Classical period Greek mathematics

statue of euclid in oxford university museum of natural history

another important figure in development of greek mathematics pythagoras of samos (ca. 580–500 bc). thales, pythagoras traveled egypt , babylon, under rule of nebuchadnezzar, settled in croton, magna graecia. pythagoras established order called pythagoreans, held knowledge , property in common , hence of discoveries individual pythagoreans attributed order. , since in antiquity customary give credit master, pythagoras himself given credit discoveries made order. aristotle 1 refused attribute pythagoras individual , discussed work of pythagoreans group. 1 of important characteristics of pythagorean order maintained pursuit of philosophical , mathematical studies moral basis conduct of life. indeed, words philosophy (love of wisdom) , mathematics (that learned) said have been coined pythagoras. love of knowledge came many achievements. has been customarily said pythagoreans discovered of material in first 2 books of euclid s elements.

distinguishing work of thales , pythagoras of later , earlier mathematicians difficult since none of original works survive, except possibly surviving thales-fragments , of disputed reliability. many historians, such hans-joachim waschkies , carl boyer, have argued of mathematical knowledge ascribed thales developed later, particularly aspects rely on concept of angles, while use of general statements may have appeared earlier, such found on greek legal texts inscribed on slabs. reason not clear either thales or pythagoras did no contemporary documentation has survived. evidence comes traditions recorded in works such proclus’ commentary on euclid written centuries later. of these later works, such aristotle’s commentary on pythagoreans, known few surviving fragments.

thales supposed have used geometry solve problems such calculating height of pyramids based on length of shadows, , distance of ships shore. credited tradition having made first proof of 2 geometric theorems – theorem of thales , intercept theorem described above. pythagoras credited recognizing mathematical basis of musical harmony and, according proclus commentary on euclid, discovered theory of proportionals , constructed regular solids. modern historians have questioned whether constructed 5 regular solids, suggesting instead more reasonable assume constructed 3 of them. ancient sources attribute discovery of pythagorean theorem pythagoras, whereas others claim proof theorem discovered. modern historians believe principle known babylonians , imported them. pythagoreans regarded numerology , geometry fundamental understanding nature of universe , therefore central philosophical , religious ideas. credited numerous mathematical advances, such discovery of irrational numbers. historians credit them major role in development of greek mathematics (particularly number theory , geometry) coherent logical system based on clear definitions , proven theorems considered subject worthy of study in own right, without regard practical applications had been primary concern of egyptians , babylonians.