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The Greeks and Proof
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Film summary
The Greek development of a rigorous system of logic and reasoning, which led to the first mathematical proofs.Transcript
In ancient Greece, the god Apollo was worshipped as the god of knowledge.
The Greeks believed that man had an immortal soul, with knowledge already contained within.
This had only to be teased out by abstract reasoning.
Euclid
Around 330-260 BC
Thales
Around 620-546 BC
Revered mathematicians such as Euclid and Thales, used rigorous logic to tap into their inner knowledge.
Axioms and Theorems
In their search to discover the mathematical truths that lay within, ancient Greek mathematicians became the pioneers of proof.
They developed axioms, or statements based on universally accepted self-evident truths.
Axioms
For instance, that a straight line can be drawn between two points.
They used these axioms as a logical basis to create universal theorems.
Theorems
Mathematical statements that can be proved beyond doubt, to be true in all cases.
Process of Proof
Thales was the first to announce that reasoning was more important than intuition, belief, or even experimentation.
He used logic to deduce that any triangle inscribed thus in any semi circle, will always be a right angle triangle.
This was one of the first proofs.
Proof:
Result obtained from deductive reasoning
Indicates a statement is true in all cases
Later, Euclid introduced a system for proving mathematical statements.
He collated all known geometric ideas of the time.
And created for them sets of definitions, axioms, theorems, and finally methods of proof.
Definition
Axiom
Theorem
Proof
Since Euclid's time, mathematicians have developed many more proofs – including over 250 proofs of Pythagoras' theorem.
But many mathematical statements remain unproven.
And mathematicians continue to build on the ancient Greeks' methods, to try and prove them true.
