Algoritma untuk aritmatika juga ditemukan dalam matematika Mesir kuno, yang berasal dari Rhind Mathematical Papyrus sekitar tahun 1550 SM.<ref name="Springer Science & Business Media2" /> Algoritma kemudian digunakan dalam matematika [[Periode Helenistik|Helenistik]] kuno. Dua contohnya adalah [[Tapis Eratosthenes]], yang dijelaskan dalam Pengenalan Aritmatika oleh [[Nicomachus]],<ref>{{cite web|last=Ast|first=Courtney|title=Eratosthenes|url=http://www.math.wichita.edu/history/men/eratosthenes.html|publisher=Wichita State University: Department of Mathematics and Statistics|archive-url=https://web.archive.org/web/20150227150653/http://www.math.wichita.edu/history/men/eratosthenes.html|archive-date=February 27, 2015|access-date=February 27, 2015|url-status=live}}</ref><ref name="Cooke20052" />{{rp|Ch 9.2}} dan [[Algoritme Euklides|Algoritma Euklides]], yang pertama kali dipaparkan dalam Euclid's Elements (sekitar 300 SM).<ref name="Cooke20052" />{{rp|Ch 9.1}}
=== Ancient Near East ===
The earliest evidence of algorithms is found in the [[Babylonian mathematics]] of ancient [[Mesopotamia]] (modern Iraq). A [[Sumer|Sumerian]] clay tablet found in [[Shuruppak]] near [[Baghdad]] and dated to circa 2500 BC described the earliest [[division algorithm]].<ref name="Springer Science & Business Media">{{cite book|last1=Chabert|first1=Jean-Luc|date=2012|title=A History of Algorithms: From the Pebble to the Microchip|publisher=Springer Science & Business Media|isbn=9783642181924|pages=7–8}}</ref> During the [[First Babylonian dynasty|Hammurabi dynasty]] circa 1800-1600 BC, [[Babylonia|Babylonian]] clay tablets described algorithms for computing [[formulas]].<ref>{{cite journal|last1=Knuth|first1=Donald E.|date=1972|title=Ancient Babylonian Algorithms|url=http://steiner.math.nthu.edu.tw/disk5/js/computer/1.pdf|journal=Commun. ACM|volume=15|issue=7|pages=671–677|doi=10.1145/361454.361514|issn=0001-0782|archive-url=https://web.archive.org/web/20121224100137/http://steiner.math.nthu.edu.tw/disk5/js/computer/1.pdf|archive-date=2012-12-24|s2cid=7829945|url-status=dead}}</ref> Algorithms were also used in [[Babylonian astronomy]]. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events.<ref>{{Citation|last=Aaboe|first=Asger|author-link=Asger Aaboe|date=2001|title=Episodes from the Early History of Astronomy|publisher=Springer|place=New York|pages=40–62|isbn=978-0-387-95136-2}}</ref>
Kata algoritme datang dari nama matematikawan Persia abad ke-9 [[al-Khwarizmi|Abu Abdullah Muhammad ibnu Musa Al-Khwarizmi]], yang hasil kerjanya dibangun dari matematikawan India abad ke-7 [[Brahmagupta]].
Kata algorisma awalnya mengacu hanya pada aturan-aturan dalam melakukan aritmetika menggunakan bilangan Hindu-Arab namun berkembang lewat penerjemahan Latin Eropa dari nama Al-Khwarizmi menjadi algoritme pada abad ke-18.
Penggunaan kata tersebut berkembang mengikutkan semua prosedur untuk menyelesaikan masalah atau melakukan unit kegiatan.
