Galileo's research in the exact sciences banished the last vestiges of Aristotelian ``science'' and replaced it with a framework within which the whole of physics would be constructed. These changes were not achieved without pain: Galileo was judged and condemned by the Inquisition and died while under house arrest after being forced to recant his Copernican beliefs.
Underlying all the discoveries made by Galileo there was a modern philosophy of science. He strongly believed, along the Pythagorean tradition, that the universe should be described by mathematics. He also adopted the view, following Ockham's razor (Sect. 1.2.5), that given various explanations of a phenomenon, the most succinct and economic one was more likely to be the correct one. Still any model must be tested again and again against experiment: no matter how beautifuland economical a theory is, should it fail to describe the data, it is useless except, perhaps, as a lesson.