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Hewwo :D Hewwo :D


==Syncopated stage== ==Syncopated Stage==


I am depression
===1st millennium BC===
* c. 1000 BC&nbsp;– ]s used by the ]. However, only unit fractions are used (i.e., those with 1 as the numerator) and ] tables are used to approximate the values of the other fractions.<ref>Carl B. Boyer, ''A History of Mathematics'', 2nd Ed.</ref>
* first half of 1st millennium BC&nbsp;– ]&nbsp;– ], in his ], 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.
* 800 BC&nbsp;– ], author of the Baudhayana ], a ] geometric text, contains ], and calculates the ] correctly to five decimal places.
* c. 8th century BC&nbsp;– the ], one of the four ] ]s, contains the earliest concept of ], and states "if you remove a part from infinity or add a part to infinity, still what remains is infinity."
* 1046 BC to 256 BC&nbsp;– China, '']'', arithmetic, geometric algorithms, and proofs.
* 624 BC – 546 BC&nbsp;– Greece, ] has various theorems attributed to him.
* c. 600 BC&nbsp;– Greece, the other Vedic "Sulba Sutras" ("rule of chords" in ]) use ], contain of a number of geometrical proofs, and approximate ] at 3.16.
* second half of 1st millennium BC&nbsp;– The ], the unique normal ] of order three, was discovered in China.
* 530 BC&nbsp;– Greece, ] studies propositional ] and vibrating lyre strings; his group also discovers the ] of the ].
* c. 510 BC&nbsp;– Greece, ]
* c. 500 BC&nbsp;– ] grammarian ] writes the '']'', which contains the use of metarules, ] and ]s, originally for the purpose of systematizing the grammar of Sanskrit.
* c. 500 BC&nbsp;– Greece, ]
* 470 BC – 410 BC&nbsp;– Greece, ] utilizes ] in an attempt to ].
* 490 BC – 430 BC – Greece, ] '']''
* 5th century BC&nbsp;– India, ], author of the Apastamba Sulba Sutra, another Vedic Sanskrit geometric text, makes an attempt at squaring the circle and also calculates the ] correct to five decimal places.
* 5th c. BC – Greece,]
* 5th century&nbsp;– Greece, ]
* 460 BC – 370 BC&nbsp;– Greece, ]
* 460 BC – 399 BC&nbsp;– Greece, ]
* 5th century (late)&nbsp;– Greece, ]
* 428 BC – 347 BC&nbsp;– Greece, ]
* 423 BC – 347 BC&nbsp;– Greece, ]
* 417 BC – 317 BC&nbsp;– Greece, ]
* c. 400 BC&nbsp;– India, ]a mathematicians write the ''Surya Prajinapti'', a mathematical text classifying all numbers into three sets: enumerable, innumerable and ]. It also recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
* 408 BC – 355 BC&nbsp;– Greece, ]
* 400 BC – 350 BC&nbsp;– Greece, ]
* 395 BC – 313 BC&nbsp;– Greece, ]
* 390 BC – 320 BC&nbsp;– Greece, ]
* 380- 290&nbsp;– Greece, ]
* 370 BC&nbsp;– Greece, ] states the ] for ] determination.
* 370 BC – 300 BC&nbsp;– Greece, ]
* 370 BC – 300 BC&nbsp;– Greece, ]
* 350 BC&nbsp;– Greece, ] discusses ]al reasoning in '']''.
* 4th century BC&nbsp;– ] texts use the Sanskrit word "Shunya" to refer to the concept of "void" (]).
