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This article is about the history of science in the Islamic civilisation between the 8th and 15th centuries. For information on science in the context of Islam, see The relation between Islam and science.

In the history of science, Islamic science refers to the science developed under the Muslim world between the 8th and 15th centuries, during what is known as the Islamic Golden Age. It is also known as Arabic science due to most texts during this period being written in Arabic language, the lingua franca of the Islamic civilization. Despite these names, not all scientists during this period were Muslim or Arab, as there were a number of notable non-Arab scientists, as well as some non-Muslim scientists, contributing to science in the Islamic civilization.

A number of modern scholars, notably Robert Briffault, Will Durant, Fielding H. Garrison, Alexander von Humboldt, Muhammad Iqbal, Abdus Salam, and Hossein Nasr, consider modern science to have begun from List of Muslim scientists, who were pioneers of the scientific method and introduced a modern Empiricism, experimental and quantitative approach to scientific inquiry. Some have referred to their achievements as a "Muslim scientific revolution".Ahmad Y Hassan and Donald Routledge Hill (1986), Islamic Technology: An Illustrated History, p. 282, Cambridge University Press.Abid Ullah Jan (2006), After Fascism: Muslims and the struggle for self-determination, "Islam, the West, and the Question of Dominance", Pragmatic Publishings, ISBN 978-0-9733687-5-8.Abdus Salam, H. R. Dalafi, Mohamed Hassan (1994). Renaissance of Sciences in Islamic Countries, p. 162. World Scientific, ISBN 9971507137.Salah Zaimeche (2003), An Introduction to Muslim Science, FSTC.

Overview Rise During the early Muslim conquests, the Muslim Arabs led by Khalid ibn al-Walid conquered the Sassanid Empire Persian Empire and more than half of the Byzantine Empire Roman Empire, establishing the Arab Empire across the Middle East, Central Asia, and North Africa, followed by further expansions across Pakistan, History of Islam in southern Italy and the Iberian Peninsula. As a result, the Islamic governments inherited "the knowledge and skills of the ancient History of the Middle East, of History of Greece, of Persian Empire and of History of India. They added new and important innovations from outside, such as positional numbering from History of India," as Bernard Lewis wrote in What Went Wrong?

Another innovation was paper - originally a secret tightly guarded by the Han Chinese. The art of papermaking was obtained from two prisoners at the Battle of Talas (751), resulting in paper mills being built in Samarkand and Baghdad. The Arabs improved upon the Chinese techniques using linen rags instead of mulberry bark.

The difference in attitudes of Byzantine scientists and the medieval Muslim scientists was firm. Byzantium added little to no new knowledge of science or medicine to the Greco-Roman scientific tradition, stagnating in awe of their classical predecessors. This could perhaps be explained by the fact that the initial Islamic surge out of Arabia had captured three of its most productive cities: Alexandria, Carthage, and Antioch. Because of the loss of a highly skilled and centralized government, as well as continuous and devastating Arab conquests into Anatolia, most Byzantine cities could not support the arts and sciences, and there was a mass return to subsistence farming. Most notable List of Arab scientists and scholars and List of Iranian scientists and scholars lived and practiced during the Islamic Golden Age.

The number of important and original Arabic works written on the mathematical sciences is much larger than the combined total of Latin and Greek language works on the mathematical sciences.N. M. Swerdlow (1993). "Montucla's Legacy: The History of the Exact Sciences", Journal of the History of Ideas 54 (2), p. 299-328 .

Scientific method (Alhazen) was a polymath who has been described as the "father of optics", the "pioneer of the modern scientific method", the "founder of psychophysics and experimental psychology", and the "first scientist".

Muslim scientists placed far greater emphasis on empiricism and experimentation than any previous ancient civilization, and they introduced quantification, precise observation, Scientific control, and careful records. Their new approach to scientific inquiry led to the development of the scientific method in the Islamic world. In particular, the empirical observations and quantitative experiments of Ibn al-Haytham (Alhacen) in his Book of Optics (1021) is seen as the beginning of the modern scientific method.David Agar (2001). Arabic Studies in Physics and Astronomy During 800 - 1400 AD. University of Jyväskylä. Other leading exponents of the experimental method included Geber (who introduced it to chemistry), Avicenna (who introduced it to medicine), and Abū Rayhān al-Bīrūnī (who introduced it to astronomy and mechanics). The most important development of the scientific method, the use of experimentation and quantification to distinguish between competing scientific theories set within a generally empirical orientation, was introduced by Muslim scientists.

