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This timeline of science and engineering in the Islamic world covers the time period from the 8th century AD to the introduction of European science to the Islamic world in the 19th and 20th centuries. All year dates are given according to the Gregorian calendar except where noted.
770–840–[mathematics] Khwarizmi (Persian: خوارزمی Khwarazmi, in Arabic became الخوارزمي al-Khwarizmi, Latinized name, Algorithm). Developed the "calculus of resolution and juxtaposition" (hisab al-jabr w'al-muqabala), more briefly referred to as al-jabr, or algebra.
800–873–[various] Ibn Ishaq Al-Kindi (Latinized, Alkindus.) Philosophy, Physics, Optics, Medicine, Mathematics, Cryptography, Metallurgy. Worked at the House of Wisdom which was set up in 810.
803 – [chemistry; glass] d. Abu-Moussa Jabir ibn Hayyan (Latinized name, Geber,). Famous Persian chemist. First chemist known to produce sulfuric acid, as well as many other chemicals and instruments. Wrote on adding color to glass by adding small quantities of metallic oxides to the glass, such as manganese dioxide. This was a new advancement in glass industry unknown in antiquity. His works include "The elaboration of the Grand Elixir"; "The chest of wisdom" in which he writes on nitric acid; Kitab al-istitmam (translated to Latin later as Summa Perfectionis); and others.
820–[mathematics] Mahani (full name Abu Abdollah Muhammad ibn Isa Mahani–in Arabic Al-Mahani). Conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. 
836–901 [anatomy; astronomy; mathematics; mechanics] Born Thabit Ibn Qurra (Latinized, Thebit.) Studied at Baghdad's House of Wisdom under the Banu Musa brothers. Made many contributions to mathematics, particularly in geometry and number theory. He discovered the theorem by which pairs of amicable numbers can be found; i.e., two numbers such that each is the sum of the proper divisors of the other. Later, al-Baghdadi (b. 980) and al-Haytham (born 965) developed variants of the theorem.
mid 9th century–[chemistry] Al-Kindi writes on the distillation of wine as that of rose water and gives 107 recipes for perfumes, in his book Kitab Kimia al-`otoor wa al-tas`eedat (book of the chemistry of perfumes and distillations.)
850–930 [mathematics] born Abu Kamil of Egypt (full name, Abu Kamil Shuja ibn Aslam ibn Muhammad ibn Shuja) Forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as .
858–929– [astronomy–mathematics] Al-Battani (Albategnius) Works on astronomy, trigonometry etc.
864–930–[chemistry; medicine; ...] Razi (Rhazes) Medicine, Ophthalmology, Smallpox, Chemistry, Astronomy. Al-Razi wrote on Naft (naphta or petroleum) and its distillates in his book "Kitab sirr al-asrar" (book of the secret of secrets.) When choosing a site to build Baghdad's hospital, he hung pieces of fresh meat in different parts of the city. The location where the meat took the longest to rot was the one he chose for building the hospital. Advocated that patients not be told their real condition so that fear or despair do not affect the healing process. Wrote on alkali, caustic soda, soap and glycerine. Gave descriptions of equipment processes and methods in his book Kitab al-Asrar (book of secrets) in 925.
888 – [various] Died 'Abbas Ibn Firnas. Mechanics of Flight, Planetarium, Artificial Crystals. According to one account written seven centuries after his death, Ibn Firnas was injured during an elevated winged trial flight.
9th century – [chemistry; petroleum] Oilfields in Baku, Azerbaijan, generate commercial activities and industry. These oilfields, were wells are dug to get the Naft (or naphta, or crude petroleum) are described by geographer Masudi in the 10th century and by Marco Polo in the 13th century.
10th century [mathematics; accounting] By this century, three systems of counting are used in the Arab world. Finger-reckoning arithmetic, with numerals written entirely in words, used by the business community; the sexagesimal system, a remnant originating with the Babylonians, with numerals denoted by letters of the arabic alphabet and used by Arab mathematicians in astronomical work; and the Indian numeral system, which was used with various sets of symbols . Its arithmetic at first required the use of a dust board (a sort of handheld blackboard) because "the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded." Al-Uqlidisi (born 920) modified these methods for pen and paper use .
920 [mathematics] Born al-Uqlidisi. Modified arithmetic methods for the Indian numeral system to make it possible for pen and paper use. Hitherto, doing calculations with the Indian numerals necessitated the use of a dust board as noted earlier.
936–1013 [medicine] Al-Zahrawi (Latinized name, Albucasis) Surgery, Medicine. Called the "Father of Modern Surgery." 
940–997 [astronomy; mathematics] Muhammad Al-Buzjani. Mathematics, Astronomy, Geometry, Trigonometry.
