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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 (see [[Lebombo bone]]).<ref>[http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm How Menstruation Created Mathematics], [[Tacoma Community College]], [https://web.archive.org/web/20051223112514/http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm (archive link).]</ref><ref>{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html|title=OLDEST Mathematical Object is in Swaziland|publisher=|accessdate=March 15, 2015}}</ref><ref>{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html|title=an old Mathematical Object|publisher=|accessdate=March 15, 2015}}</ref> |
* ca. [[35,000 BC]] to [[Upper Paleolithic|20,000 BC]] – Africa and France, earliest known [[prehistory|prehistoric]] attempts to quantify time (see [[Lebombo bone]]).<ref>[http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm How Menstruation Created Mathematics], [[Tacoma Community College]], [https://web.archive.org/web/20051223112514/http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm (archive link).]</ref><ref>{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html|title=OLDEST Mathematical Object is in Swaziland|publisher=|accessdate=March 15, 2015}}</ref><ref>{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html|title=an old Mathematical Object|publisher=|accessdate=March 15, 2015}}</ref> |
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* c. 20,000 BC – [[Nile Valley]], [[Ishango bone]]: possibly the earliest reference to [[prime number]]s and [[Egyptian multiplication]]. |
* 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 [[Sumer]]ians invent the first [[numeral system]], and a system of [[Ancient Mesopotamian units of measurement|weights and measures]]. |
* c. 3400 BC – [[Mesopotamia]], the [[Sumer]]ians invent the first [[Babylonian cuneiform numerals|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">{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html#berlin.|title=Egyptian Mathematical Papyri - Mathematicians of the African Diaspora|publisher=|accessdate=March 15, 2015}}</ref> |
* c. 3100 BC – [[Egypt]], earliest known [[decimal|decimal system]] allows indefinite counting by way of introducing new symbols.<ref name="buffalo1">{{cite web|url=http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html#berlin.|title=Egyptian Mathematical Papyri - Mathematicians of the African Diaspora|publisher=|accessdate=March 15, 2015}}</ref> |
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* c. 2800 BC – [[Indus Valley Civilisation]] 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. |
* c. 2800 BC – [[Indus Valley Civilisation]] 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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* 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. |
* 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, though it is not known if this was deliberate. |
* c. 2000 BC – Scotland, [[carved stone balls]] exhibit a variety of symmetries including all of the symmetries of [[Platonic solid]]s, though it is not known if this was deliberate. |
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* c. 1800 BC – The [[Plimpton 322]] Babylonian tablet records the oldest known examples of [[Pythagorean triple]]s.<ref>{{citation |last=Joyce |first=David E. |year=1995 |title=Plimpton 322 |url=http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.html}} and {{citation |last=Maor |first=Eli |year=1993 |title=Trigonometric Delights |publisher=Princeton University Press |isbn=978-0-691-09541-7 |chapter=Plimpton 322: The Earliest Trigonometric Table? |chapter-url=http://press.princeton.edu/titles/6287.html |accessdate=November 28, 2010 |url-status=dead |pages=30–34 |archiveurl=https://web.archive.org/web/20100805230810/http://press.princeton.edu/titles/6287.html |archivedate=5 August 2010}}</ref> |
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* 1800 BC – Egypt, [[Moscow Mathematical Papyrus]], finding the volume of a [[frustum]]. |
* 1800 BC – Egypt, [[Moscow Mathematical Papyrus]], finding the volume of a [[frustum]]. |
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* c. 1800 BC – [[Berlin Papyrus 6619]] (Egypt, 19th dynasty) contains a quadratic equation and its solution.<ref name="buffalo1"/> |
* c. 1800 BC – [[Berlin Papyrus 6619]] (Egypt, 19th dynasty) contains a quadratic equation and its solution.<ref name="buffalo1"/> |
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* c. 1000 BC – [[Simple 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> |
* c. 1000 BC – [[Simple 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 [[Yajnavalkya 95 Years Cycle|95-year cycle]] to synchronize the motions of the Sun and the Moon. |
* 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 [[Yajnavalkya 95 Years Cycle|95-year cycle]] to synchronize the motions of the Sun and the Moon. |
