Sejarah matematika: Perbedaan antara revisi

Benda matematika tertua yang sudah diketahui adalah [[tulang Lebombo]], ditemukan di pegunungan Lebombo di [[Swaziland]] dan mungkin berasal dari tahun 35000 SM.<ref>http://mathworld.wolfram.com/LebomboBone.html</ref> Tulang ini berisi 29 torehan yang berbeda yang sengaja digoreskan pada tulang fibula baboon.<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 | accessdate = 2006-05-06}}</ref> Terdapat bukti bahwa kaum perempuan biasa menghitung untuk mengingat [[siklus haid]] mereka; 28 sampai 30 goresan pada [[tulang]] atau [[batu]], diikuti dengan tanda yang berbeda.<ref>{{cite web | last = Kellermeier | first = John | year = 2003 | url = http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm | title = How Menstruation Created Mathematics | work = Ethnomathematics | publisher = Tacoma Community College | accessdate = 2006-05-06}}</ref> Juga [[artefak]] [[prasejarah]] ditemukan di [[Afrika]] dan [[Perancis]], dari tahun 35.000 SM dan berumur 20.000 tahun,<ref>[http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html Benda matematika kuno]</ref> menunjukkan upaya dini untuk menghitung waktu.<ref>[http://etopia.sintlucas.be/3.14/Ishango_meeting/Mathematics_Africa.pdf Matematika di Afrika bagian tengah sebelum pendudukan]</ref>

 

 

== Timur Dekat kuno ==

{{Main|Greek mathematics}}

[[Image:Kapitolinischer Pythagoras.jpg|left|thumb|180px|Pythagoras of Samos]]

 

[[Image:Thales.jpg|thumb|180px|Thales of Miletus]] Greek mathematics was more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used [[mathematical rigor]] to [[mathematical proof|prove]] them.<ref>Martin Bernal, "Animadversions on the Origins of Western Science", pp. 72–83 in Michael H. Shank, ed., ''The Scientific Enterprise in Antiquity and the Middle Ages'', (Chicago: University of Chicago Press) 2000, p. 75.</ref>

Thales used [[geometry]] to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited the first use of deductive reasoning applied to geometry, by deriving four corollaries to the [[Thales' Theorem]]. As a result, he has been hailed as the first true mathematician and the firs known individual to whom a mathematical discovery has been attributed to.<ref>{{Harv|Boyer|1991|loc="Ionia and the Pythagoreans" p. 43}}</ref> Pythagoras established the [[Pythagoreans|Pythagorean School]], whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".<ref>{{Harv|Boyer|1991|loc="Ionia and the Pythagoreans" p. 49}}</ref> It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the [[Pythagorean theorem]],<ref>Eves, Howard, An Introduction to the History of Mathematics, Saunders, 1990, ISBN 0-03-029558-0.</ref> though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.{{Citation needed|date=February 2010}}

 

 

[[Archimedes]] (c.287–212 BC) of [[Syracuse, Italy|Syracuse]] used the [[method of exhaustion]] to calculate the [[area]] under the arc of a [[parabola]] with the [[Series (mathematics)|summation of an infinite series]], and gave remarkably accurate approximations of [[Pi]].<ref>{{cite web | title = A history of calculus |author=O'Connor, J.J. and Robertson, E.F. | publisher = [[University of St Andrews]]| url = http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html |date= February 1996|accessdate= 2007-08-07}}</ref> He also studied the [[Archimedes spiral|spiral]] bearing his name, formulas for the [[volume]]s of [[surface of revolution|surfaces of revolution]], and an ingenious system for expressing very large numbers.

Early Chinese mathematics is so different from that of other parts of the world that it is reasonable to assume independent development.<ref>{{Harv|Boyer|1991|loc="China and India" p. 201}}</ref> The oldest extant mathematical text from China is the ''Chou Pei Suan Ching'', variously dated to between 1200 BC and 100 BC, though a date of about 300 BC appears reasonable.<ref>{{Harv|Boyer|1991|loc="China and India" p. 196}}</ref>

 

 

The oldest existent work on [[geometry]] in China comes from the philosophical [[Mohism|Mohist]] canon c. 330 BC, compiled by the followers of [[Mozi]] (470–390 BC). The ''Mo Jing'' described various aspects of many fields associated with physical science, and provided a small wealth of information on mathematics as well.

