# Timeline of mathematics

This is a timeline of pure and applied mathematics history.

## 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 [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.

[14]

## References

1. ^ Art Prehistory, Sean Henahan, January 10, 2002. Archived July 19, 2008, at the Wayback Machine.
2. ^
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. ^
11. ^ a b c
12. ^ a b Various AP Lists and Statistics Archived July 28, 2012, at the Wayback Machine.
13. ^ https://www.agnesscott.edu/lriddle/women/germain-FLT/SGandFLT.htm
14. ^ Paul Benacerraf and Hilary Putnam, Cambridge University Press, Philosophy of Mathematics: Selected Readings, ISBN 0-521-29648-X
15. ^ Elizabeth A. Thompson, MIT News Office, Math research team maps E8 Mathematicians Map E8, Harminka, 2007-03-20
16. ^ Laumon, G.; Ngô, B. C. (2004), Le lemme fondamental pour les groupes unitaires, arXiv:, Bibcode:2004math......4454L
17. ^ "UNH Mathematician's Proof Is Breakthrough Toward Centuries-Old Problem". University of New Hampshire. May 1, 2013. Retrieved May 20, 2013.
18. ^ Announcement of Completion. Project Flyspeck, Google Code.
19. ^ Team announces construction of a formal computer-verified proof of the Kepler conjecture. August 13, 2014 by Bob Yirk.
20. ^ Proof confirmed of 400-year-old fruit-stacking problem, 12 August 2014; New Scientist.
21. ^
22. ^ Solved: 400-Year-Old Maths Theory Finally Proven. Sky News, 16:39, UK, Tuesday 12 August 2014.
23. ^ "y-cruncher - A Multi-Threaded Pi Program". numberworld.org. Retrieved 29 August 2015.
24. ^ "y-cruncher - A Multi-Threaded Pi Program". numberworld.org. Retrieved 15 December 2016.