Rosanna Gorini writes:

Ibn al-Haytham, who is now known as the father of optics,R. L. Verma "Al-Hazen: father of modern optics", Al-Arabi, 8 (1969): 12-13. used the scientific method to obtain the results in his Book of Optics. In particular, he combined observations, experiments and rational arguments to show that his modern intromission theory of visual perception, where Ray (optics) of light are emitted from objects rather than from the eyes, is scientifically correct, and that the ancient Emission theory (vision) supported by Ptolemy and Euclid (where the eyes emit rays of light), and the ancient intromission theory supported by Aristotle (where objects emit physical particles to the eyes), were both wrong.D. C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago, Univ. of Chicago Pr., 1976), pp. 60-7. It is known that Roger Bacon (who was sometimes erroneously given credit for the scientific method) was familiar with Ibn al-Haytham's work.

Ibn al-Haytham developed rigorous experimental methods of controlled Test method in order to verify theoretical Hypothesis and substantiate Inductive reasoning conjectures. Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:Bradley Steffens (2006). Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246. (cf. Bradley Steffens, "Who Was the First Scientist?", Ezine Articles.)

Observation

Statement of problem

Formulation of hypothesis

Testing of hypothesis using experimentation

Analysis of experimental results

Interpretation of data and formulation of conclusion

Publication of findings

The development of the scientific method is considered to be so fundamental to science that some — especially Philosophy of science and practicing scientists — consider earlier inquiries into nature to be pre-scientific. Some have described Ibn al-Haytham as the "first scientist" for this reason.Bradley Steffens (2006). Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246.

In The Model of the Motions, Ibn al-Haytham also describes an early version of Occam's razor, where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmology hypotheses that cannot be observed from Earth.Roshdi Rashed (2007). "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy 17, p. 7-55 . Cambridge University Press.

Robert Briffault wrote in The Making of Humanity:

George Sarton, the father of the history of science, wrote:

Oliver Joseph Lodge wrote in the Pioneers of Science:

Muhammad Iqbal wrote in The Reconstruction of Religious Thought in Islam:

Decline From the 12th century onwards, Islamic science and the numbers of Islamic scientists began declining. After the 13th century, the Islamic civilization would still produce occasional scientists but they became the exception, rather than the rule (see List of Islamic scholars). Some historians have recently come to question the traditional picture of decline, pointing to continued astronomical activity as a sign of a continuing and creative scientific tradition through to the 16th century, of which the work of Ibn al-Shatir (1304–1375) in Damascus is considered the most noteworthy example.George Saliba, A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, (New York: New York University, 1994), p.vii: "The main thesis, for which this collection of articles cam be used as evidence, is the one claiming that the period often called a period of decline in Islamic intellectual history was, scientifically speaking from the point of view of astronomy, a very productive period in which astronomical thories of the highest order were produced."David A. King, "The Astronomy of the Mamluks", Isis, 74 (1983):531-555

One reason for the scientific decline can be traced back to the 10th century, when the orthodox school of Ash'ari theology challenged the more rational school of Mu'tazili theology. Other reasons include conflicts between the Sunni and Shia Muslims, and invasions by Crusades and Mongol Empire on Islamic lands between the 11th and 13th centuries, especially the Mongol Empire of the 13th century. The Mongols destroyed Muslim libraries, observatories, hospitals, and universities, culminating in the Battle of Baghdad (1258), the Abbasid capital and intellectual centre, in 1258, which marked end of the Islamic Golden Age.Erica Fraser. The Islamic World to 1600, University of Calgary.

By the 13th century, the more strict Ash'ari school replaced Mu'tazili thoughts in Islamic lands. That replacement and numerous wars and conflicts created a climate which made Islamic science less successful than before. With the fall of Al-Andalus in 1492, scientific and technological initiative generally passed to Christian Europe and led to what are now known as the European Renaissance and Scientific Revolution.

Influence on European science Contributing to the growth of European science was the major search by European scholars for new learning which they could only find among Muslims, especially in Al-Andalus and History of Islam in southern Italy. These scholars translated new scientific and philosophical texts from Arabic language into Latin.

