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A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1] The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into themathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC),[2] theRhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The study of mathematics as a subject in its own right begins in the 6th century BC with thePythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα(mathema), meaning "subject of instruction".[4] Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigorin proofs) and expanded the subject matter of mathematics.[5] Chinese mathematics made early contributions, including a place value system.[6][7] The Hindu-Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and were transmitted to the west via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī.[8][9] Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations.[10] Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe. From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at anincreasing pace that continues through the present day. Prehistoric mathematics[edit]

The origins of mathematical thought lie in the concepts of number, magnitude, and form.[11] Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.[11] Prehistoric artifacts discovered in Africa, dated 20,000 years old or more suggest early attempts to quantify time.[12] The evidence is against the Lebombo bone being a mathematical object, but the Ishango bone, found near the headwaters of the Nileriver (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known demonstration of sequences ofprime numbers[13] or a six-month lunar calendar.[14] In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10."[15] The Ishango bone, according to scholar Alexander Marshack, may have influenced the later development...