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| {{Use dmy dates|date=September 2010}}
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| A [[timeline]] of [[pure mathematics|pure]] and [[applied mathematics]] [[History of mathematics|history]].
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| {{also|history of mathematical notation}}
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| ==Timeline==
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| ===Rhetorical stage===
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| ====Before 1000 BC====
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| * ca. [[Middle Paleolithic|70,000 BC]] — South Africa, ochre rocks adorned with scratched [[Geometry|geometric]] patterns.<ref>[http://www.accessexcellence.org/WN/SU/caveart.html Art Prehistory], Sean Henahan, January 10, 2002.</ref>
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| * ca. [[35,000 BC]] to [[Upper Paleolithic|20,000 BC]] — Africa and France, earliest known [[prehistory|prehistoric]] attempts to quantify time.<ref>[http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm How Menstruation Created Mathematics], [[Tacoma Community College]], [http://web.archive.org/web/20051223112514/http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm archive link]</ref><ref>[http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html OLDEST Mathematical Object is in Swaziland<!-- Bot generated title -->]</ref><ref>[http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html an old Mathematical Object<!-- Bot generated title -->]</ref>
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| * c. 20,000 BC — [[Nile Valley]], [[Ishango Bone]]: possibly the earliest reference to [[prime number]]s and [[Egyptian multiplication]].
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| * c. 3400 BC — [[Mesopotamia]], the [[Sumerians]] invent the first [[numeral system]], and a system of [[Ancient Mesopotamian units of measurement|weights and measures]].
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| * c. 3100 BC — [[Egypt]], earliest known [[decimal|decimal system]] allows indefinite counting by way of introducing new symbols.<ref name="buffalo1">[http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html#berlin. Egyptian Mathematical Papyri - Mathematicians of the African Diaspora<!-- Bot generated title -->]</ref>
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| * c. 2800 BC — [[Indus Valley Civilization]] on the [[Indian subcontinent]], earliest use of decimal ratios in a uniform system of [[Ancient Indus Valley units of measurement|ancient weights and measures]], the smallest unit of measurement used is 1.704 millimetres and the smallest unit of mass used is 28 grams.
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| * 2700 BC — Egypt, precision [[surveying]].
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| * 2400 BC — Egypt, precise [[Egyptian calendar|astronomical calendar]], used even in the [[Middle Ages]] for its mathematical regularity.
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| * c. 2000 BC — Mesopotamia, the [[Babylonians]] use a base-60 positional numeral system, and compute the first known approximate value of [[pi|π]] at 3.125.
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| * c. 2000 BC — Scotland, [[Carved Stone Balls]] exhibit a variety of symmetries including all of the symmetries of [[Platonic solid]]s.
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| * 1800 BC — [[Moscow Mathematical Papyrus]], findings volume of a [[frustum]].
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| * c. 1800 BC — [[Berlin papyrus 6619]] (19th dynasty) contains a quadratic equation and its solution.<ref name="buffalo1"/>
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| * 1650 BC — [[Rhind Mathematical Papyrus]], copy of a lost scroll from around 1850 BC, the scribe [[Ahmes]] presents one of the first known approximate values of π at 3.16, the first attempt at [[squaring the circle]], earliest known use of a sort of [[cotangent]], and knowledge of solving first order linear equations.
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| * 1046 BC to 256 BC — ''[[Chou Pei Suan Ching]]'', the oldest Chinese mathematical text, is written
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| ===Syncopated stage===
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| ====1st millennium BC====
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| * c. 1000 BC — [[Vulgar fraction]]s used by the [[Egyptians]]. However, only unit fractions are used (i.e., those with 1 as the numerator) and [[interpolation]] tables are used to approximate the values of the other fractions.<ref>Carl B. Boyer, A History of Mathematics, 2nd Ed.</ref>
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| * first half of 1st millennium BC — [[Vedic civilization|Vedic India]] — [[Yajnavalkya]], in his [[Shatapatha Brahmana]], describes the motions of the sun and the moon, and advances a 95-year cycle to synchronize the motions of the sun and the moon.
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| * c. 8th century BC — the [[Yajur Veda]], one of the four [[Hindu]] [[Veda]]s, contains the earliest concept of [[infinity]], and states that “if you remove a part from infinity or add a part to infinity, still what remains is infinity.”
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| * 800 BC — [[Baudhayana]], author of the Baudhayana [[Sulba Sutras|Sulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equations]], and calculates the [[square root of two]] correctly to five decimal places.
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| * early 6th century BC — [[Thales|Thales of Miletus]] has various theorems attributed to him.
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| * c. 600 BC — the other Vedic “Sulba Sutras” (“rule of chords” in [[Sanskrit]]) use [[Pythagorean triples]], contain of a number of geometrical proofs, and approximate [[pi|π]] at 3.16.
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| * second half of 1st millennium BC — The [[Lo Shu Square]], the unique normal [[magic square]] of order three, was discovered in China.
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| * 530 BC — [[Pythagoras]] studies propositional [[geometry]] and vibrating lyre strings; his group also discovers the [[irrational number|irrationality]] of the [[square root of two]].
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| * c. 500 BC — [[History of India|Indian]] grammarian [[Pāṇini|Pānini]] writes the [[Astadhyayi]], which contains the use of metarules, [[transformation (mathematics)|transformations]] and [[recursion]]s, originally for the purpose of systematizing the grammar of Sanskrit.
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| * 5th century BC — [[Hippocrates of Chios]] utilizes [[Lune (mathematics)|lunes]] in an attempt to [[squaring the circle|square the circle]].
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| * 5th century BC — [[Apastamba]], author of the Apastamba Sulba Sutra, another Vedic Sanskrit geometric text, makes an attempt at squaring the circle and also calculates the square root of 2 correct to five decimal places.
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| * c. 400 BC — [[Jain]]a mathematicians in India write the “Surya Prajinapti”, a mathematical text which classifies all numbers into three sets: enumerable, innumerable and [[Infinite set|infinite]]. It also recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
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| * 4th century BC — [[Indian mathematics|Indian]] texts use the Sanskrit word “Shunya” to refer to the concept of ‘void’ ([[0 (number)|zero]]).
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| * 370 BC — [[Eudoxus of Cnidus|Eudoxus]] states the [[method of exhaustion]] for [[area]] determination.
