Editing Mathematics (section)

=== Ancient ===
[[File:Plimpton 322.jpg|thumb|The Babylonian mathematical tablet ''[[Plimpton 322]]'', dated to 1800&nbsp;BC]]
In addition to recognizing how to [[counting|count]] physical objects, [[prehistoric]] peoples may have also known how to count abstract quantities, like time{{emdash}}days, seasons, or years.<ref>See, for example, {{cite book | first=Raymond L. | last=Wilder|author-link=Raymond L. Wilder|title=Evolution of Mathematical Concepts; an Elementary Study|at=passim}}</ref><ref>{{Cite book|last=Zaslavsky|first=Claudia|author-link=Claudia Zaslavsky|title=Africa Counts: Number and Pattern in African Culture.|date=1999|publisher=Chicago Review Press|isbn=978-1-61374-115-3|oclc=843204342}}</ref> Evidence for more complex mathematics does not appear until around 3000&nbsp;{{Abbr|BC|Before Christ}}, when the [[Babylonia]]ns and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy.{{sfn|Kline|1990|loc=Chapter 1}} The oldest mathematical texts from [[Mesopotamia]] and [[Ancient Egypt|Egypt]] are from 2000 to 1800&nbsp;BC.<ref>[https://www.ms.uky.edu/~dhje223/CrestOfThePeacockCh4-pages-2-21.pdf/ Mesopotamia] pg 10. Retrieved June 1, 2024</ref> Many early texts mention [[Pythagorean triple]]s and so, by inference, the [[Pythagorean theorem]] seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It is in Babylonian mathematics that [[elementary arithmetic]] ([[addition]], [[subtraction]], [[multiplication]], and [[division (mathematics)|division]]) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a [[sexagesimal]] numeral system which is still in use today for measuring angles and time.{{sfn|Boyer|1991|loc="Mesopotamia" pp. 24–27}}

In the 6th century BC, [[Greek mathematics]] began to emerge as a distinct discipline and some [[Ancient Greeks]] such as the [[Pythagoreans]] appeared to have considered it a subject in its own right.<ref>{{cite book | last=Heath | first=Thomas Little | author-link=Thomas Heath (classicist) |url=https://archive.org/details/historyofgreekma0002heat/page/n14 |url-access=registration |page=1 |title=A History of Greek Mathematics: From Thales to Euclid |location=New York |publisher=Dover Publications |date=1981 |orig-date=1921 |isbn=978-0-486-24073-2}}</ref> Around 300 BC, [[Euclid]] organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof.<ref>{{Cite journal |last=Mueller |first=I. |year=1969 |title=Euclid's Elements and the Axiomatic Method |journal=The British Journal for the Philosophy of Science |volume=20 |issue=4 |pages=289–309 |doi=10.1093/bjps/20.4.289 |jstor=686258 |issn=0007-0882}}</ref> His book, ''[[Euclid's Elements|Elements]]'', is widely considered the most successful and influential textbook of all time.{{sfn|Boyer|1991|loc="Euclid of Alexandria" p. 119}} The greatest mathematician of antiquity is often held to be [[Archimedes]] ({{Circa|287|212 BC}}) of [[Syracuse, Italy|Syracuse]].{{sfn|Boyer|1991|loc="Archimedes of Syracuse" p. 120}} He developed formulas for calculating the surface area and volume of [[solids of revolution]] and used the [[method of exhaustion]] to calculate the [[area]] under the arc of a [[parabola]] with the [[Series (mathematics)|summation of an infinite series]], in a manner not too dissimilar from modern calculus.{{sfn|Boyer|1991|loc="Archimedes of Syracuse" p. 130}} Other notable achievements of Greek mathematics are [[conic sections]] ([[Apollonius of Perga]], 3rd century BC),{{sfn|Boyer|1991|loc="Apollonius of Perga" p. 145}} [[trigonometry]] ([[Hipparchus of Nicaea]], 2nd century BC),{{sfn|Boyer|1991|loc="Greek Trigonometry and Mensuration" p. 162}} and the beginnings of algebra (Diophantus, 3rd century AD).{{sfn|Boyer|1991|loc="Revival and Decline of Greek Mathematics" p. 180}}
[[File:Bakhshali numerals 2.jpg|thumb|right|upright=1.5|The numerals used in the [[Bakhshali manuscript]], dated between the 2nd century BC and the 2nd century AD]]
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]].<ref>{{cite book
 | title=Number Theory and Its History
 | first=Øystein
 | last=Ore
 | author-link=Øystein Ore
 | publisher=Courier Corporation
 | pages=19–24
 | year=1988
 | isbn=978-0-486-65620-5
 | url={{GBurl|id=Sl_6BPp7S0AC|pg=IA19}}
 | access-date=November 14, 2022
}}</ref> Other notable developments of Indian mathematics include the modern definition and approximation of [[sine]] and [[cosine]], and an early form of [[infinite series]].<ref>{{cite journal
 | title=On the Use of Series in Hindu Mathematics
 | first=A. N. | last=Singh | journal=Osiris
 | volume=1 | date=January 1936 | pages=606–628
 | doi=10.1086/368443 | jstor=301627
| s2cid=144760421 }}</ref><ref>{{cite book
 | chapter=Use of series in India
 | last1=Kolachana | first1=A. | last2=Mahesh | first2=K.
 | last3=Ramasubramanian | first3=K.
 | title=Studies in Indian Mathematics and Astronomy
 | series=Sources and Studies in the History of Mathematics and Physical Sciences
 | pages=438–461 | publisher=Springer | publication-place=Singapore
 | isbn=978-981-13-7325-1  | year=2019
 | doi=10.1007/978-981-13-7326-8_20 | s2cid=190176726 }}</ref>