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Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem . As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. [36] Pythagoras established the Pythagorean School , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". [37] It was the Pythagoreans who coined the term "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 , [38] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers . [39] [40] Although he was preceded by the Babylonians and the Chinese , [41] the Neopythagorean mathematician Nicomachus (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 ). [42] The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later Medieval name: the mensa Pythagorica . [43]

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