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| * 350 BC — [[Aristotle]] discusses [[logic]]al reasoning in ''[[Organon]]''.
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| * 330 BC — the earliest work on [[History of geometry#Chinese geometry|Chinese geometry]], the ''Mo Jing'', is compiled
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| * 300 BC — [[Jain]] mathematicians in India write the “Bhagabati Sutra”, which contains the earliest information on [[combinations]].
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| * 300 BC — [[Euclid]] in his ''[[Euclid's Elements|Elements]]'' studies geometry as an [[axiomatic system]], proves the infinitude of [[prime number]]s and presents the [[Euclidean algorithm]]; he states the law of reflection in ''Catoptrics'', and he proves the [[fundamental theorem of arithmetic]].
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| * c. 300 BC — [[Brahmi numeral]]s (ancestor of the common modern [[base 10]] [[numeral system]]) are conceived in India.
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| * 300 BC — [[Mesopotamia]], the [[Babylonians]] invent the earliest calculator, the [[abacus]].
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| * c. 300 BC — [[Indian mathematicians|Indian mathematician]] [[Pingala]] writes the “Chhandah-shastra”, which contains the first Indian use of zero as a digit (indicated by a dot) and also presents a description of a [[binary numeral system]], along with the first use of [[Fibonacci numbers]] and [[Pascal's triangle]].
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| * 202 BC to 186 BC — ''[[Book on Numbers and Computation]]'', a mathematical treatise, is written in [[Han Dynasty]] China
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| * 260 BC — [[Archimedes]] proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He also gave a very accurate estimate of the value of the square root of 3.
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| * c. 250 BC — late [[Olmec]]s had already begun to use a true zero (a shell glyph) several centuries before [[Ptolemy]] in the New World. See [[0 (number)]].
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| * 240 BC — [[Eratosthenes]] uses [[Sieve of Eratosthenes|his sieve algorithm]] to quickly isolate prime numbers.
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| * 225 BC — [[Apollonius of Perga]] writes ''On [[Conic section|Conic Sections]]'' and names the [[ellipse]], [[parabola]], and [[hyperbola]].
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| * 206 BC to 8 AD — [[Counting rods]] are invented in China
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| * 150 BC — [[Jainism|Jain]] mathematicians in India write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, geometry, operations with [[fractions]], simple equations, [[cubic equations]], quartic equations, and [[permutations]] and combinations.
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| * 150 BC — A method of [[Gaussian elimination]] appears in the Chinese text ''[[The Nine Chapters on the Mathematical Art]]''
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| * 150 BC — [[Horner's method]] appears in the Chinese text ''[[The Nine Chapters on the Mathematical Art]]''
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| * 150 BC — [[Negative numbers]] first appear in the Chinese text ''[[The Nine Chapters on the Mathematical Art]]''
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| * 140 BC — [[Hipparchus]] develops the bases of [[trigonometry]].
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| * 50 BC — [[Indian numerals]], a descendant of the [[Brahmi numerals]] (the first [[positional notation]] [[base-10]] [[numeral system]]), begins development in [[History of India|India]].
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| * final centuries BC — Indian astronomer [[Lagadha]] writes the “Vedanga Jyotisha”, a Vedic text on [[astronomy]] that describes rules for tracking the motions of the sun and the moon, and uses geometry and trigonometry for astronomy.
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| ====1st millennium AD====
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| * 1st century — [[Heron of Alexandria]], the earliest fleeting reference to square roots of negative numbers.
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| * c. 3rd century — [[Ptolemy]] of [[Alexandria]] wrote the [[Almagest]]
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| * 250 — [[Diophantus]] uses symbols for unknown numbers in terms of syncopated [[algebra]], and writes ''[[Arithmetica]]'', one of the earliest treatises on algebra
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| * 263 — [[Liu Hui]] computes [[pi|π]] using [[Liu Hui's π algorithm]]
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| * 300 — the earliest known use of [[0 (number)|zero]] as a decimal digit is introduced by [[Indian mathematicians]]
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| * 300 to 500 — the [[Chinese remainder theorem]] is developed by [[Sun Tzu (mathematician)|Sun Tzu]]
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| * 300 to 500 — a description of [[rod calculus]] is written by [[Sun Tzu (mathematician)|Sun Tzu]]
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| * c. 340 — [[Pappus of Alexandria]] states his [[Pappus's hexagon theorem|hexagon theorem]] and his [[Pappus's centroid theorem|centroid theorem]]
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| * c. 400 — the [[Bakhshali manuscript]] is written by [[Jain]]a mathematicians, which describes a theory of the infinite containing different levels of [[Infinite set|infinity]], shows an understanding of [[Index (mathematics)|indices]]{{dn|date=November 2012}}, as well as [[logarithms]] to [[base 2]], and computes [[square roots]] of numbers as large as a million correct to at least 11 decimal places
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| * 450 — [[Zu Chongzhi]] computes [[pi|π]] to seven decimal places,
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| * 500 — [[Aryabhata]] writes the “Aryabhata-Siddhanta”, which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of [[sine]] and [[cosine]], and also contains the [[Aryabhata's sine table|earliest tables of sine]] and cosine values (in 3.75-degree intervals from 0 to 90 degrees)
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| * 6th century — Aryabhata gives accurate calculations for astronomical constants, such as the [[solar eclipse]] and [[lunar eclipse]], computes π to four decimal places, and obtains whole number solutions to [[linear equations]] by a method equivalent to the modern method
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| * 550 — [[Hindu]] mathematicians give zero a numeral representation in the [[positional notation]] [[Indian numerals|Indian numeral]] system
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| * 7th century — [[Bhaskara I]] gives a rational approximation of the sine function
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| * 7th century — [[Brahmagupta]] invents the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon
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| * 628 — Brahmagupta writes the ''[[Brahmasphutasiddhanta|Brahma-sphuta-siddhanta]]'', where zero is clearly explained, and where the modern [[place-value]] Indian numeral system is fully developed. It also gives rules for manipulating both [[negative and positive numbers]], methods for computing square roots, methods of solving [[linear equation|linear]] and [[quadratic equation]]s, and rules for summing [[series (mathematics)|series]], [[Brahmagupta's identity]], and the [[Brahmagupta theorem]]
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| * 8th century — [[Virasena]] gives explicit rules for the [[Fibonacci sequence]], gives the derivation of the [[volume]] of a [[frustum]] using an [[Infinity|infinite]] procedure, and also deals with the [[logarithm]] to base 2 and knows its laws
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| * 8th century — [[Shridhara]] gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations
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| * 773 — Kanka brings Brahmagupta's Brahma-sphuta-siddhanta to [[Baghdad]] to explain the Indian system of arithmetic [[astronomy]] and the Indian numeral system
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| * 773 — Al Fazaii translates the Brahma-sphuta-siddhanta into Arabic upon the request of King Khalif Abbasid Al Mansoor
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| * 9th century — [[Govindsvamin]] discovers the Newton-Gauss interpolation formula, and gives the fractional parts of Aryabhata's tabular [[Sine (trigonometric function)|sines]]
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| * 810 — The [[House of Wisdom]] is built in Baghdad for the translation of Greek and [[Sanskrit]] mathematical works into Arabic.