940 [mathematics] Born Abu'l-Wafa al-Buzjani. Wrote several treatises using the finger-counting system of arithmetic, and was also an expert on the Indian numerals system. About the Indian system he wrote: "[it] did not find application in business circles and among the population of the Eastern Caliphate for a long time."  Using the Indian numeral system, abu'l Wafa was able to extract roots.
953 [mathematics] Born al-Karaji of Karaj and Baghdad (full name, Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji or al-Karkhi). Believed to be 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 monomials , , , ... and , , , ... and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years" . Discovered the binomial theorem for integerexponents.  states that this "was a major factor in the development of numerical analysis based on the decimal system."
957 [geography; cartography; exploration; chemistry] died Abul Hasan Ali Al-Masudi, best known as a cartographer, was also a traveler historian, etc. Al-mas`oudi described his visit to the oilfields of Baku. Wrote on the reaction of alkali water with zaj (vitriol) water giving sulfuric acid.
965–1040 [mathematics; optics; physics] Born ibn al-Haitham (full name, ; Latinized name, Alhazen). Possibly the first to classify all even perfect numbers (i.e., numbers equal to the sum of their proper divisors) as those of the form where is prime number . Al-Haytham is also the first person to state Wilson's theorem. if is prime then is divisible by .  says "It is called Wilson's theorem because of a comment by Waring in 1770 that John Wilson had noticed the result. There is no evidence that Wilson knew how to prove it. It was over 750 years later that Lagrange gave the first known proof to the statement in 1771.
980 [mathematics] Born al-Baghdadi (full name, ). Studied a slight variant of Thabit ibn Qurra's theorem on amicable numbers. Al-Baghdadi also wrote texts comparing the three systems of counting and arithmetic used in the region during this period. Made improvements on the decimal system.
981–1037 [astronomy; mathematics; medicine; philosophy] Ibn Sina (Avicenna). Persian philosopher and physician; Medicine, Philosophy, Mathematics, Astronomy.
1044 or 1048–1123 [mathematics] Omar Al-Khayyam. Persian mathematician and poet. "Gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work: 'If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared.' " . Extracted roots using the decimal system (the Indian numeral system). There is dispute whether the Maqamat, a famous diwan of poetry translated to English are actually his work.
1058–1111 [law; theology] Al-Ghazali (Algazel), judge and prolific thinker and writer on topis such as sociology, theology and philosophy. He critiqued the so-called Greek philosophers Ibn Sina, aka Avicenna and al-Farabi, aka Farabius. Wrote extensive expositions on Islamic tenets and foundations of jurisprudence. Also critiqued the Muslim scholastics (al-mutakallimun.) Was associated with sufism but he later critiqued it as well.
1091–1161 [medicine] Ibn Zuhr (Avenzoar) Surgery, Medicine.
1100–1166 (AH 493–560) [cartography, geography] Muhammad al-Idrissi, aka Idris al-Saqalli aka al-sharif al-idrissi of Andalusia and Sicily. Known for having drawn some of the most advanced ancient world maps, as well as writing on travels and geography.
1106–1138 [polymath] Abu Bakr Muhammad Ibn Yahya (Ibn Bajjah) Philosophy, Medicine, Mathematics, Astronomy, Poetry, Music.
1110–1185 [literature, philosophy] Abdubacer Ibn Tufayl of Spain. Philosophy, medicine, poetry, fiction. His most famous work is Hayy ibn Yaqzan, which is a spiritual investigation into the reality of the world narrated by a man who was raised from infancy by a roe or gazelle.
1128–1198 [philosophy] Ibn Rushd (Averroes) Philosophy, Law, Medicine, Astronomy, Theology.
1130 [mathematics] Born al-Samawal. An important member of al-Karaji's school of algebra. Gave this definition of algebra: "[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known." 
1135 [mathematics] Born Sharafeddin Tusi. Follows al-Khayyam's application of algebra of geometry, rather than follow the general development that came through al-Karaji's school of algebra. Wrote a treatise on cubic equations which  describes thus: "[the treatise] represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry." (quoted in ).
13th century–[medicine; scientific method] Ibn Al-Nafis b. ca. 607AH, d. ca. 689AH. Damascene physician and anatomist. Discovered the lesser circulatory system (the cycle involving the ventricles of the heart and the lungs), and described the mechanism of breathing and its relation to the blood and how it nourishes on air in the lungs. Followed a "constructivist" path of the smaller circulatory system: "blood is purified in the lungs for the continuance of life and providing the body with the ability to work". During his time, the common view was that blood originates in the liver then travels to the right ventricle, then on to the organs of the body; another contemporary view was that blood is filtered through the diaphragm where it mixes with the air coming from the lungs. Ibn al-Nafis discredited all these views including ones by Galen and Avicenna (ibn Sina). At least an illustration of his manuscript is still extant. William Harvey explained the circulatory system without reference to ibn al-Nafis in 1628. Ibn al-Nafis extolled the study of comparative anatomy in his "Explaining the dissection of [Avicenna's] Al-Qanoon" which includes a prefaces, and citations of sources. Emphasized the rigours of verification by measurement, observation and experiment. Subjected conventional wisdom of his time to a critical review and verified it with experiment and observation, discarding errors.
