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Timeline of mathematics

Rhetorical stageEdit

Before 1000 BCEdit

Syncopated stageEdit

1st millennium BCEdit

1st millennium ADEdit

Symbolic stageEdit


15th centuryEdit

  • 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 [Paolo] Ruffini and [William George] 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.
  • 15th century – Ibn al-Banna and al-Qalasadi introduced symbolic notation for algebra and for mathematics in general.[11]
  • 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.


16th centuryEdit

17th centuryEdit

18th centuryEdit

19th centuryEdit


20th centuryEdit


21st centuryEdit

See alsoEdit


  1. ^ Art Prehistory, Sean Henahan, January 10, 2002. Archived July 19, 2008, at the Wayback Machine
  2. ^ How Menstruation Created Mathematics, Tacoma Community College, (archive link).
  3. ^ "OLDEST Mathematical Object is in Swaziland". Retrieved March 15, 2015.
  4. ^ "an old Mathematical Object". Retrieved March 15, 2015.
  5. ^ a b "Egyptian Mathematical Papyri - Mathematicians of the African Diaspora". Retrieved March 15, 2015.
  6. ^ Carl B. Boyer, A History of Mathematics, 2nd Ed.
  7. ^ Corsi, Pietro; Weindling, Paul (1983). Information sources in the history of science and medicine. Butterworth Scientific. ISBN 9780408107648. Retrieved July 6, 2014.
  8. ^ Victor J. Katz (1998). History of Mathematics: An Introduction, p. 255–259. Addison-Wesley. ISBN 0-321-01618-1.
  9. ^ F. Woepcke (1853). Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi. Paris.
  10. ^ O'Connor, John J.; Robertson, Edmund F., "Abu l'Hasan Ali ibn Ahmad Al-Nasawi", MacTutor History of Mathematics archive, University of St Andrews.
  11. ^ a b c Arabic mathematics, MacTutor History of Mathematics archive, University of St Andrews, Scotland
  12. ^ a b Various AP Lists and Statistics Archived July 28, 2012, at the Wayback Machine
  13. ^ D'Alembert (1747) "Recherches sur la courbe que forme une corde tenduë mise en vibration" (Researches on the curve that a tense cord [string] forms [when] set into vibration), Histoire de l'académie royale des sciences et belles lettres de Berlin, vol. 3, pages 214-219.
  14. ^
  15. ^ Paul Benacerraf and Hilary Putnam, Cambridge University Press, Philosophy of Mathematics: Selected Readings, ISBN 0-521-29648-X
  16. ^ Elizabeth A. Thompson, MIT News Office, Math research team maps E8 Mathematicians Map E8, Harminka, 2007-03-20
  17. ^ Laumon, G.; Ngô, B. C. (2004), Le lemme fondamental pour les groupes unitaires, arXiv:math/0404454, Bibcode:2004math......4454L
  18. ^ "UNH Mathematician's Proof Is Breakthrough Toward Centuries-Old Problem". University of New Hampshire. May 1, 2013. Retrieved May 20, 2013.
  19. ^ Announcement of Completion. Project Flyspeck, Google Code.
  20. ^ Team announces construction of a formal computer-verified proof of the Kepler conjecture. August 13, 2014 by Bob Yirk.
  21. ^ Proof confirmed of 400-year-old fruit-stacking problem, 12 August 2014; New Scientist.
  22. ^ A formal proof of the Kepler conjecture, arXiv.
  23. ^ Solved: 400-Year-Old Maths Theory Finally Proven. Sky News, 16:39, UK, Tuesday 12 August 2014.
  24. ^ "y-cruncher - A Multi-Threaded Pi Program". Retrieved August 29, 2015.
  25. ^ "y-cruncher - A Multi-Threaded Pi Program". Retrieved December 15, 2016.
  26. ^ Google Cloud Topples the Pi By Alexander J. Yee March 14, 2019

External linksEdit