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| * 820 — [[Al-Khwarizmi]] — [[Persian people|Persian]] mathematician, father of algebra, writes the ''[[The Compendious Book on Calculation by Completion and Balancing|Al-Jabr]]'', later transliterated as ''[[Algebra]]'', which introduces systematic algebraic techniques for solving linear and quadratic equations. Translations of his book on [[arithmetic]] will introduce the [[Arabic numerals|Hindu-Arabic]] [[decimal]] number system to the Western world in the 12th century. The term ''[[algorithm]]'' is also named after him.
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| * 820 — [[Al-Mahani]] conceived the idea of reducing [[Geometry|geometrical]] problems such as [[doubling the cube]] to problems in algebra.
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| * c. 850 — [[Al-Kindi]] pioneers [[cryptanalysis]] and [[frequency analysis]] in his book on [[cryptography]].
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| * 895 — [[Thabit ibn Qurra]]: the only surviving fragment of his original work contains a chapter on the solution and properties of [[cubic equation]]s. He also generalized the [[Pythagorean theorem]], and discovered the [[Thabit number|theorem]] by which pairs of [[amicable number]]s can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other).
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| * c. 900 — [[Abu Kamil]] of Egypt had begun to understand what we would write in symbols as <math>x^n \cdot x^m = x^{m+n}</math>
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| * 940 — [[Abu'l-Wafa al-Buzjani]] extracts [[root of a function|roots]] using the Indian numeral system.
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| * 953 — The arithmetic of the [[Hindu-Arabic numeral system]] at first required the use of a dust board (a sort of handheld [[blackboard]]) because “the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded.” [[Al-Uqlidisi]] modified these methods for pen and paper use. Eventually the advances enabled by the decimal system led to its standard use throughout the region and the world.
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| * 953 — [[Al-Karaji]] is the “first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the [[monomial]]s <math>x</math>, <math>x^2</math>, <math>x^3</math>, … and <math>1/x</math>, <math>1/x^2</math>, <math>1/x^3</math>, … and to give rules for [[product (mathematics)|products]] of any two of these. He started a school of algebra which flourished for several hundreds of years”. He also discovered the [[binomial theorem]] for [[integer]] [[exponent]]s, which “was a major factor in the development of [[numerical analysis]] based on the decimal system.”
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| * 975 — [[Al-Batani]] extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formulae: <math> \sin \alpha = \tan \alpha / \sqrt{1+\tan^2 \alpha} </math> and <math> \cos \alpha = 1 / \sqrt{1 + \tan^2 \alpha}</math>.
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| ===Symbolic stage===
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| ====1000–1500====
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| * c. 1000 — [[Abū Sahl al-Qūhī]] (Kuhi) solves [[equation]]s higher than the [[Quadratic equation|second degree]].
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| * c. 1000 — [[Abu-Mahmud al-Khujandi]] first states a special case of [[Fermat's Last Theorem]].
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| * c. 1000 — [[Law of sines]] is discovered by [[Islamic mathematics|Muslim mathematicians]], but it is uncertain who discovers it first between Abu-Mahmud al-Khujandi, [[Abu Nasr Mansur]], and [[Abū al-Wafā' al-Būzjānī|Abu al-Wafa]].
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| * c. 1000 — [[Pope Sylvester II]] introduces the [[abacus]] using the [[Hindu-Arabic numeral system]] to Europe.
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| * 1000 — [[Al-Karaji]] writes a book containing the first known [[Mathematical proof|proofs]] by [[mathematical induction]]. He used it to prove the [[binomial theorem]], [[Pascal's triangle]], and the sum of [[Integer|integral]] [[Cube (algebra)|cubes]].<ref>Victor J. Katz (1998). ''History of Mathematics: An Introduction'', p. 255–259. [[Addison-Wesley]]. ISBN 0-321-01618-1.</ref> He was “the first who introduced the theory of [[algebra]]ic [[calculus]].”<ref>F. Woepcke (1853). ''Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi''. Paris.</ref>
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| * c. 1000 — [[Ibn Tahir al-Baghdadi]] studied a slight variant of [[Thabit ibn Qurra]]'s theorem on [[amicable number]]s, and he also made improvements on the decimal system.
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| * 1020 — [[Abul Wáfa]] gave this famous formula: sin (α + β) = sin α cos β + sin β cos α. Also discussed the quadrature of the [[parabola]] and the volume of the [[paraboloid]].
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| * 1021 — [[Ibn al-Haytham]] formulated and solved [[Alhazen's problem]] geometrically.
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| * 1030 — [[Ali Ahmad Nasawi]] writes a treatise on the [[decimal]] and [[sexagesimal]] number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner.<ref>{{MacTutor|id=Al-Nasawi|title=Abu l'Hasan Ali ibn Ahmad Al-Nasawi}}</ref>
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| * 1070 — [[Omar Khayyám]] begins to write ''Treatise on Demonstration of Problems of Algebra'' and classifies cubic equations.
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| * c. 1100 — Omar Khayyám “gave a complete classification of [[cubic equation]]s with geometric solutions found by means of intersecting [[conic section]]s.” He became the first to find general [[geometry|geometric]] solutions of cubic equations and laid the foundations for the development of [[analytic geometry]] and [[non-Euclidean geometry]]. He also extracted [[root of a function|roots]] using the decimal system (Hindu-Arabic numeral system).
