Mathematics

=== Medieval and later ===
[[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|A page from al-Khwārizmī's ''Algebra'']]
During the [[Islamic Golden Age|Golden Age of Islam]], especially during the 9th and 10th&nbsp;centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other achievements of the Islamic period include advances in [[spherical trigonometry]] and the addition of the [[decimal point]] to the Arabic numeral system.<ref>{{Cite book | last=Saliba | first=George | author-link=George Saliba | title=A history of Arabic astronomy: planetary theories during the golden age of Islam | date=1994 | publisher=New York University Press | isbn=978-0-8147-7962-0 | oclc=28723059 }}</ref> Many notable mathematicians from this period were Persian, such as Al-Khwarismi, [[Omar Khayyam]] and [[Sharaf al-Dīn al-Ṭūsī]].<ref>{{cite journal
 | title=Contributions of Islamic scholars to the scientific enterprise
 | first=Yasmeen M.
 | last=Faruqi
 | journal=International Education Journal
 | year=2006
 | volume=7
 | issue=4
 | pages=391–399
 | publisher=Shannon Research Press
 | url=https://eric.ed.gov/?id=EJ854295
 | access-date=November 14, 2022
 | archive-date=November 14, 2022
| archive-url=https://web.archive.org/web/20221114165547/https://eric.ed.gov/?id=EJ854295
 | url-status=live
 }}</ref> The Greek and Arabic mathematical texts were in turn translated to Latin during the Middle Ages and made available in Europe.<ref>{{cite journal | title=Greek-Arabic-Latin: The Transmission of Mathematical Texts in the Middle Ages | first=Richard | last=Lorch | journal=Science in Context | volume=14 | issue=1–2 | date=June 2001 | pages=313–331 | publisher=Cambridge University Press | doi=10.1017/S0269889701000114 | s2cid=146539132 | url=https://epub.ub.uni-muenchen.de/15929/1/greek-arabic-latin.pdf | access-date=December 5, 2022 | archive-date=December 17, 2022 | archive-url=https://web.archive.org/web/20221217160922/https://epub.ub.uni-muenchen.de/15929/1/greek-arabic-latin.pdf | url-status=live }}</ref>

During the [[early modern period]], mathematics began to develop at an accelerating pace in [[Western Europe]], with innovations that revolutionized mathematics, such as the introduction of variables and [[#Symbolic notation and terminology|symbolic notation]] by François Viète (1540–1603), the introduction of [[History of logarithms|logarithms]] by [[John Napier]] in 1614, which greatly simplified numerical calculations, especially for [[astronomy]] and [[marine navigation]], the introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1642–1726/27) and [[Gottfried Wilhelm Leibniz|Gottfried Leibniz]] (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and the proof of numerous theorems.

[[File:Carl Friedrich Gauss 1840 by Jensen.jpg|thumb|left|[[Carl Friedrich Gauss]]]]
Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss, who made numerous contributions to fields such as algebra, analysis, [[differential geometry and topology|differential geometry]], [[matrix theory]], number theory, and [[statistics]].<ref>{{cite journal
 | title=History of Mathematics After the Sixteenth Century
 | first=Raymond Clare | last=Archibald | author-link=Raymond Clare Archibald
 | journal=The American Mathematical Monthly
 | series=Part 2: Outline of the History of Mathematics
 | volume=56 | issue=1 | date=January 1949 | pages=35–56
 | doi=10.2307/2304570 | jstor=2304570
}}</ref> In the early 20th century, [[Kurt Gödel]] transformed mathematics by publishing his incompleteness theorems, which show in part that any consistent axiomatic system{{emdash}}if powerful enough to describe arithmetic{{emdash}}will contain true propositions that cannot be proved.<ref name=Raatikainen_2005/>

Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and [[science]], to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January&nbsp;2006 issue of the ''[[Bulletin of the American Mathematical Society]]'', "The number of papers and books included in the ''[[Mathematical Reviews]]'' database since 1940 (the first year of operation of MR) is now more than 1.9&nbsp;million, and more than 75&nbsp;thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."{{sfn|Sevryuk|2006|pp=101–109}}
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