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* 800 BC – [[Baudhayana]], author of the Baudhayana [[Shulba Sutras|Shulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equation]]s, |
* c. 800 BC – [[Baudhayana]], author of the Baudhayana [[Shulba Sutras|Shulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equation]]s, calculates the [[Square root of 2|square root of two]] correctly to five decimal places, and contains "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians."<ref>*{{cite book| last1=Hayashi| first1=Takao| year=1995| title=The Bakhshali Manuscript, An ancient Indian mathematical treatise| publisher=Groningen: Egbert Forsten, 596 pages| isbn=90-6980-087-X|page=363}}</ref> |
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* c. 8th century BC – the [[Yajurveda]], one of the four [[Hindu]] [[Vedas]], contains the earliest concept of [[infinity]], and states "if you remove a part from infinity or add a part to infinity, still what remains is infinity." |
* c. 8th century BC – the [[Yajurveda]], one of the four [[Hindu]] [[Vedas]], contains the earliest concept of [[infinity]], and states "if you remove a part from infinity or add a part to infinity, still what remains is infinity." |
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* 1046 BC to 256 BC – China, ''[[Zhoubi Suanjing]]'', arithmetic, geometric algorithms, and proofs. |
* 1046 BC to 256 BC – China, ''[[Zhoubi Suanjing]]'', arithmetic, geometric algorithms, and proofs. |
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* 335 – 405– Greece, [[Theon of Alexandria]] |
* 335 – 405– Greece, [[Theon of Alexandria]] |
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* c. 340 – Greece, [[Pappus of Alexandria]] states his [[Pappus's hexagon theorem|hexagon theorem]] and his [[Pappus's centroid theorem|centroid theorem]]. |
* c. 340 – Greece, [[Pappus of Alexandria]] states his [[Pappus's hexagon theorem|hexagon theorem]] and his [[Pappus's centroid theorem|centroid theorem]]. |
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* 350 – 415 – |
* 350 – 415 – Eastern Roman Empire, [[Hypatia]] |
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* c. 400 – India, the [[Bakhshali manuscript]] |
* c. 400 – India, the [[Bakhshali manuscript]], which describes a theory of the infinite containing different levels of [[Infinite set|infinity]], shows an understanding of [[Indexed family|indices]], 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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* 300 to 500 – the [[Chinese remainder theorem]] is developed by [[Sun Tzu (mathematician)|Sun Tzu]]. |
* 300 to 500 – the [[Chinese remainder theorem]] is developed by [[Sun Tzu (mathematician)|Sun Tzu]]. |
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* 300 to 500 – China, a description of [[rod calculus]] is written by [[Sun Tzu (mathematician)|Sun Tzu]]. |
* 300 to 500 – China, a description of [[rod calculus]] is written by [[Sun Tzu (mathematician)|Sun Tzu]]. |
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* 12th century – the Arabic numeral system reaches Europe through the [[Arabs]]. |
* 12th century – the Arabic numeral system reaches Europe through the [[Arabs]]. |
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* 12th century – [[Bhāskara 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]]. |
* 12th century – [[Bhāskara 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. Furthermore, it also gives the ''[[Chakravala method]]'' which was the first generalized solution of so |
* 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. Furthermore, it also gives the ''[[Chakravala method]]'' which was the first generalized solution of so-called ''[[Pell's equation]]'' |
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* 12th century – Bhaskara Acharya develops preliminary concepts of [[Derivative|differentiation]] |
* 12th century – Bhaskara Acharya develops preliminary concepts of [[Derivative|differentiation]], 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 al-Maghribi]] 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/> |
* 1130 – [[Al-Samawal al-Maghribi]] 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 – [[Sharaf al-Din al-Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on cubic equations that "represents an essential contribution to another algebra which aimed to study curves 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> |
* 1135 – [[Sharaf al-Din al-Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on cubic equations that "represents an essential contribution to another algebra which aimed to study curves 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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* 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 that have also been jointly 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] {{Webarchive|url=https://web.archive.org/web/20120728163824/http://amicable.homepage.dk/apstat.htm#discoverer |date=July 28, 2012 }}</ref> |