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| * 12th century — [[Indian numerals]] have been modified by Arab mathematicians to form the modern [[Hindu-Arabic numeral]] system (used universally in the modern world)
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| * 12th century — the Hindu-Arabic numeral system reaches Europe through the [[Arabs]]
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| * 12th century — [[Bhaskara II|Bhaskara Acharya]] writes the [[Lilavati]], which covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, [[solid geometry]], the shadow of the [[gnomon]], methods to solve indeterminate equations, and [[combinations]]
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| * 12th century — [[Bhāskara II]] (Bhaskara Acharya) writes the “[[Bijaganita]]” (“[[Algebra]]”), which is the first text to recognize that a positive number has two square roots
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| * 12th century — Bhaskara Acharya conceives [[differential calculus]], and also develops [[Rolle's theorem]], [[Pell's equation]], a proof for the [[Pythagorean Theorem]], proves that division by zero is infinity, computes [[pi|π]] to 5 decimal places, and calculates the time taken for the earth to orbit the sun to 9 decimal places
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| * 1130 — [[Al-Samawal]] gave a definition of algebra: “[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.”<ref name=MacTutor/>
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| * 1135 — [[Sharafeddin Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on cubic equations which “represents an essential contribution to another algebra which aimed to study [[curve]]s by means of equations, thus inaugurating the beginning of [[algebraic geometry]].”<ref name=MacTutor>[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics], ''[[MacTutor History of Mathematics archive]]'', [[University of St Andrews]], Scotland</ref>
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| * 1202 — [[Leonardo of Pisa|Leonardo Fibonacci]] demonstrates the utility of [[Hindu-Arabic numerals]] in his [[Liber Abaci]] (''Book of the Abacus'').
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| * 1247 — [[Qin Jiushao]] publishes ''Shùshū Jiǔzhāng'' (“[[Mathematical Treatise in Nine Sections]]”).
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| * 1260 — [[Al-Farisi]] gave a new proof of Thabit ibn Qurra's theorem, introducing important new ideas concerning [[factorization]] and [[Combinatorics|combinatorial]] methods. He also gave the pair of amicable numbers 17296 and 18416 which have also been joint attributed to [[Fermat]] as well as Thabit ibn Qurra.<ref name="Various AP Lists and Statistics">[http://amicable.homepage.dk/apstat.htm#discoverer Various AP Lists and Statistics]</ref>
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| * c. 1250 — [[Nasir Al-Din Al-Tusi]] attempts to develop a form of non-Euclidean geometry.
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| * 1303 — [[Zhu Shijie]] publishes ''Precious Mirror of the Four Elements'', which contains an ancient method of arranging [[binomial coefficient]]s in a triangle.
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| * 14th century — [[Madhava of Sangamagrama|Madhava]] is considered the father of [[mathematical analysis]], who also worked on the power series for π and for sine and cosine functions, and along with other [[Kerala school of astronomy and mathematics|Kerala school]] mathematicians, founded the important concepts of [[Calculus]]
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| * 14th century — [[Parameshvara]], a Kerala school mathematician, presents a series form of the [[sine function]] that is equivalent to its [[Taylor series]] expansion, states the [[mean value theorem]] of differential calculus, and is also the first mathematician to give the radius of circle with inscribed [[cyclic quadrilateral]]
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| * 1400 — Madhava discovers the series expansion for the inverse-tangent function, the infinite series for arctan and sin, and many methods for calculating the circumference of the circle, and uses them to compute π correct to 11 decimal places
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| * c. 1400 — [[Ghiyath al-Kashi]] “contributed to the development of [[decimal fraction]]s not only for approximating [[algebraic number]]s, but also for [[real number]]s such as π. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating [[nth root]]s which is a special case of the methods given many centuries later by [[Paolo Ruffini|Ruffini]] and [[William George Horner|Horner]].” He is also the first to use the [[decimal point]] notation in [[arithmetic]] and [[Arabic numerals]]. His works include ''The Key of arithmetics, Discoveries in mathematics, The Decimal point'', and ''The benefits of the zero''. The contents of the ''Benefits of the Zero'' are an introduction followed by five essays: “On whole number arithmetic”, “On fractional arithmetic”, “On astrology”, “On areas”, and “On finding the unknowns [unknown variables]”. He also wrote the ''Thesis on the sine and the chord'' and ''Thesis on finding the first degree sine''.
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| * 15th century — [[Ibn al-Banna]] and [[al-Qalasadi]] introduced [[Mathematical notation|symbolic notation]] for algebra and for mathematics in general.<ref name=MacTutor/>
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| * 15th century — [[Nilakantha Somayaji]], a Kerala school mathematician, writes the “Aryabhatiya Bhasya”, which contains work on infinite-series expansions, problems of algebra, and spherical geometry
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| * 1424 — Ghiyath al-Kashi computes π to sixteen decimal places using inscribed and circumscribed polygons.
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| * 1427 — [[Al-Kashi]] completes ''The Key to Arithmetic'' containing work of great depth on decimal fractions. It applies arithmetical and algebraic methods to the solution of various problems, including several geometric ones.
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| * 1478 — An anonymous author writes the [[Treviso Arithmetic]].
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| * 1494 — [[Luca Pacioli]] writes "Summa de arithmetica, geometria, proportioni et proportionalità"; introduces primitive symbolic algebra using "co" (cosa) for the unknown.
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| ====Modern====
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| =====16th century=====
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| * 1501 — [[Nilakantha Somayaji]] writes the [[Tantrasamgraha]].
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| * 1520 — [[Scipione dal Ferro]] develops a method for solving “depressed” cubic equations (cubic equations without an x<sup>2</sup> term), but does not publish.
