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The Classical period corresponds to most of the 5th and 4th centuries BC (the most common dates being the fall of the last Athenian tyrant in 510 BC and the death of Alexander the Great in 323 BC). The achievements were developments include the basic rules of geometry, the idea of a formal mathematical proof, and discoveries in number theory, mathematical analysis, and applied mathematics. The Greeks also developed the field of astronomy, which they treated as a branch of mathematics to a highly sophisticated level.