* 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 that have also been jointly 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] {{Webarchive|url=https://web.archive.org/web/20120728163824/http://amicable.homepage.dk/apstat.htm#discoverer |date=July 28, 2012 }}</ref> |
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* c. 1250 – [[Nasir al-Din al-Tusi]] attempts to develop a form of non-Euclidean geometry. |
* c. 1250 – [[Nasir al-Din al-Tusi]] attempts to develop a form of non-Euclidean geometry. |
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*1280 – Guo Shoujing and Wang Xun |
*1280 – Guo Shoujing and Wang Xun use cubic interpolation for generating sine. |
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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. |
* 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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*1356- [[Narayana Pandita (mathematician)|Narayana Pandita]] completes his treatise [[Ganita Kaumudi |
*1356- [[Narayana Pandita (mathematician)|Narayana Pandita]] completes his treatise [[Ganita Kaumudi]], generalized fibonacci sequence, and the first ever algorithm to systematically generate all permutations as well as many new magic figure techniques. |
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* 14th century – [[Madhava of Sangamagrama|Madhava]] discovers the [[power series]] expansion for <math>\sin x</math>, <math>\cos x</math>, <math>\arctan x</math> and <math>\pi/4</math> <ref>{{Cite web |last=Weisstein |first=Eric W. |title=Taylor Series |url=https://mathworld.wolfram.com/ |access-date=2022-11-03 |website=mathworld.wolfram.com |language=en}}</ref><ref>{{Cite journal |date=August 1932 |title=The Taylor Series: an Introduction to the Theory of Functions of a Complex Variable |journal=Nature |language=en |volume=130 |issue=3275 |pages=188 |doi=10.1038/130188b0 |bibcode=1932Natur.130R.188. |s2cid=4088442 |issn=1476-4687|doi-access=free }}</ref> This theory is now well known in the Western world as the [[Taylor series]] or infinite series.<ref>{{Cite web |last=Saeed |first=Mehreen |date=2021-08-19 |title=A Gentle Introduction to Taylor Series |url=https://machinelearningmastery.com/a-gentle-introduction-to-taylor-series/ |access-date=2022-11-03 |website=Machine Learning Mastery |language=en-US}}</ref> |
* 14th century – [[Madhava of Sangamagrama|Madhava]] discovers the [[power series]] expansion for <math>\sin x</math>, <math>\cos x</math>, <math>\arctan x</math> and <math>\pi/4</math> <ref>{{Cite web |last=Weisstein |first=Eric W. |title=Taylor Series |url=https://mathworld.wolfram.com/ |access-date=2022-11-03 |website=mathworld.wolfram.com |language=en}}</ref><ref>{{Cite journal |date=August 1932 |title=The Taylor Series: an Introduction to the Theory of Functions of a Complex Variable |journal=Nature |language=en |volume=130 |issue=3275 |pages=188 |doi=10.1038/130188b0 |bibcode=1932Natur.130R.188. |s2cid=4088442 |issn=1476-4687|doi-access=free }}</ref> This theory is now well known in the Western world as the [[Taylor series]] or infinite series.<ref>{{Cite web |last=Saeed |first=Mehreen |date=2021-08-19 |title=A Gentle Introduction to Taylor Series |url=https://machinelearningmastery.com/a-gentle-introduction-to-taylor-series/ |access-date=2022-11-03 |website=Machine Learning Mastery |language=en-US}}</ref> |
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* 14th century – [[Parameshvara Nambudiri]], 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]]. |
* 14th century – [[Parameshvara Nambudiri]], 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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====16th century==== |
====16th century==== |
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* 1501 – [[Nilakantha Somayaji]] writes the [[Tantrasamgraha]]. |
* 1501 – [[Nilakantha Somayaji]] writes the [[Tantrasamgraha]] which is the first treatment of all 10 cases in spherical trigonometry. |
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* 1520 – [[Scipione del Ferro]] develops a method for solving "depressed" cubic equations (cubic equations without an x<sup>2</sup> term), but does not publish. |
* 1520 – [[Scipione del 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. |
* 1522 – [[Adam Ries]] explained the use of Arabic digits and their advantages over Roman numerals. |
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* 1837 – [[Pierre Wantzel]] 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. |
* 1837 – [[Pierre Wantzel]] 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. |
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* 1837 – [[Peter Gustav Lejeune Dirichlet]] develops [[Analytic number theory]]. |
* 1837 – [[Peter Gustav Lejeune Dirichlet]] develops [[Analytic number theory]]. |
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* 1838 – First mention of [[uniform convergence]] in a paper by [[Christoph Gudermann]]; later formalized by [[Karl Weierstrass]]. Uniform convergence is required to fix [[Augustin-Louis Cauchy]] erroneous “proof” that the [[Pointwise convergence|pointwise limit]] of continuous functions is continuous from |
