Editing History of mathematics (section)

== Prehistoric{{anchor|Science_education#United_States}} ==
The origins of mathematical thought lie in the concepts of [[number]], [[patterns in nature]], [[magnitude (mathematics)|magnitude]], and [[Configuration (geometry)|form]].<ref name="Boyer 1991 loc=Origins p. 3">{{Harv|Boyer|1991|loc="Origins" p. 3}}</ref> Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in [[hunter-gatherer]] societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.<ref name="Boyer 1991 loc=Origins p. 3"/>

The use of yarn by [[Neanderthal|Neanderthals]] some 40,000 years ago at a site in Abri du Maras in the south of [[France]] suggests they knew basic concepts in mathematics.<ref>{{Cite journal |last1=Hardy |first1=B. L. |last2=Moncel |first2=M.-H. |last3=Kerfant |first3=C. |last4=Lebon |first4=M. |last5=Bellot-Gurlet |first5=L. |last6=Mélard |first6=N. |date=2020-04-09 |title=Direct evidence of Neanderthal fibre technology and its cognitive and behavioral implications |journal=Scientific Reports |language=en |volume=10 |issue=1 |page=4889 |doi=10.1038/s41598-020-61839-w |pmid=32273518 |issn=2045-2322|pmc=7145842 |bibcode=2020NatSR..10.4889H }}</ref><ref>{{Cite web |last=Rigby |first=Sara |date=2020-04-14 |title=40,000-year-old yarn suggests Neanderthals had basic maths skills |url=https://www.sciencefocus.com/news/40000-year-old-yarn-suggests-neanderthals-had-basic-maths-skills |access-date=2025-02-21 |website=BBC Science Focus Magazine |language=en}}</ref> The [[Ishango bone]], found near the headwaters of the [[Nile]] river (northeastern [[Democratic Republic of the Congo|Congo]]), may be more than [[Upper Paleolithic|20,000]] years old and consists of a series of marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either a ''tally'' of the earliest known demonstration of [[sequence]]s of [[prime number]]s<ref name="Diaspora">{{cite web | last = Williams | first = Scott W. | year = 2005 | url = http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html | title = The Oldest Mathematical Object is in Swaziland | work = Mathematicians of the African Diaspora | publisher = SUNY Buffalo mathematics department | access-date = 2006-05-06}}</ref>{{Failed verification|date=April 2024}} or a six-month lunar calendar.<ref name=Marshack>Marshack, Alexander (1991). ''The Roots of Civilization'', Colonial Hill, Mount Kisco, NY.</ref> Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10."<ref>{{cite book|last=Rudman|first=Peter Strom|title=How Mathematics Happened: The First 50,000 Years|year=2007|publisher=Prometheus Books|isbn=978-1-59102-477-4|page=[https://archive.org/details/howmathematicsha0000rudm/page/64 64]|url=https://archive.org/details/howmathematicsha0000rudm/page/64}}</ref> The Ishango bone, according to scholar [[Alexander Marshack]], may have influenced the later development of mathematics in Egypt as, like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2; this however, is disputed.<ref>Marshack, A. (1972). ''The Roots of Civilization: the Cognitive Beginning of Man's First Art, Symbol and Notation''. New York: McGraw-Hill.</ref>

[[Predynastic Egypt]]ians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that [[megalith]]ic monuments in [[England]] and [[Scotland]], dating from the 3rd millennium BC, incorporate geometric ideas such as [[circle]]s, [[ellipse]]s, and [[Pythagorean triple]]s in their design.<ref>Thom, Alexander; Archie Thom (1988). "The metrology and geometry of Megalithic Man", pp. 132–51 in Ruggles, C. L. N. (ed.), ''Records in Stone: Papers in memory of Alexander Thom''. Cambridge University Press. {{ISBN|0-521-33381-4}}.</ref> All of the above are disputed however, and the currently oldest undisputed mathematical documents are from Babylonian and dynastic Egyptian sources.<ref>{{cite book|first=Peter|last=Damerow|date=1996 |chapter-url=https://books.google.com/books?id=c4yBmjnY1JIC&pg=PA199|title=Abstraction & Representation: Essays on the Cultural Evolution of Thinking (Boston Studies in the Philosophy & History of Science)|chapter=The Development of Arithmetical Thinking: On the Role of Calculating Aids in Ancient Egyptian & Babylonian Arithmetic|isbn=0792338162|publisher=Springer|access-date=2019-08-17}}</ref>