Greek mathematics refers to the mathematics written in the Greek language from the time of Thales塔莱斯 of Miletus米利都 城 (~600 BC) to the closure关闭 of the Academy of Athens雅典 in 529 AD. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean地中海, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic希腊化的 mathematics.
Greek mathematics was much more sophisticated先进的 than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive归纳法的 reasoning推理、推想, that is, repeated observations used to establish建立 rules of thumb经验法则. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms公理, and used mathematical rigor to prove them.
Greek mathematics is thought to have begun with Thales of Miletus (c. 624–c.546 BC) and Pythagoras of Samos (c. 582–c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests牧师.
Thales used geometry to solve problems such as calculating计算 the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive推理的 reasoning applied to geometry, by deriving four corollaries推论 to Thales' Theorem定理. As a result, he has been hailed赞誉 as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine教义、主义 it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term术语 "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem无理数, though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers. Although he was preceded在之前发生过 by the Babylonians and the Chinese, the Neopythagorean mathematician Nicomachus尼克马库斯 (60–120 AD) provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet. dated to the 1st century AD (now found in the British Museum). The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later Medieval name: the mensa支持物 Pythagorica.