished.

But, what is a proof? Simply put, a proof is a convincing argument to demonstrate whether something is true or false. For example, if all dogs have four legs, then: is this a dog? It's easy to prove that just because all dogs have four legs, not everything with four legs is a dog.

How about a mathematical proof? You've probably heard of Pythagoras's theorem, a mathematical fact about the sides of a right-angled triangle. Here's one demonstration of the theorem. Does it convince you? Good proofs are undeniably true.

200 years after Pythagoras was around, another Greek mathematician called Euclid perfected the way to write proofs. With just a few basic assumptions known as axioms, Euclid was able to prove many other mathematical results. He compiled these results into one remarkable book called The Elements, and his proofs are as true today as when it was first written and have formed the foundations of modern mathematics.

From proofs about infinite prime numbers used internet encryption to mathematical formulae used in engineering, the ancient Greeks have provided scientists, economists, lawyers, architects, and well, just about everyone, with a new mathematical understanding of our world. [MUSIC]

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