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| * 1522 — [[Adam Ries]] explained the use of Arabic digits and their advantages over Roman numerals.
| |
| * 1535 — [[Niccolo Tartaglia]] independently develops a method for solving depressed cubic equations but also does not publish.
| |
| * 1539 — [[Gerolamo Cardano]] learns Tartaglia's method for solving depressed cubics and discovers a method for depressing cubics, thereby creating a method for solving all cubics.
| |
| * 1540 — [[Lodovico Ferrari]] solves the [[quartic equation]].
| |
| * 1544 — [[Michael Stifel]] publishes “Arithmetica integra”.
| |
| * 1550 — [[Jyeshtadeva]], a [[Kerala school of astronomy and mathematics|Kerala school]] mathematician, writes the “[[Yuktibhāṣā]]", the world's first [[calculus]] text, which gives detailed derivations of many calculus theorems and formulae.
| |
| * 1572 — [[Rafael Bombelli]] writes "Algebra" teatrise and uses imaginary numbers to solve cubic equations.
| |
| * 1584 — [[Zhu Zaiyu]] calculates [[equal temperament]]
| |
| * 1596 — [[Ludolf van Ceulen]] computes π to twenty decimal places using inscribed and circumscribed polygons.
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| | |
| =====17th century=====
| |
| * 1614 — [[John Napier]] discusses Napierian [[logarithm]]s in ''Mirifici Logarithmorum Canonis Descriptio'',
| |
| * 1617 — [[Henry Briggs (mathematician)|Henry Briggs]] discusses decimal logarithms in ''Logarithmorum Chilias Prima'',
| |
| * 1618 — John Napier publishes the first references to [[E (mathematical constant)|''e'']] in a work on [[logarithms]].
| |
| * 1619 — [[René Descartes]] discovers [[analytic geometry]] ([[Pierre de Fermat]] claimed that he also discovered it independently),
| |
| * 1619 — [[Johannes Kepler]] discovers two of the [[Kepler-Poinsot polyhedra]].
| |
| * 1629 — Pierre de Fermat develops a rudimentary [[differential calculus]],
| |
| * 1634 — [[Gilles de Roberval]] shows that the area under a [[cycloid]] is three times the area of its generating circle,
| |
| * 1636 — [[Muhammad Baqir Yazdi]] jointly discovered the pair of [[amicable number]]s 9,363,584 and 9,437,056 along with [[Descartes]] (1636).<ref name="Various AP Lists and Statistics"/>
| |
| * 1637 — Pierre de Fermat claims to have proven [[Fermat's Last Theorem]] in his copy of [[Diophantus]]' ''Arithmetica'',
| |
| * 1637 — First use of the term [[imaginary number]] by René Descartes; it was meant to be derogatory.
| |
| * 1654 — [[Blaise Pascal]] and Pierre de Fermat create the theory of [[probability]],
| |
| * 1655 — [[John Wallis]] writes ''Arithmetica Infinitorum'',
| |
| * 1658 — [[Christopher Wren]] shows that the length of a cycloid is four times the diameter of its generating circle,
| |
| * 1665 — [[Isaac Newton]] works on the [[fundamental theorem of calculus]] and develops his version of [[infinitesimal calculus]],
| |
| * 1668 — [[Nicholas Mercator]] and [[William Brouncker, 2nd Viscount Brouncker|William Brouncker]] discover an [[infinite series]] for the logarithm while attempting to calculate the area under a [[hyperbolic segment]],
| |
| * 1671 — [[James Gregory (astronomer and mathematician)|James Gregory]] develops a series expansion for the inverse-[[tangent (trigonometric function)|tangent]] function (originally discovered by [[Madhava of Sangamagrama|Madhava]])
| |
| * 1673 — [[Gottfried Leibniz]] also develops his version of infinitesimal calculus,
| |
| * 1675 — Isaac Newton invents an algorithm for the [[Newton's method|computation of functional roots]],
| |
| * 1680s – Gottfried Leibniz works on symbolic logic,
| |
| * 1691 — Gottfried Leibniz discovers the technique of separation of variables for ordinary [[differential equation]]s,
| |
| * 1693 — [[Edmund Halley]] prepares the first mortality tables statistically relating death rate to age,
| |
| * 1696 — [[Guillaume François Antoine, Marquis de l'Hôpital|Guillaume de L'Hôpital]] states [[L'Hôpital's rule|his rule]] for the computation of certain [[limit (mathematics)|limits]],
| |
| * 1696 — [[Jakob Bernoulli]] and [[Johann Bernoulli]] solve [[brachistochrone curve|brachistochrone problem]], the first result in the [[calculus of variations]],
| |
| | |
| =====18th century=====
| |
| * 1706 — [[John Machin]] develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places,
| |
| * 1712 — [[Brook Taylor]] develops [[Taylor series]],
| |
| * 1722 — [[Abraham de Moivre]] states [[de Moivre's formula]] connecting [[trigonometric function]]s and [[complex number]]s,
| |
| * 1724 — Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in ''Annuities on Lives'',
| |
| * 1730 — [[James Stirling (mathematician)|James Stirling]] publishes ''The Differential Method'',
| |
| * 1733 — [[Giovanni Gerolamo Saccheri]] studies what geometry would be like if [[parallel postulate|Euclid's fifth postulate]] were false,
| |
| * 1733 — Abraham de Moivre introduces the [[normal distribution]] to approximate the [[binomial distribution]] in probability,
| |
| * 1734 — [[Leonhard Euler]] introduces the [[integrating factor technique]] for solving first-order ordinary [[differential equation]]s,
| |
| * 1735 — Leonhard Euler solves the [[Basel problem]], relating an infinite series to π,
| |
| * 1736 — Leonhard Euler solves the problem of the [[Seven bridges of Königsberg]], in effect creating [[graph theory]],
| |
| * 1739 — Leonhard Euler solves the general [[homogeneous linear ordinary differential equation]] with [[constant coefficients]],
| |
| * 1742 — [[Christian Goldbach]] conjectures that every even number greater than two can be expressed as the sum of two primes, now known as [[Goldbach's conjecture]],
| |
| * 1748 — [[Maria Gaetana Agnesi]] discusses analysis in ''Instituzioni Analitiche ad Uso della Gioventu Italiana'',
| |
| * 1761 — [[Thomas Bayes]] proves [[Bayes' theorem]],
| |
| * 1761 — [[Johann Heinrich Lambert]] proves that π is irrational,
| |
| * 1762 — [[Joseph Louis Lagrange]] discovers the [[divergence theorem]],
| |
| * 1789 — [[Jurij Vega]] improves Machin's formula and computes π to 140 decimal places,
| |
| * 1794 — Jurij Vega publishes ''[[Thesaurus Logarithmorum Completus]]'',
| |
| * 1796 — [[Carl Friedrich Gauss]] proves that the [[heptadecagon|regular 17-gon]] can be constructed using only a [[compass and straightedge]]
| |
| * 1796 — [[Adrien-Marie Legendre]] conjectures the [[prime number theorem]],
| |
| * 1797 — [[Caspar Wessel]] associates vectors with complex numbers and studies complex number operations in geometrical terms,
| |
| * 1799 — Carl Friedrich Gauss proves the [[fundamental theorem of algebra]] (every polynomial equation has a solution among the complex numbers),
| |
| * 1799 — [[Paolo Ruffini]] partially proves the [[Abel–Ruffini theorem]] that [[Quintic equation|quintic]] or higher equations cannot be solved by a general formula,
| |
| | |
| =====19th century=====
| |
| * 1801 — ''[[Disquisitiones Arithmeticae]]'', Carl Friedrich Gauss's [[number theory]] treatise, is published in Latin
| |
| * 1805 — Adrien-Marie Legendre introduces the [[method of least squares]] for fitting a curve to a given set of observations,
| |
| * 1806 — [[Louis Poinsot]] discovers the two remaining [[Kepler-Poinsot polyhedra]].