* 330 BC&nbsp;–China, the earliest known work on ], the ''Mo Jing'', is compiled.
* 310 BC – 230 BC&nbsp;– Greece, ]
* 390 BC – 310 BC&nbsp;– Greece, ]
* 380 BC – 320 BC&nbsp;– Greece, ]
* 300 BC&nbsp;– India, ] mathematicians in India write the ''Bhagabati Sutra'', which contains the earliest information on ].
* 300 BC&nbsp;&nbsp;– Greece, ] in his '']'' studies geometry as an ], proves the infinitude of ]s and presents the ]; he states the law of reflection in ''Catoptrics'', and he proves the ].
* c. 300 BC&nbsp;– India, ]s (ancestor of the common modern ] ])
* 370 BC – 300 BC&nbsp;– Greece, ] works on histories of arithmetic, geometry and astronomy now lost.<ref name="CorsiWeindling1983">{{cite book|last1=Corsi|first1=Pietro|last2=Weindling|first2=Paul|title=Information sources in the history of science and medicine|url=https://books.google.com/books?id=sV0ZAAAAMAAJ|accessdate=July 6, 2014|year=1983|publisher=Butterworth Scientific|isbn=9780408107648}}</ref>
* 300 BC&nbsp;– ], the ] invent the earliest calculator, the ].
* c. 300 BC&nbsp;– ] ] 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 ], along with the first use of ] and ].
* 280 BC – 210 BC&nbsp;– Greece, ]
* 280 BC – 220BC&nbsp;– Greece, ]
* 280 BC – 220 BC&nbsp;– Greece, ]
* 279 BC – 206 BC&nbsp;– Greece, ]
* c. 3rd century BC – India, ]
* 250 BC – 190 BC&nbsp;– Greece, ]
* 262 -198 BC&nbsp;– Greece, ]
* 260 BC&nbsp;– Greece, ] 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.
* c. 250 BC&nbsp;– late ]s had already begun to use a true zero (a shell glyph) several centuries before ] in the New World. See ].
* 240 BC – Greece, ] uses ] to quickly isolate prime numbers.
* 240 BC 190 BC– Greece, ]
* 225 BC&nbsp;– Greece, ] writes ''On ]'' and names the ], ], and ].
* 202 BC to 186 BC&nbsp;–China, '']'', a mathematical treatise, is written in ].
* 200 BC – 140 BC – Greece, ]
* 150 BC&nbsp;– India, ] mathematicians in India write the ''Sthananga Sutra'', which contains work on the theory of numbers, arithmetical operations, geometry, operations with ], simple equations, ], quartic equations, and ] and combinations.
* c. 150 BC&nbsp;– Greece, ]
* 150 BC&nbsp;– China, A method of ] appears in the Chinese text '']''.
* 150 BC&nbsp;– China, ] appears in the Chinese text '']''.
* 150 BC&nbsp;– China, ] appear in the Chinese text '']''.
* 150 BC – 75 BC – Phoenician, ]
* 190 BC – 120 BC – Greece, ] develops the bases of ].
* 190 BC - 120 BC – Greece, ]
* 160 BC – 100 BC – Greece, ]
* 135 BC – 51 BC – Greece, ]
* 206 BC to 8 AD&nbsp;– China, ]
* 78 BC – 37 BC – China, ]
* 50 BC&nbsp;– ], a descendant of the ] (the first ] ] ]), begins development in ].
* mid 1st century ] (as late as 400 AD)
* final centuries BC&nbsp;– Indian astronomer ] writes the ''Vedanga Jyotisha'', a Vedic text on ] that describes rules for tracking the motions of the sun and the moon, and uses geometry and trigonometry for astronomy.
* 1st C. BC – Greece, ]
* 50 BC – 23 AD – China, ]

