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575
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Varahamihira produces Pancasiddhantika (The Five Astronomical Canons). He makes
important contributions to trigonometry.
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594
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Decimal notation is used for numbers in India. This is the system on which our
current notation is based.
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628
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Brahmagupta writes Brahmasphutasiddanta (The Opening of the Universe), a work
on astronomy; on mathematics. He uses zero and negative numbers, gives methods
to solve quadratic equations, sum series, and compute square roots.
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About 700
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Mathematicians in the Mayan civilization introduce a symbol for zero into their
number system.
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About 810
|
Al-Khwarizmi writes important works on arithmetic, algebra, geography, and
astronomy. In particular Hisab al-jabr w'al-muqabala (Calculation by Completion
and Balancing), gives us the word "algebra", from "al-jabr". From
al-Khwarizmi's name, as a consequence of his arithmetic book, comes the word
"algorithm".
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About 810
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House of Wisdom set up in Baghdad. There Greek and Indian mathematical and
astronomy works are translated into Arabic.
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About 850
|
Thabit ibn Qurra makes important mathematical discoveries such as the extension
of the concept of number to (positive) real numbers, integral calculus,
theorems in spherical trigonometry, analytic geometry, and non-euclidean
geometry.
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About 900
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Abu Kamil writes Book on algebra which studies applications of algebra to
geometrical problems. It will be the book on which Fibonacci will base his
works.
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920
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Al-Battani writes Kitab al-Zij a major work on astronomy in 57 chapters. It
contains advances in trigonometry.
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950
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Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into
Europe. He uses Indian/Arabic numerals without having a zero.
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About 970
|
Abu'l-Wafa invents the wall quadrant for the accurate measurement of the
declination of stars in the sky. He writes important books on arithmetic and
geometric constructions. He introduces the tangent function and produces
improved methods of calculating trigonometric tables.
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976
|
Codex Vigilanus copied in Spain. Contains the first evidence of decimal numbers
in Europe.
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About 990
|
Al-Karaji writes Al-Fakhri in Baghdad which develops algebra. He gives Pascal's
triangle.
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About 1020
|
Ibn Sina (usually called Avicenna) writes on philosophy, medicine, psychology,
geology, mathematics, astronomy, and logic. His important mathematical work
Kitab al-Shifa' (The Book of Healing) divides mathematics into four major
topics, geometry, astronomy, arithmetic, and music.
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1072
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Al-Khayyami (usually known as Omar Khayyam) writes Treatise on Demonstration of
Problems of Algebra which contains a complete classification of cubic equations
with geometric solutions found by means of intersecting conic sections. He
measures the length of the year to be 365.24219858156 days, a remarkably
accurate result.
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|
About 1140
|
Bhaskara II (sometimes known as Bhaskaracharya) writes Lilavati (The Beautiful)
on arithmetic and geometry, and Bijaganita (Seed Arithmetic), on algebra.
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1142
|
Adelard of Bath produces two or three translations of Euclid's Elements from
Arabic.
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1144
|
Gherard of Cremona begins translating Arabic works (and Arabic translations of
Greek works) into Latin.
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|
1149
|
Al-Samawal writes al-Bahir fi'l-jabr (The brilliant in algebra). He develops
algebra with polynomials using negative powers and zero. He solves quadratic
equations, sums the squares of the first n natural numbers, and looks at
combinatorial problems.
|
|
1150
|
Arabic numerals are introduced into Europe with Gherard of Cremona's
translation of Ptolemy's Almagest. The name of the "sine" function comes from
this translation.
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|
About 1200
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Chinese start to use a symbol for zero.
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1202
|
Fibonacci writes Liber abaci (The Book of the Abacus), which sets out the
arithmetic and algebra he had learnt in Arab countries. It also introduces the
famous sequence of numbers now called the "Fibonacci sequence".
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|
1225
|
Fibonacci writes Liber quadratorum (The Book of the Square), his most
impressive work. It is the first major European advance in number theory since
the work of Diophantus a thousand years earlier.
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|
About 1225
|
Jordanus Nemorarius writes on astronomy. In mathematics he uses letters in an
early form of algebraic notation.
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|
1247
|
Ch'in Chiu-Shao writes Mathematical Treatise in Nine Sections. It contains
simultaneous integer congruences and the Chinese Remainder Theorem. It
considers indeterminate equations, Horner's method, areas of geometrical
figures and linear simultaneous equations.
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|
1248
|
Li Yeh writes a book which contains negative numbers, denoted by putting a
diagonal stroke through the last digit.
|
|
About 1260
|
Campanus of Novara, chaplain to Pope Urban IV, writes on astronomy and
publishes a Latin edition of Euclid's Elements which became the standard Euclid
for the next 200 years.
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|
1275
|
Yang Hui writes Cheng Chu Tong Bian Ben Mo (Alpha and omega of variations on
multiplication and division). It uses decimal fractions (in the modern form)
and gives the first account of Pascal's triangle.
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|
1303
|
Chu Shih-Chieh writes Szu-yuen Yu-chien (The Precious Mirror of the Four
Elements), which contains a number of methods for solving equations up to
degree 14. He also defines what is now called Pascal's triangle and shows how
to sum certain sequences.
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|
1321
|
Levi ben Gerson (sometimes known as Gersonides) writes Book of Numbers dealing
with arithmetical operations, permutations and combinations.
|
|
1335
|
Richard of Wallingford writes Quadripartitum de sinibus demonstratis, the first
original Latin treatise on trigonometry.
|
|
1336
|
Mathematics becomes a compulsory subject for a degree at the University of
Paris.
|
|
1342
|
Levi ben Gerson (Gersonides) writes De sinibus, chordis et arcubus (Concerning
Sines, Chords and Arcs), a treatise on trigonometry which gives a proof of the
sine theorem for plane triangles and gives five figure sine tables.
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|
1343
|
Levi ben Gerson (Gersonides) writes De harmonicis numeris (Concerning the
Harmony of Numbers), which is a commentary on the first five books of Euclid.
|
|
1364
|
Nicole d'Oresme writes Latitudes of Forms, an early work on coordinate systems
which may have influence Descartes. Another work by Oresme contains the first
use of a fractional exponent.
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|
1382
|
Nicole d'Oresme publishes Le Livre du ciel et du monde (The Book of Heaven and
Earth). It is a compilation of treatises on mathematics, mechanics, and related
areas. Oresme opposed the theory of a stationary Earth.
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