| |
| * 1806 — [[Jean-Robert Argand]] publishes proof of the [[Fundamental theorem of algebra]] and the [[Argand diagram]],
| |
| * 1807 — [[Joseph Fourier]] announces his discoveries about the [[Fourier series|trigonometric decomposition of functions]],
| |
| * 1811 — Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,
| |
| * 1815 — [[Siméon Denis Poisson]] carries out integrations along paths in the complex plane,
| |
| * 1817 — [[Bernard Bolzano]] presents the [[intermediate value theorem]]---a [[continuous function]] which is negative at one point and positive at another point must be zero for at least one point in between,
| |
| * 1822 — [[Augustin-Louis Cauchy]] presents the [[Cauchy integral theorem]] for integration around the boundary of a rectangle in the [[complex plane]],
| |
| * 1824 — [[Niels Henrik Abel]] partially proves the [[Abel–Ruffini theorem]] that the general [[Quintic equation|quintic]] or higher equations cannot be solved by a general formula involving only arithmetical operations and roots,
| |
| * 1825 — Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths—he assumes the function being integrated has a continuous derivative, and he introduces the theory of [[residue (complex analysis)|residue]]s in [[complex analysis]],
| |
| * 1825 — [[Peter Gustav Lejeune Dirichlet]] and Adrien-Marie Legendre prove Fermat's Last Theorem for ''n'' = 5,
| |
| * 1825 — [[André-Marie Ampère]] discovers [[Stokes' theorem]],
| |
| * 1828 — George Green proves [[Green's theorem]],
| |
| * 1829 — [[Bolyai]], [[Carl Friedrich Gauss|Gauss]], and [[Nikolai Ivanovich Lobachevsky|Lobachevsky]] invent hyperbolic [[non-Euclidean geometry]],
| |
| * 1831 — [[Mikhail Vasilievich Ostrogradsky]] rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,
| |
| * 1832 — [[Évariste Galois]] presents a general condition for the solvability of [[algebraic equation]]s, thereby essentially founding [[group theory]] and [[Galois theory]],
| |
| * 1832 — Lejeune Dirichlet proves Fermat's Last Theorem for ''n'' = 14,
| |
| * 1835 — Lejeune Dirichlet proves [[Dirichlet's theorem on arithmetic progressions|Dirichlet's theorem]] about prime numbers in arithmetical progressions,
| |
| * 1837 — [[Pierre Wantsel]] proves that doubling the cube and [[trisecting the angle]] are impossible with only a compass and straightedge, as well as the full completion of the problem of constructability of regular polygons
| |
| * 1841 — [[Karl Weierstrass]] discovers but does not publish the [[Laurent expansion theorem]],
| |
| * 1843 — [[Pierre-Alphonse Laurent]] discovers and presents the Laurent expansion theorem,
| |
| * 1843 — [[William Rowan Hamilton|William Hamilton]] discovers the calculus of [[quaternion]]s and deduces that they are non-commutative,
| |
| * 1847 — [[George Boole]] formalizes [[symbolic logic]] in ''The Mathematical Analysis of Logic'', defining what is now called [[Boolean algebra (logic)|Boolean algebra]],
| |
| * 1849 — [[George Gabriel Stokes]] shows that [[soliton|solitary wave]]s can arise from a combination of periodic waves,
| |
| * 1850 — [[Victor Alexandre Puiseux]] distinguishes between poles and branch points and introduces the concept of [[mathematical singularity|essential singular points]],
| |
| * 1850 — George Gabriel Stokes rediscovers and proves Stokes' theorem,
| |
| * 1854 — [[Bernhard Riemann]] introduces [[Riemannian geometry]],
| |
| * 1854 — [[Arthur Cayley]] shows that quaternions can be used to represent rotations in four-dimensional [[space]],
| |
| * 1858 — [[August Ferdinand Möbius]] invents the [[Möbius strip]],
| |
| * 1858 — [[Charles Hermite]] solves the general quintic equation by means of elliptic and modular functions,
| |
| * 1859 — Bernhard Riemann formulates the [[Riemann hypothesis]] which has strong implications about the distribution of [[prime number]]s,
| |
| * 1870 — [[Felix Klein]] constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate,
| |
| * 1872 — [[Richard Dedekind]] invents what is now called the Dedekind Cut for defining irrational numbers, and now used for defining surreal numbers,
| |
| * 1873 — [[Charles Hermite]] proves that [[e (mathematical constant)|e]] is transcendental,
| |
| * 1873 — [[Georg Frobenius]] presents his method for finding series solutions to linear differential equations with [[regular singular point]]s,
| |
| * 1874 — [[Georg Cantor]] proves that the set of all [[real number]]s is [[uncountable|uncountably infinite]] but the set of all real [[algebraic number]]s is [[countable|countably infinite]]. [[Cantor's first uncountability proof|His proof]] does not use his famous [[Cantor's diagonal argument|diagonal argument]], which he published in 1891.