===1st millennium AD===
* 1st century&nbsp;– Greece, ], (Hero) the earliest fleeting reference to square roots of negative numbers.
* c 100 – Greece, ]
* 60 – 120 – Greece, ]
* 70 – 140 – Greece, ] ]
* 78 – 139 – China, ]
* c. 2nd century&nbsp;– Greece, ] of ] wrote the '']''.
* 132 – 192 – China, ]
* 240 – 300 – Greece, ]
* 250&nbsp;– Greece, ] uses symbols for unknown numbers in terms of syncopated ], and writes '']'', one of the earliest treatises on algebra.
* 263&nbsp;– China, ] computes ] using ].
* 300&nbsp;– the earliest known use of ] as a decimal digit is introduced by ].
* 234 – 305 – Greece, ]
* 300 – 360 – Greece, ]
* 335 – 405– Greece, ]
* c. 340&nbsp;– Greece, ] states his ] and his ].
* 350 – 415 – Byzantine Empire, ]
* c. 400&nbsp;– India, the ] is written by ]a mathematicians, which describes a theory of the infinite containing different levels of ], shows an understanding of ], as well as ] to ], and computes ] of numbers as large as a million correct to at least 11 decimal places.
* 300 to 500&nbsp;– the ] is developed by ].
* 300 to 500&nbsp;– China, a description of ] is written by ].
* 412 – 485 – Greece,]
* 420 – 480 – Greece, ]
* b 440 – Greece, ] "I wish everything was mathematics."
* 450&nbsp;– China, ] computes ] to seven decimal places. This calculation remains the most accurate calculation for π for close to a thousand years.
* c. 474 – 558 – Greece, ]
* 500&nbsp;– India, ] writes the ''Aryabhata-Siddhanta'', which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of ] and ], and also contains the ] and cosine values (in 3.75-degree intervals from 0 to 90 degrees).
* 480 – 540 – Greece, ]
* 490 – 560 – Greece, ]
* 6th century&nbsp;– Aryabhata gives accurate calculations for astronomical constants, such as the ] and ], computes π to four decimal places, and obtains whole number solutions to ] by a method equivalent to the modern method.
* 505 – 587 – India, ]
* 6th century – India, ]
* 535 – 566 – China, ]
* 550&nbsp;– ] mathematicians give zero a numeral representation in the ] ] system.
* 7th century&nbsp;– India, ] gives a rational approximation of the sine function.
* 7th century&nbsp;– India, ] 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.
* 628&nbsp;– Brahmagupta writes the '']'', where zero is clearly explained, and where the modern ] Indian numeral system is fully developed. It also gives rules for manipulating both ], methods for computing square roots, methods of solving ] and ]s, and rules for summing ], ], and the ].
* 602 – 670 – China, ]
* 8th century&nbsp;– India, ] gives explicit rules for the ], gives the derivation of the ] of a ] using an ] procedure, and also deals with the ] to base 2 and knows its laws.
* 8th century&nbsp;– India, ] gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations.
* 773&nbsp;– Iraq, Kanka brings Brahmagupta's Brahma-sphuta-siddhanta to ] to explain the Indian system of arithmetic ] and the Indian numeral system.
* 773&nbsp;– ] translates the Brahma-sphuta-siddhanta into Arabic upon the request of King Khalif Abbasid Al Mansoor.
* 9th century&nbsp;– India, ] discovers the Newton-Gauss interpolation formula, and gives the fractional parts of Aryabhata's tabular ].
* 810&nbsp;– The ] is built in Baghdad for the translation of Greek and ] mathematical works into Arabic.
* 820&nbsp;– ]&nbsp;– ] mathematician, father of algebra, writes the '']'', later transliterated as '']'', which introduces systematic algebraic techniques for solving linear and quadratic equations. Translations of his book on ] will introduce the ] ] number system to the Western world in the 12th century. The term '']'' is also named after him.
* 820&nbsp;– Iran, ] conceived the idea of reducing ] problems such as ] to problems in algebra.
* c. 850&nbsp;– Iraq, ] pioneers ] and ] in his book on ].
* c. 850&nbsp;– India, ] writes the Gaṇitasārasan̄graha otherwise known as the Ganita Sara Samgraha which gives systematic rules for expressing a fraction as the ].
* 895&nbsp;– Syria, ]: the only surviving fragment of his original work contains a chapter on the solution and properties of ]s. He also generalized the ], and discovered the ] by which pairs of ]s can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other).
* c. 900&nbsp;– Egypt, ] had begun to understand what we would write in symbols as <math>x^n \cdot x^m = x^{m+n}</math>
* 940&nbsp;– Iran, ] extracts ] using the Indian numeral system.
* 953&nbsp;– The arithmetic of the ] at first required the use of a dust board (a sort of handheld ]) because "the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded." ] 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.
* 953&nbsp;– Persia, ] 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 ]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 ] of any two of these. He started a school of algebra which flourished for several hundreds of years". He also discovered the ] for ] ]s, which "was a major factor in the development of ] based on the decimal system".
* 975&nbsp;– Mesopotamia, ] 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>.


