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Mathematics |
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While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analyses and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid's Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of Descartes, which a modern finds incomparably easier to follow.
Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many odd numbers as there are whole numbers including both even and odd. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.
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