| |
| * 1882 — [[Ferdinand von Lindemann]] proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,
| |
| * 1882 — Felix Klein invents the [[Klein bottle]],
| |
| * 1895 — [[Diederik Korteweg]] and [[Gustav de Vries]] derive the [[Korteweg–de Vries equation]] to describe the development of long solitary water waves in a canal of rectangular cross section,
| |
| * 1895 — Georg Cantor publishes a book about set theory containing the arithmetic of infinite [[cardinal number]]s and the [[continuum hypothesis]],
| |
| * 1896 — [[Jacques Hadamard]] and [[Charles Jean de la Vallée-Poussin]] independently prove the [[prime number theorem]],
| |
| * 1896 — [[Hermann Minkowski]] presents ''Geometry of numbers'',
| |
| * 1899 — Georg Cantor discovers a contradiction in his set theory,
| |
| * 1899 — [[David Hilbert]] presents a set of self-consistent geometric axioms in ''Foundations of Geometry'',
| |
| * 1900 — David Hilbert states his [[Hilbert's problems|list of 23 problems]] which show where some further mathematical work is needed.
| |
| | |
| ====Contemporary====
| |
| =====20th century=====
| |
| <ref>Paul Benacerraf and Hilary Putnam, Cambridge U.P., ''Philosophy of Mathematics: Selected Readings, ISBN 0-521-29648-X''</ref>
| |
| * 1900 — [[David Hilbert]] publishes [[Hilbert's problems]], a list of unsolved problems
| |
| * 1901 — [[Élie Cartan]] develops the [[exterior derivative]],
| |
| * 1903 — [[Carle David Tolmé Runge]] presents a [[fast Fourier Transform]] algorithm{{cn|date=August 2013}}
| |
| * 1903 — [[Edmund Georg Hermann Landau]] gives considerably simpler proof of the prime number theorem.
| |
| * 1908 — [[Ernst Zermelo]] axiomizes [[set theory]], thus avoiding Cantor's contradictions,
| |
| * 1908 — [[Josip Plemelj]] solves the Riemann problem about the existence of a differential equation with a given [[monodromic group]] and uses Sokhotsky – Plemelj formulae,
| |
| * 1912 — [[Luitzen Egbertus Jan Brouwer]] presents the [[Brouwer fixed-point theorem]],
| |
| * 1912 — Josip Plemelj publishes simplified proof for the Fermat's Last Theorem for exponent ''n'' = 5,
| |
| * 1919 — [[Viggo Brun]] defines [[Brun's constant]] ''B''<sub>2</sub> for [[twin prime]]s,
| |
| * 1928 — [[John von Neumann]] begins devising the principles of [[game theory]] and proves the [[minimax theorem]],
| |
| * 1930 — [[Casimir Kuratowski]] shows that the [[three-cottage problem]] has no solution,
| |
| * 1931 — [[Kurt Gödel]] proves [[Gödel's incompleteness theorem|his incompleteness theorem]] which shows that every axiomatic system for mathematics is either incomplete or inconsistent,
| |
| * 1931 — [[Georges de Rham]] develops theorems in [[cohomology]] and [[characteristic class]]es,
| |
| * 1933 — [[Karol Borsuk]] and [[Stanislaw Ulam]] present the [[Borsuk–Ulam Theorem|Borsuk–Ulam antipodal-point theorem]],
| |
| * 1933 — [[Andrey Nikolaevich Kolmogorov]] publishes his book ''Basic notions of the calculus of probability'' (''Grundbegriffe der Wahrscheinlichkeitsrechnung'') which contains an [[probability axiom|axiomatization of probability]] based on [[measure theory]],
| |
| * 1940 — Kurt Gödel shows that neither the [[continuum hypothesis]] nor the [[axiom of choice]] can be disproven from the standard axioms of set theory,
| |
| * 1942 — [[G.C. Danielson]] and [[Cornelius Lanczos]] develop a [[Fast Fourier Transform]] algorithm,
| |
| * 1943 — [[Kenneth Levenberg]] proposes a method for nonlinear least squares fitting,
| |
| * 1945 — [[Stephen Cole Kleene]] introduces [[realizability]],
| |
| * 1945 — [[Saunders Mac Lane]] and [[Samuel Eilenberg]] start [[category theory]]
| |
| * 1945 — [[Norman Steenrod]] and [[Samuel Eilenberg]] give the [[Eilenberg–Steenrod axioms]] for (co-)homology
| |
| * 1948 — John von Neumann mathematically studies [[Self-replicating machine|self-reproducing machines]],
| |
| * 1949 — John von Neumann computes π to 2,037 decimal places using [[ENIAC]],
| |
| * 1950 — [[Stanisław Ulam]] and John von Neumann present [[cellular automata]] dynamical systems,
| |
| * 1953 — [[Nicholas Metropolis]] introduces the idea of thermodynamic [[simulated annealing]] algorithms,
| |
| * 1955 — [[H. S. M. Coxeter]] et al. publish the complete list of [[uniform polyhedron]],
| |
| * 1955 — [[Enrico Fermi]], [[John Pasta]], and Stanisław Ulam numerically study a nonlinear spring model of heat conduction and discover solitary wave type behavior,
| |
| * 1956 — [[Noam Chomsky]] describes an [[Chomsky hierarchy|hierarchy]] of [[formal language]]s,
| |
| * 1958 — [[Alexander Grothendieck]]'s proof of the [[Grothendieck–Riemann–Roch theorem]] is published
| |
| * 1960 — [[C. A. R. Hoare]] invents the [[quicksort]] algorithm,
| |
| * 1960 — [[Irving S. Reed]] and [[Gustave Solomon]] present the [[Reed–Solomon code|Reed–Solomon error-correcting code]],
| |
| * 1961 — [[Daniel Shanks]] and [[John Wrench]] compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer,
| |
| * 1962 — [[Donald Marquardt]] proposes the [[Levenberg–Marquardt nonlinear least squares fitting algorithm]],
| |
| * 1963 — [[Paul Cohen (mathematician)|Paul Cohen]] uses his technique of [[forcing (mathematics)|forcing]] to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory,
| |
| * 1963 — [[Martin Kruskal]] and [[Norman Zabusky]] analytically study the [[Fermi–Pasta–Ulam problem|Fermi–Pasta–Ulam heat conduction problem]] in the continuum limit and find that the [[KdV equation]] governs this system,
| |
| * 1963 — meteorologist and mathematician [[Edward Norton Lorenz]] published solutions for a simplified mathematical model of atmospheric turbulence – generally known as chaotic behaviour and [[strange attractor]]s or [[Lorenz Attractor]] – also the [[Butterfly Effect]],
| |
| * 1965 — Iranian mathematician [[Lotfi Asker Zadeh]] founded [[fuzzy set]] theory as an extension of the classical notion of [[Set (mathematics)|set]] and he founded the field of [[Fuzzy Mathematics]],
| |
| * 1965 — Martin Kruskal and Norman Zabusky numerically study colliding [[Soliton|solitary waves]] in [[Plasma (physics)|plasmas]] and find that they do not disperse after collisions,
| |
| * 1965 — [[James Cooley]] and [[John Tukey]] present an influential Fast Fourier Transform algorithm,
| |
| * 1966 — [[E. J. Putzer]] presents two methods for computing the [[Matrix exponential|exponential of a matrix]] in terms of a polynomial in that matrix,
| |
| * 1966 — [[Abraham Robinson]] presents [[non-standard analysis]].