* 1838 – First mention of [[uniform convergence]] in a paper by [[Christoph Gudermann]]; later formalized by [[Karl Weierstrass]]. Uniform convergence is required to fix [[Augustin-Louis Cauchy]] erroneous “proof” that the [[Pointwise convergence|pointwise limit]] of continuous functions is continuous from Cauchy's 1821 [[Cours d'Analyse]]. |
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* 1841 – [[Karl Weierstrass]] discovers but does not publish the [[Laurent expansion theorem]]. |
* 1841 – [[Karl Weierstrass]] discovers but does not publish the [[Laurent expansion theorem]]. |
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* 1843 – [[Pierre-Alphonse Laurent]] discovers and presents the Laurent expansion theorem. |
* 1843 – [[Pierre-Alphonse Laurent]] discovers and presents the Laurent expansion theorem. |
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* 1901 – [[Élie Cartan]] develops the [[exterior derivative]]. |
* 1901 – [[Élie Cartan]] develops the [[exterior derivative]]. |
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* 1901 – [[Henri Lebesgue]] publishes on [[Lebesgue integration]]. |
* 1901 – [[Henri Lebesgue]] publishes on [[Lebesgue integration]]. |
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* 1903 – [[Carle David Tolmé Runge]] presents a [[fast Fourier transform]] algorithm{{citation needed|date=August 2013}} |
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* 1903 – [[Edmund Georg Hermann Landau]] gives considerably simpler proof of the prime number theorem. |
* 1903 – [[Edmund Georg Hermann Landau]] gives considerably simpler proof of the prime number theorem. |
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* 1908 – [[Ernst Zermelo]] axiomizes [[set theory]], thus avoiding Cantor's contradictions. |
* 1908 – [[Ernst Zermelo]] axiomizes [[set theory]], thus avoiding Cantor's contradictions. |
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* 2014 – Project Flyspeck<ref>[https://code.google.com/p/flyspeck/wiki/AnnouncingCompletion Announcement of Completion.] Project Flyspeck, [[Google Code]].</ref> announces that it completed a proof of [[Kepler conjecture|Kepler's conjecture]].<ref>[http://phys.org/news/2014-08-team-formal-computer-verified-proof-kepler.html Team announces construction of a formal computer-verified proof of the Kepler conjecture.] August 13, 2014 by Bob Yirk.</ref><ref>[https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/ Proof confirmed of 400-year-old fruit-stacking problem], 12 August 2014; [[New Scientist]]. |
* 2014 – Project Flyspeck<ref>[https://code.google.com/p/flyspeck/wiki/AnnouncingCompletion Announcement of Completion.] Project Flyspeck, [[Google Code]].</ref> announces that it completed a proof of [[Kepler conjecture|Kepler's conjecture]].<ref>[http://phys.org/news/2014-08-team-formal-computer-verified-proof-kepler.html Team announces construction of a formal computer-verified proof of the Kepler conjecture.] August 13, 2014 by Bob Yirk.</ref><ref>[https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/ Proof confirmed of 400-year-old fruit-stacking problem], 12 August 2014; [[New Scientist]]. |
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</ref><ref>[https://arxiv.org/abs/1501.02155 A formal proof of the Kepler conjecture], [[arXiv]].</ref><ref>[http://pnews.sky.com/story/1317501/solved-400-year-old-maths-theory-finally-proven Solved: 400-Year-Old Maths Theory Finally Proven.] [[Sky News]], 16:39, UK, Tuesday 12 August 2014.</ref> |
</ref><ref>[https://arxiv.org/abs/1501.02155 A formal proof of the Kepler conjecture], [[arXiv]].</ref><ref>[http://pnews.sky.com/story/1317501/solved-400-year-old-maths-theory-finally-proven Solved: 400-Year-Old Maths Theory Finally Proven.] [[Sky News]], 16:39, UK, Tuesday 12 August 2014.</ref> |
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* 2015 – [[Terence Tao]] solves |
* 2015 – [[Terence Tao]] solves the [[Paul Erdős|Erdős]] [[Sign sequence#Erdős discrepancy problem|discrepancy problem]]. |
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* 2015 – [[László Babai]] finds that a quasipolynomial complexity algorithm would solve the [[Graph isomorphism problem]]. |
* 2015 – [[László Babai]] finds that a quasipolynomial complexity algorithm would solve the [[Graph isomorphism problem]]. |
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* 2016 – [[Maryna Viazovska]] solves the [[sphere packing]] problem in dimension 8. Subsequent work building on this leads to a solution for dimension 24. |
* 2016 – [[Maryna Viazovska]] solves the [[sphere packing]] problem in dimension 8. Subsequent work building on this leads to a solution for dimension 24. |
This is a timelineofpure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.
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By topic |
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Numeral systems |
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