Editing 0 (section)

===Middle Ages===
====Transmission to Islamic culture====
{{See also|History of the Hindu–Arabic numeral system}}
The [[Arabic]]-language inheritance of science was largely [[Greece|Greek]],<ref>{{Cite book |last=Pannekoek |first=Anton |title=A History of Astronomy |publisher=George Allen & Unwin |year=1961 |page=165 | oclc=840043 | author-link=Anton Pannekoek | url= https://archive.org/details/historyofastrono0000pann}}</ref> followed by Hindu influences.<ref name="Durant">{{cite book | first= Will | last= Durant |date=1950|title=The Story of Civilization, Volume IV, The Age of Faith: Constantine to Dante – A.D. 325–1300|publisher= Simon & Schuster |quote-page= 241 | quote=The Arabic inheritance of science was overwhelmingly Greek, but Hindu influences ranked next. In 773, at Mansur's behest, translations were made of the ''Siddhantas'' – Indian astronomical treatises dating as far back as 425 BC; these versions may have the vehicle through which the "Arabic" numerals and the zero were brought from India into Islam. In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables. | author-link=Will Durant |url=https://archive.org/details/ageoffaithahisto012288mbp}}</ref> In 773, at [[Al-Mansur]]'s behest, translations were made of many ancient treatises including Greek, Roman, Indian, and others.

In AD 813, astronomical tables were prepared by a [[Persian people|Persian]] mathematician, [[Muḥammad ibn Mūsā al-Khwārizmī]], using Hindu numerals;<ref name="Durant" /> and about 825, he published a book synthesizing Greek and Hindu knowledge and also contained his own contribution to mathematics including an explanation of the use of zero.<ref>{{Cite book |last=Brezina |first=Corona |url=https://books.google.com/books?id=955jPgAACAAJ |title=Al-Khwarizmi: The Inventor of Algebra |publisher=The Rosen Publishing Group |year=2006 |isbn=978-1-4042-0513-0 |access-date=26 September 2016 }}</ref> This book was later translated into [[Latin]] in the 12th century under the title ''Algoritmi de numero Indorum''. This title means "al-Khwarizmi on the Numerals of the Indians". The word "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name, and the word "[[Algorithm]]" or "[[Algorism]]" started to acquire a meaning of any arithmetic based on decimals.<ref name="Durant" />

[[Muhammad ibn Ahmad al-Khwarizmi]], in 976, stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows". This circle was called ''ṣifr''.<ref>{{harvnb|Durant|1950|p=241}}: "In 976, Muhammad ibn Ahmad, in his ''Keys of the Sciences'', remarked that if, in a calculation, no number appears in the place of tens, a little circle should be used "to keep the rows". This circle the Mosloems called ''ṣifr'', "empty" whence our cipher."</ref>

====Transmission to Europe====
The [[Hindu–Arabic numeral system]] (base 10) reached Western Europe in the 11th century, via [[Al-Andalus]], through Spanish [[Muslim]]s, the [[Moors]], together with knowledge of [[classical astronomy]] and instruments like the [[astrolabe]]. [[Pope Sylvester II|Gerbert of Aurillac]] is credited with reintroducing the lost teachings into Catholic Europe. For this reason, the numerals came to be known in Europe as "Arabic numerals". The Italian mathematician [[Fibonacci]] or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating:

<blockquote>After my father's appointment by [[Republic of Pisa|his homeland]] as state official in the customs house of [[Béjaïa|Bugia]] for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business. I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the [[algorism]], as well as the art of [[Pythagoras]], I considered as almost a mistake in respect to the method of the [[Hinduism|Hindus]] [{{lang|la-x-medieval|Modus Indorum}}]. Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of [[Euclid]]'s geometric art. I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the [[Latin people]] might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things. The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0{{nbsp}}... any number may be written.<ref>{{multiref2|{{cite book | translator-last=Sigler|translator-first= Laurence E.| title= Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation |publisher= Springer|date= 2003| isbn =978-1-4613-0079-3 | doi=10.1007/978-1-4613-0079-3 |series= Sources and Studies in the History of Mathematics and Physical Sciences|last1= Sigler|first1= Laurence}}|{{cite periodical| last=Grimm | first= Richard E. | title=The Autobiography of Leonardo Pisano|  magazine =[[Fibonacci Quarterly]]| volume= 11 | number=1 |date=February 1973|pages= 99–104 |archive-url=https://web.archive.org/web/20231126180044/https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=318a17253f745e2af400eb2ebb4dc4e762560a5b | archive-date= 26 November 2023 |url-status=live | url = https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=318a17253f745e2af400eb2ebb4dc4e762560a5b}}|{{Cite book |last=Hansen |first=Alice |url=https://books.google.com/books?id=COJsbuUI1h8C&pg=PT31 |title=Primary Mathematics: Extending Knowledge in Practice |date=2008 |publisher=SAGE | doi = 10.4135/9781446276532|isbn=978-0-85725-233-3 |language=en |access-date=7 November 2020 |archive-date=7 March 2021 |archive-url=https://web.archive.org/web/20210307234959/https://books.google.com/books?id=COJsbuUI1h8C&q=%22Therefore%2C+embracing+more+stringently+that+method+of+the+Hindus%2C+and+taking+stricter+pains+in+its+study%2C+while+adding+certain+things+from+my+own+understanding+and+inserting+also+certain+things+from+the+niceties+of+Euclid%27s+geometric+art.%22&pg=PT31 |url-status=live }} }}</ref></blockquote>

From the 13th century, manuals on calculation (adding, multiplying, extracting roots, etc.) became common in Europe where they were called {{lang|la-x-medieval|algorismus}} after the Persian mathematician [[al-Khwārizmī]]. One popular manual was written by [[Johannes de Sacrobosco]] in the early 1200s and was one of the earliest scientific books to be [[History of printing|printed]], in 1488.<ref name=Karpinski1911>{{cite book |first1=D. E. |last1=Smith |first2=L. C. |last2=Karpinski |year=1911 |chapter=The spread of the <nowiki>[Hindu–Arabic]</nowiki> numerals in Europe |title=The Hindu–Arabic Numerals |pages=134–136 |publisher=Ginn and Company |via=Internet Archive |chapter-url=https://archive.org/stream/hinduarabicnume02karpgoog#page/n145/mode/1up
}}</ref><ref>{{cite journal |last1=Pedersen |first1=Olaf |date=1985 |title=In Quest of Sacrobosco |journal=Journal for the History of Astronomy |volume=16 |issue=3 |pages=175–221 |doi=10.1177/002182868501600302  |bibcode=1985JHA....16..175P |s2cid=118227787 }}</ref> The practice of calculating on paper using Hindu–Arabic numerals only gradually displaced calculation by abacus and recording with [[Roman numerals]].{{sfn|Ifrah|2000|pp=588–590}} In the 16th century, Hindu–Arabic numerals became the predominant numerals used in Europe.<ref name=Karpinski1911/>