| |
| * 1967 — [[Robert Langlands]] formulates the influential [[Langlands program]] of conjectures relating number theory and representation theory,
| |
| * 1968 — [[Michael Atiyah]] and [[Isadore Singer]] prove the [[Atiyah–Singer index theorem]] about the index of [[elliptic operator]]s,
| |
| * 1973 — [[Lotfi Zadeh]] founded the field of [[fuzzy logic]],
| |
| * 1975 — [[Benoît Mandelbrot]] publishes ''Les objets fractals, forme, hasard et dimension'',
| |
| * 1976 — [[Kenneth Appel]] and [[Wolfgang Haken]] use a computer to prove the [[Four color theorem]],
| |
| * 1981 — [[Richard Feynman]] gives an influential talk "Simulating Physics with Computers" (in 1980 [[Yuri Manin]] proposed the same idea about quantum computations in "Computable and Uncomputable" (in Russian)),
| |
| * 1983 — [[Gerd Faltings]] proves the [[Mordell conjecture]] and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem,
| |
| * 1983 — the [[classification of finite simple groups]], a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
| |
| * 1985 — [[Louis de Branges de Bourcia]] proves the [[Bieberbach conjecture]],
| |
| * 1987 — [[Yasumasa Kanada]], [[David H. Bailey|David Bailey]], [[Jonathan Borwein]], and [[Peter Borwein]] use iterative modular equation approximations to elliptic integrals and a [[NEC SX-2]] [[supercomputer]] to compute π to 134 million decimal places,
| |
| * 1991 — [[Alain Connes]] and [[John W. Lott]] develop [[non-commutative geometry]],
| |
| * 1992 — [[David Deutsch]] and [[Richard Jozsa]] develop the [[Deutsch–Jozsa algorithm]], one of the first examples of a [[quantum algorithm]] that is exponentially faster than any possible deterministic classical algorithm.
| |
| * 1994 — [[Andrew Wiles]] proves part of the [[Taniyama–Shimura conjecture]] and thereby proves [[Fermat's Last Theorem]],
| |
| * 1994 — [[Peter Shor]] formulates [[Shor's algorithm]], a [[quantum algorithm]] for [[integer factorization]],
| |
| * 1998 — [[Thomas Callister Hales]] (almost certainly) proves the [[Kepler conjecture]],
| |
| * 1999 — the full Taniyama–Shimura conjecture is proved,
| |
| * 2000 — the [[Clay Mathematics Institute]] proposes the seven [[Millennium Prize Problems]] of unsolved important classic mathematical questions.
| |
| | |
| =====21st century=====
| |
| * 2002 — [[Manindra Agrawal]], [[Nitin Saxena]], and [[Neeraj Kayal]] of [[IIT Kanpur]] present an unconditional deterministic [[polynomial time]] algorithm to determine whether a given number is [[prime number|prime]] (the [[AKS primality test]]),
| |
| * 2002 — [[Yasumasa Kanada]], Y. Ushiro, [[Hisayasu Kuroda]], [[Makoto Kudoh]] and a team of nine more compute π to 1241.1 billion digits using a [[Hitachi, Ltd.|Hitachi]] 64-node [[supercomputer]],
| |
| * 2002 — [[Preda Mihăilescu]] proves [[Catalan's conjecture]],
| |
| * 2003 — [[Grigori Perelman]] proves the [[Poincaré conjecture]],
| |
| * 2007 — a team of researchers throughout North America and Europe used networks of computers to map [[E8 (mathematics)|E<sub>8</sub>]].<ref>Elizabeth A. Thompson, MIT News Office, ''Math research team maps E8'' [http://www.huliq.com/15695/mathematicians-map-e8 Mathematicians Map E8], Harminka, 2007-03-20</ref>
| |
| * 2009 — [[Fundamental lemma (Langlands program)]] had been [[Mathematical proof|proved]] by [[Ngo Bao Chau]].<ref>{{citation|first1=G.|last1=Laumon|first2=B. C.|last2=Ngô|id={{arxiv|math/0404454}}|year=2004|title=Le lemme fondamental pour les groupes unitaires}}</ref>
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| ==See also==
| |
| * {{portal-inline|Mathematics}}
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| | |
| ==Notes==
| |
| # This article is based on a timeline developed by Niel Brandt (1994) who has given permission for its use in Wikipedia. (See [[Talk:Timeline of mathematics]].)
| |
| # In 1966 IBM printed a famous timeline poster called [[Men of Modern Mathematics]] for the years 1000 AD to 1950 AD. It was based on personal stories about (mainly Western) mathematicians and their mathematical achievements. The poster was designed by the famous [[Charles Eames]], with the content concerning mathematicians contributed by Professor [[Raymond Redheffer]] of UCLA.
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| ==References==
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| {{reflist}}
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| * David Eugene Smith, 1929 and 1959, ''A Source Book in Mathematics'', [[Dover]]. ISBN 0-486-64690-4.
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| ==External links==
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| * {{MacTutor Biography|class=Chronology|id=full|title=A Mathematical Chronology}}
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| {{DEFAULTSORT:Timeline Of Mathematics}}
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| [[Category:History of mathematics| ]]
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| [[Category:Mathematics timelines|*]]
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