Timeline of mathematics

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This is a timeline of pure 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.

Contents

Rhetorical stage

Before 1000 BC

Syncopated stage

1st millennium BC

1st millennium AD

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 Jamshid 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' al-Marrakushi and Abu'l-Hasan ibn Ali al-Qalasadi introduced symbolic notation for algebra and for mathematics in general. [12]
  • 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 Jamshid 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

[19]

21st century

See also

Related Research Articles

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