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I have ever found it, when I have thought the battle was over and the conquest gained, and so let down my watch, the enemy has risen up and done me the greatest injury.

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Simon Singh

What seems certain is that Pythagoras developed the idea of mathematical logic. He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute than any previous knowledge.