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[MUSIC]
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.
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