==Symbolic Stage== ==Symbolic Stage==

Revision as of 22:43, 14 January 2020

This is a timeline of pure and applied mathematics history.

Rhetorical Stage

Hewwo :D

Syncopated Stage

I am depression

Symbolic Stage

1000–1500

15th Century

  • 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.
  • c. 1400 – Ghiyath al-Kashi "contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers 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 roots, which is a special case of the methods given many centuries later by Ruffini and 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 ". He also wrote the Thesis on the sine and the chord and Thesis on finding the first degree sine.
  • 15th century – Ibn al-Banna and al-Qalasadi introduced symbolic notation for algebra and for mathematics in general.
  • 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.
  • 1424 – Ghiyath al-Kashi computes π to sixteen decimal places using inscribed and circumscribed polygons.
  • 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.
  • 1464 – Regiomontanus writes De Triangulis omnimodus which is one of the earliest texts to treat trigonometry as a separate branch of mathematics.
  • 1478 – An anonymous author writes the Treviso Arithmetic.
  • 1494 – Luca Pacioli writes Summa de arithmetica, geometria, proportioni et proportionalità; introduces primitive symbolic algebra using "co" (cosa) for the unknown.

Modern

16th Century

17th Century

18th Century

19th Century

Contemporary

20th Century

21st Century

See also

References

  1. Victor J. Katz (1998). History of Mathematics: An Introduction, p. 255–259. Addison-Wesley. ISBN 0-321-01618-1.
  2. F. Woepcke (1853). Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi. Paris.
  3. O'Connor, John J.; Robertson, Edmund F., "Abu l'Hasan Ali ibn Ahmad Al-Nasawi", MacTutor History of Mathematics Archive, University of St Andrews
  4. ^ Arabic mathematics, MacTutor History of Mathematics archive, University of St Andrews, Scotland
  5. ^ Various AP Lists and Statistics Archived July 28, 2012, at the Wayback Machine
  6. D'Alembert (1747) "Recherches sur la courbe que forme une corde tenduë mise en vibration" (Researches on the curve that a tense cord forms set into vibration), Histoire de l'académie royale des sciences et belles lettres de Berlin, vol. 3, pages 214-219.
  7. https://www.agnesscott.edu/lriddle/women/germain-FLT/SGandFLT.htm
  8. Paul Benacerraf and Hilary Putnam, Cambridge University Press, Philosophy of Mathematics: Selected Readings, ISBN 0-521-29648-X
  9. Elizabeth A. Thompson, MIT News Office, Math research team maps E8 Mathematicians Map E8, Harminka, 2007-03-20
  10. Laumon, G.; Ngô, B. C. (2004), Le lemme fondamental pour les groupes unitaires, arXiv:math/0404454, Bibcode:2004math......4454L
  11. "UNH Mathematician's Proof Is Breakthrough Toward Centuries-Old Problem". University of New Hampshire. May 1, 2013. Retrieved May 20, 2013.
  12. Announcement of Completion. Project Flyspeck, Google Code.
  13. Team announces construction of a formal computer-verified proof of the Kepler conjecture. August 13, 2014 by Bob Yirk.
  14. Proof confirmed of 400-year-old fruit-stacking problem, 12 August 2014; New Scientist.
  15. A formal proof of the Kepler conjecture, arXiv.
  16. Solved: 400-Year-Old Maths Theory Finally Proven. Sky News, 16:39, UK, Tuesday 12 August 2014.
  17. "y-cruncher - A Multi-Threaded Pi Program". numberworld.org. Retrieved August 29, 2015.
  18. "y-cruncher - A Multi-Threaded Pi Program". numberworld.org. Retrieved December 15, 2016.
  19. Google Cloud Topples the Pi By Alexander J. Yee March 14, 2019

External links

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