Editing History of mathematics (section)

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[[File:Euclid-proof.jpg|thumb|right|upright=1.5|A proof from [[Euclid]]'s ''[[Euclid's Elements|Elements]]'' ({{circa|300 BC}}), widely considered the most influential textbook of all time.<ref name="Boyer 1991 loc=Euclid of Alexandria p. 119">{{Harv|Boyer|1991|loc="Euclid of Alexandria" p. 119}}</ref>]]
{{Math topics TOC}}
The '''history of mathematics''' deals with the origin of discoveries in [[mathematics]] and the [[History of mathematical notation|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. From 3000 BC the [[Mesopotamian]] states of [[Sumer]], [[Akkad (region)|Akkad]] and [[Assyria]], followed closely by [[Ancient Egypt]] and the Levantine state of [[Ebla]] began using [[arithmetic]], [[algebra]] and [[geometry]] for purposes of [[taxation]], [[commerce]], trade and also in the field of [[astronomy]] to record time and formulate [[calendars]].

The earliest mathematical texts available are from [[Mesopotamia]] and [[Ancient Egypt|Egypt]] – ''[[Plimpton 322]]'' ([[Babylonian mathematics|Babylonian]] {{circa|2000}} – 1900 BC),<ref name=":0">Friberg, J. (1981). "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", ''Historia Mathematica'', 8, pp. 277–318.</ref> the ''[[Rhind Mathematical Papyrus]]'' ([[Egyptian mathematics|Egyptian]] c. 1800 BC)<ref name=":1">{{Cite book | edition = 2 | publisher = [[Dover Publications]] | last = Neugebauer | first = Otto | author-link = Otto E. Neugebauer | title = The Exact Sciences in Antiquity | series = Acta Historica Scientiarum Naturalium et Medicinalium | orig-year = 1957 | year = 1969 | volume = 9 | pages = 1–191 | pmid = 14884919 | isbn = 978-0-486-22332-2 | url = https://books.google.com/books?id=JVhTtVA2zr8C}} Chap. IV "Egyptian Mathematics and Astronomy", pp. 71–96.</ref> and the ''[[Moscow Mathematical Papyrus]]'' (Egyptian c. 1890 BC). All of these texts mention the so-called [[Pythagorean triple]]s, so, by inference, the [[Pythagorean theorem]] seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.

The study of mathematics as a "demonstrative discipline" began in the 6th century BC with the [[Pythagoreans]], who coined the term "mathematics" from the ancient [[Greek language|Greek]] ''μάθημα'' (''mathema''), meaning "subject of instruction".<ref>{{cite journal|author=Turnbull|title=A Manual of Greek Mathematics|journal=Nature|volume=128|issue=3235|page=5|bibcode=1931Natur.128..739T|year=1931|doi=10.1038/128739a0|s2cid=3994109}}</ref> [[Greek mathematics]] greatly refined the methods (especially through the introduction of deductive reasoning and [[mathematical rigor]] in [[mathematical proof|proofs]]) and expanded the subject matter of mathematics.<ref>Heath, Thomas L. (1963). ''A Manual of Greek Mathematics'', Dover, 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."</ref> The [[ancient Romans]] used [[applied mathematics]] in [[surveying]], [[structural engineering]], [[mechanical engineering]], [[bookkeeping]], creation of [[Lunar calendar|lunar]] and [[solar calendar]]s, and even [[Roman art|arts and crafts]]. [[Chinese mathematics]] made early contributions, including a [[place value system]] and the first use of [[negative numbers]].<ref name=":2">Joseph, George Gheverghese (1991). ''The Crest of the Peacock: Non-European Roots of Mathematics''. Penguin Books, London, pp. 140–48.</ref><ref>Ifrah, Georges (1986). ''Universalgeschichte der Zahlen''. Campus, Frankfurt/New York, pp. 428–37.</ref> The [[Hindu–Arabic numeral system]] and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium AD in [[Indian mathematics|India]] and were transmitted to the [[Western world]] via [[Islamic mathematics]] through the work of [[Muḥammad ibn Mūsā al-Khwārizmī]].<ref>Kaplan, Robert (1999). ''The Nothing That Is: A Natural History of Zero''. Allen Lane/The Penguin Press, London.</ref><ref>"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</ref> Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations.<ref>[[Adolf Yushkevich|Juschkewitsch, A. P.]] (1964). ''Geschichte der Mathematik im Mittelalter''. Teubner, Leipzig.</ref> Contemporaneous with but independent of these traditions were the mathematics developed by the [[Maya civilization]] of [[Mexico]] and [[Central America]], where the concept of [[zero]] was given a standard symbol in [[Maya numerals]].

Many Greek and Arabic texts on mathematics were [[Latin translations of the 12th century|translated into Latin]] from the 12th century onward, leading to further development of mathematics in [[Middle Ages|Medieval Europe]]. From ancient times through the [[Postclassical age|Middle Ages]], periods of mathematical discovery were often followed by centuries of stagnation.<ref>Eves, Howard (1990). ''History of Mathematics'', 6th Edition, "After Pappus, Greek mathematics ceased to be a living study, ..." p. 185; "The Athenian school struggled on against growing opposition from Christians until the latter finally, in A.D. 529, obtained a decree from Emperor Justinian that closed the doors of the school forever." p. 186; "The period starting with the fall of the Roman Empire, in the middle of the fifth century, and extending into the eleventh century is known in Europe as the Dark Ages... Schooling became almost nonexistent." p. 258.</ref> Beginning in [[Renaissance]] [[Italy]] in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an [[exponential growth|increasing pace]] that continues through the present day. This includes the groundbreaking work of both [[Isaac Newton]] and [[Gottfried Wilhelm Leibniz]] in the development of infinitesimal [[calculus]] during the course of the 17th century and following discoveries of [[List of German mathematicians|German mathematicians]] like [[Carl Friedrich Gauss]] and [[David Hilbert]].