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A history of mathematics from cultures during BCE.

Events

First Notched Tally BonesEarliest documented counting and measuring systemEarliest fully-developed base 10 number system in useMultiplication tables, geometrical exercises and division problemsEarliest papyri showing numeration system and basic arithmeticClay tablets dealing with fractions, algebra and equationsRhind Papyrus (instruction manual in arithmetic, geometry, unit fractions, etc)First decimal numeration system with place value conceptEarly Vedic mantras invoke powers of ten from a hundred all the way up to a trillion“Sulba Sutra” lists several Pythagorean triples and simplified Pythagorean theorem for the sides of a square and a rectangle, quite accurate approximation to √2Lo Shu order three (3 x 3) “magic square” in which each row, column and diagonal sums to 15Early developments in geometry, including work on similar and right trianglesExpansion of geometry, rigorous approach building from first principles, square and triangular numbers, Pythagoras’ theoremDiscovered potential existence of irrational numbers while trying to calculate the value of √2Describes a series of paradoxes concerning infinity and infinitesimalsFirst systematic compilation of geometrical knowledge, Lune of HippocratesDevelopments in geometry and fractions, volume of a conePlatonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methodsMethod for rigorously proving statements about areas and volumes by successive approximationsDevelopment and standardization of logic (although not then considered part of mathematics) and deductive reasoningDefinitive statement of classical (Euclidean) geometry, use of axioms and postulates, many formulas, proofs and theorems including Euclid’s Theorem on infinitude of primesFormulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities“Nine Chapters on the Mathematical Art”, including guide to how to solve equations using sophisticated matrix-based methodsPre-classic Mayans developed the concept of zero by at least this time