In the 9th century, {{Unicode|[[Muhammad ibn Mūsā al-Khwārizmī|Muḥammad ibn Mūsā al-Ḵwārizmī]]}} wrote several important books on the Hindu-Arabic numerals and on methods for solving equations. His book ''On the Calculation with Hindu Numerals'', written about 825, along with the work of [[Al-Kindi]], were instrumental in spreading [[Indian mathematics]] and [[Hindu-Arabic numeral system|Indian numerals]] to the West. The word ''[[algorithm]]'' is derived from the Latinization of his name, Algoritmi, and the word ''[[algebra]]'' from the title of one of his works, ''[[The Compendious Book on Calculation by Completion and Balancing|Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala]]'' (''The Compendious Book on Calculation by Completion and Balancing''). Al-Khwarizmi is often called the "father of algebra", for his fundamental contributions to the field.<ref>[http://www.ucs.louisiana.edu/~sxw8045/history.htm The History of Algebra]. [[Louisiana State University]].</ref> He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots,<ref>{{Harv|Boyer|1991|loc="The Arabic Hegemony" p. 230}} "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions."</ref> and he was the first to teach algebra in an [[Elementary algebra|elementary form]] and for its own sake.<ref>Gandz and Saloman (1936), ''The sources of al-Khwarizmi's algebra'', Osiris i, pp. 263–77: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".</ref> He also introduced the fundamental method of "[[Reduction (mathematics)|reduction]]" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which Al-Khwarizmi originally described as ''al-jabr''.<ref name=Boyer-229>{{Harv|Boyer|1991|loc="The Arabic Hegemony" p. 229}} "It is not certain just what the terms ''al-jabr'' and ''muqabalah'' mean, but the usual interpretation is similar to that implied in the translation above. The word ''al-jabr'' presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word ''muqabalah'' is said to refer to "reduction" or "balancing" - that is, the cancellation of like terms on opposite sides of the equation."</ref> His algebra was also no longer concerned "with a series of [[problem]]s to be resolved, but an [[Expository writing|exposition]] which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."<ref name=Rashed-Armstrong>{{Cite book | last1=Rashed | first1=R. | last2=Armstrong | first2=Angela | year=1994 | title=The Development of Arabic Mathematics | publisher=[[Springer Science+Business Media|Springer]] | isbn=0792325656 | oclc=29181926 | pages=11–12}}</ref>

 

 

In the late 11th century, [[Omar Khayyam]] wrote ''Discussions of the Difficulties in Euclid'', a book about flaws in [[Euclid's Elements|Euclid's ''Elements'']], especially the [[parallel postulate]], and laid the foundations for [[analytic geometry]] and [[non-Euclidean geometry]].{{Citation needed|date=March 2009}} He was also the first to find the general geometric solution to [[cubic equation]]s. He was also very influential in [[calendar reform]].{{Citation needed|date=March 2009}}

Notable historical conjectures were finally proved. In 1976, [[Wolfgang Haken]] and [[Kenneth Appel]] used a computer to prove the [[four color theorem]]. [[Andrew Wiles]], building on the work of others, proved [[Fermat's Last Theorem]] in 1995. [[Paul Cohen (mathematician)|Paul Cohen]] and [[Kurt Gödel]] proved that the [[continuum hypothesis]] is [[logical independence|independent]] of (could neither be proved nor disproved from) the [[ZFC|standard axioms of set theory]]. In 1998 [[Thomas Callister Hales]] proved the [[Kepler conjecture]].

 

 

[[Differential geometry]] came into its own when [[Einstein]] used it in [[general relativity]]. Entire new areas of mathematics such as [[mathematical logic]], [[topology]], and [[John von Neumann]]'s [[game theory]] changed the kinds of questions that could be answered by mathematical methods. All kinds of [[Mathematical structure|structures]] were abstracted using axioms and given names like [[metric space]]s, [[topological space]]s etc. As mathematicians do, the concept of an abstract structure was itself abstracted and led to [[category theory]]. [[Grothendieck]] and [[Jean-Pierre Serre|Serre]] recast [[algebraic geometry]] using [[Sheaf (mathematics)|sheaf theory]]. Large advances were made in the qualitative study of [[dynamical systems theory|dynamical systems]] that [[Poincaré]] had began in the 1890s. [[Measure theory]] was developed in the late 19th and early 20th century. Applications of measures include the [[Lebesgue integral]], [[Kolmogorov]]'s axiomatisation of [[probability theory]], and [[ergodic theory]]. [[Knot theory]] greatly expanded. Other new areas include [[functional analysis]], [[Laurent Schwarz]]'s [[Distribution (mathematics)|distribution theory]], [[fixed point theory]], [[singularity theory]] and [[René Thom]]'s [[catastrophe theory]], [[model theory]], and [[Mandelbrot]]'s [[fractals]].

* [[Paul Hoffman (science writer)|Hoffman, Paul]], ''The Man Who Loved Only Numbers: The Story of [[Paul Erdős]] and the Search for Mathematical Truth''. New York: Hyperion, 1998 ISBN 0-7868-6362-5.

*{{cite book|first=Ivor|last=Grattan-Guinness|title=Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences|publisher=The Johns Hopkins University Press|year=2003|isbn=0801873975}}

* O'Connor, John J. and Robertson, Edmund F. ''[http://www-groups.dcs.st-andrews.ac.uk/~history/ The MacTutor History of Mathematics Archive]''. This website contains biographies, timelines and historical articles about mathematical concepts; at the School of Mathematics and Statistics, [[University of St. Andrews]], Scotland. (Or see the [http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Hist_Topics_alph.html alphabetical list of history topics].)

*{{cite book| last = Stigler| first = Stephen M.| authorlink = Stephen Stigler| year = 1990| title = The History of Statistics: The Measurement of Uncertainty before 1900| publisher = Belknap Press | isbn = 0-674-40341-X}}

| first1=Kim

| year=2009

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| publisher=Princeton, NJ: Princeton University Press. Pp. 384.

 

=== Jurnal ===

 

=== Direktori ===

*[http://www.dm.unipi.it/~tucci/index.html History of Mathematics] (Roberta Tucci)

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