13th century–[chemistry] Al-Jawbari describes the preparation of rose water in the work "Book of Selected Disclosure of Secrets" (Kitab kashf al-Asrar).
13th century–[chemistry; materials; glassmaking] Arabic manuscript on the manufacture of false gemstones and diamonds. Also describes spirits of alum, spirits of saltpetre and spirits of salts (hydrochloric acid).
1248–[pharmacy; veterinary medicine] Died Ibn Al-Baitar. Studied and wrote on botany, pharmacy and is best known for studying animal anatomy and medicine. The Arabic term for veterinary medicine is named after him.
1304–1369 [exploration; travel] Abu Abdullah Muhammad ibn Battuta; World Traveler. 75,000 mile voyage from Morocco to China and back.
1332–1395 [history; political science; humanities] Ibn Khaldun. Sociology, Philosophy of History, general science, Political Science. His most famous work, al-Muqqadima (Prolegomena), encyclopedic in breadth, surveys the state of knowledge of his day, covering geography, accounts of the peoples of the world and their known history, the classification and aims of the sciences and the religious sciences.
1380 [mathematics] Born al-Kashi. According to , "contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as pi. 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."
15th century [mathematics] Ibn al-Banna and al-Qalasadi used symbols for mathematics in the 15th century "and, although we do not know exactly when their use began, we know that symbols were used at least a century before this." 
15th century–[astronomy and mathematics] Ibn Masoud (Ghayyathuddin Jamshid ibn Mohamed ibn mas`oud, d. 1424 or 1436.) Wrote on the decimal system. First to introduce the zero (Indian mathematicians had used only nine glyphs for numerals). Computed and observed the solar eclipses of 809AH, 810AH and 811AH, after being invited by Ulugh Bek, based in Samarqand to pursue his study of mathematics, astronomy and physics. His works include "The Key of arithmetics"; "Discoveries in mathematics"; "The Decimal point"; "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; on finding the unknowns [unknown variables]. He also wrote a "Thesis on the sine and the chord"; "thesis on the circumference" in which he found the ratio of the circumference to the radius of a circle to the 16th decimal; "The garden of gardens" or "promenade of the gardens" describing an instrument he devised and used at the Samarqand observatory to compile an ephemeris, and for computing solar and lunar eclipses; The ephemeresis "Zayj Al-Khaqani" which also includes mathematical tables and corrections of the ephemeresis by Al-Tusi; "Thesis on finding the first degree sine"; and more.
1411 [mathematics] Al-Kashi writes Compendium of the Science of Astronomy .
1424 [mathematics] Al-Kashi writes Treatise on the Circumference giving a remarkably good approximation to pi in both sexagesimal and decimal forms .
1427 [mathematics] 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 and is one of the best textbooks in the whole of medieval literature .
1437 [mathematics] Ulugh Beg publishes his star catalogueZij-i Sultani. It contains trigonometric tables correct to eight decimal places based on Ulugh Beg's calculation of the sine of one degree which he calculated correctly to 16 decimal places .
1502 - [standards] First law about standarts of the world. “Kanunname-i Ihtisab-i Bursa (The Law of Bursa Municipality) was the first law about the standards. This law was imposed in the period of Sultan Bayezid II, in 1502. In this law, animal products, fruits and vegetables, salt, bread, industrial products, textile products, forest products, and leather products were bounded to a standard and their prices were fixed. Some of these standards are that: Vegetables: For fresh courgette no official price will be fixed for 3 days. After 3 days 3 okka will be sold for one coin. In the first week 4 okka, in the second week 5 okka, in the third week 6 okka, in the fourth week 8 okka will be sold for one coin. Jewelers: Silver will be not under 80 standard. 1.5 drams of gold will be not under 60 coins.
16th century [Aviation] A Turk in Istanbul attempted to fly. In 1648 John Wilkins cites Busbecq, the Austrian ambassador to Istanbul 1554-1562, as recording that "a Turk in Istanbul" attempted to fly.
^Hacaoglu, Selcan. Mar. 10, 2002, The Miami Herald
^Wilkins, John. Mathematicall Magick or the Wonders that may be performed by Mechanicall Geometry. In two books. Concerning Mechanicall Powers and Motions, London 1648, 204; also see a reprint of the same book in The Mathematical and Philosophical Works of John Wilkins to which is prefixed the author's life and an account of his works, 1802, vol. II, 201