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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 the mathematical 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 c. 1900 BC),〔J. Friberg, "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, 1981, pp. 277—318.〕 the ''Rhind Mathematical Papyrus'' (Egyptian c. 2000-1800 BC)〔 Chap. IV "Egyptian Mathematics and Astronomy", pp. 71–96.〕 and the ''Moscow Mathematical Papyrus'' (Egyptian 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 demonstrative discipline begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek ''μάθημα'' (''mathema''), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics.〔Sir Thomas L. Heath, ''A Manual of Greek Mathematics'', Dover, 1963, p. 1: "In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science."〕 Chinese mathematics made early contributions, including a place value system.〔George Gheverghese Joseph, ''The Crest of the Peacock: Non-European Roots of Mathematics'',Penguin Books, London, 1991, pp.140—148〕〔Georges Ifrah, ''Universalgeschichte der Zahlen'', Campus, Frankfurt/New York, 1986, pp.428—437〕 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.〔Robert Kaplan, "The Nothing That Is: A Natural History of Zero", Allen Lane/The Penguin Press, London, 1999〕〔"The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius." - Pierre Simon Laplace http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html〕 Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations.〔A.P. Juschkewitsch, "Geschichte der Mathematik im Mittelalter", Teubner, Leipzig, 1964〕 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, periods of mathematical discovery 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 an increasing pace that continues through the present day. == Prehistoric mathematics == The origins of mathematical thought lie in the concepts of number, magnitude, and form. 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.〔 Prehistoric artifacts discovered in Africa, dated 20,000 years old or more suggest early attempts to quantify time.〔(Mathematics in (central) Africa before colonization )〕 The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be more than 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 of prime numbers or a six-month lunar calendar.〔Marshack, Alexander (1991): ''The Roots of Civilization'', Colonial Hill, Mount Kisco, NY.〕 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." The Ishango bone, according to scholar Alexander Marshack, may have influenced the later development of mathematics in Egypt as, like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2; this, however, is disputed.〔Marshack, A. 1972. The Roots of Civilization: the Cognitive Beginning of Man’s First Art, Symbol and Notation. New York: McGraw-Hil〕 Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that megalithic monuments in England and Scotland, dating from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.〔Thom, Alexander, and Archie Thom, 1988, "The metrology and geometry of Megalithic Man", pp 132-151 in C.L.N. Ruggles, ed., ''Records in Stone: Papers in memory of Alexander Thom''. Cambridge University Press. ISBN 0-521-33381-4.〕 All of the above are disputed however, and the currently oldest undisputed mathematical documents are from Babylonian and dynastic Egyptian sources. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「History of mathematics」の詳細全文を読む スポンサード リンク
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