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About 700 BC Babylonians began to apply mathematics to research of movements of the Moon and planets. It allowed them to foretell provisions of planets that was important both for an astrology, and for astronomy.

Diophantus's works became a major landmark in algebra of the Alexandria Greeks (apprx. 2 One of his main achievements is connected with introduction to algebra of the beginnings of symbolics. In the works Diophantus did not offer the general methods, he dealt with concrete positive rational numbers, but not with their alphabetic references. It laid the foundation of the so-called Diophantine analysis – research of the uncertain equations.

Deductive character of the Greek mathematics was completely built up by the time of Platon and Aristotle. The invention of deductive mathematics can be attributed to Thales Miletsky (apprx. 640–546 BC) who, as well as many Ancient Greek mathematics of the classical period, was also a philosopher. It was suggested that Thales used deduction for the proof of some results in geometry though it is doubtful.

Alexandria period. During this period which began about 300 BC, character of the Greek mathematics changed. The Alexandria mathematics resulted from merge of classical Greek mathematics to mathematics of Babylonia and Egypt. In general mathematics of the Alexandria period was more inclined to the solution of purely technical tasks, than to philosophy. Great Alexandria mathematicians – Eratosthenes, Archimedes, Gipparkh, Ptolemaeus, Diophantus and Pappus – showed strength of the Greek genius in theoretical abstraction, but so willingly applied the talent for the solution of practical problems and purely quantitative tasks.