One of the most productive translators in Spain was Gerard of Cremona, who translated 87 books from Arabic to Latin,including Muhammad ibn Mūsā al-Khwārizmī's The Compendious Book on Calculation by Completion and Balancing, Jabir ibn Aflah's Elementa astronomica,al-Kindi's On Optics, Ahmad ibn Muhammad ibn Kathīr al-Farghānī's On Elements of Astronomy on the Celestial Motions, al-Farabi's On the Classification of the Sciences,For a list of Gerard of Cremona's translations see: Edward Grant (1974) A Source Book in Medieval Science, (Cambridge: Harvard Univ. Pr.), pp. 35-8 or Charles Burnett, "The Coherence of the Arabic-Latin Translation Program in Toledo in the Twelfth Century," Science in Context, 14 (2001): at 249-288, at pp. 275-281.the Alchemy (Islam) and Islamic medicine works of al-Razi,the works of Thabit ibn Qurra and Hunayn ibn Ishaq,D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 6.and the works of Arzachel, Jabir ibn Aflah, the Banū Mūsā, Abū Kāmil Shujā ibn Aslam, Abu al-Qasim, and Ibn al-Haytham (including the Book of Optics).

Other Arabic works translated into Latin during the 12th century include the works of Muhammad ibn Jābir al-Harrānī al-Battānī and Muhammad ibn Mūsā al-Khwārizmī (including The Compendious Book on Calculation by Completion and Balancing),the works of Abu al-Qasim (including the al-Tasrif),D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 3.Muhammad al-Fazari's Great Sindhind (based on the Surya Siddhanta and the works of Brahmagupta),G. G. Joseph, The Crest of the Peacock, p. 306.the works of al-Razi and Avicenna (including The Book of Healing and The Canon of Medicine),M.-T. d'Alverny, "Translations and Translators," pp. 444-6, 451the works of Averroes,the works of Thabit ibn Qurra, al-Farabi, Ahmad ibn Muhammad ibn Kathīr al-Farghānī, Hunayn ibn Ishaq, and his nephew Hubaysh ibn al-Hasan,D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 4-5.the works of al-Kindi, Abraham bar Hiyya's Liber embadorum, Ibn Sarabi's (Serapion Junior) De Simplicibus,the works of Qusta ibn Luqa,D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 5.the works of Maslamah Ibn Ahmad al-Majriti, Ja'far ibn Muhammad Abu Ma'shar al-Balkhi, and al-Ghazali,Salah Zaimeche (2003). Aspects of the Islamic Influence on Science and Learning in the Christian West, p. 10. Foundation for Science Technology and Civilisation.the works of Nur Ed-Din Al Betrugi, including On the Motions of the Heavens, Biographisch-Bibliographisches KirchenlexiconAli ibn Abbas al-Majusi's medical encyclopedia, The Complete Book of the Medical Art,Jerome B. Bieber. Medieval Translation Table 2: Arabic Sources, Santa Fe Community College (Florida).Abu Mashar's Introduction to Astrology,Charles Burnett, ed. Adelard of Bath, Conversations with His Nephew, (Cambridge: Cambridge University Press, 1999), p. xi.the works of Maimonides, Ibn Zezla (Byngezla), Masawaiyh, Serapion, al-Qifti, and Albe'thar.D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 4.Abū Kāmil Shujā ibn Aslam's Algebra,V. J. Katz, A History of Mathematics: An Introduction, p. 291.the Alchemy (Islam) works of Geber, and the De Proprietatibus Elementorum, an Arabic work on geology written by a pseudo-Aristotle. By the beginning of the 13th century, Mark of Toledo translated the Qur'an and various Islamic medicine.M.-T. d'Alverny, "Translations and Translators," pp. 429, 455

Fibonacci presented the first complete European account of the Hindu-Arabic numeral system from Arabic numerals in his Liber Abaci (1202).Jerome B. Bieber. Medieval Translation Table 2: Arabic Sources, Santa Fe Community College (Florida). Al-Khazini's Zij as-Sanjari was translated into Greek language by Gregory Choniades in the 13th century and was studied in the Byzantine Empire.David Pingree (1964), "Gregory Chioniades and Palaeologan Astronomy", Dumbarton Oaks Papers 18, p. 135-160. The Islamic astronomy to the Geocentric model made by al-Battani, Averroes, Mo'ayyeduddin Urdi (Urdi lemma), Nasir al-Din al-Tusi (Tusi-couple) and Ibn al-Shatir were later adapted into the Copernican heliocentrism model. Al-Kindi's (Alkindus) law of Terrestrial planet Gravitation influenced Robert Hooke's law of Celestial spheres gravity, which in turn inspired Newton's law of universal gravitation. Abū al-Rayhān al-Bīrūnī's Ta'rikh al-Hind and Kitab al-qanun al-Mas’udi were translated into Latin as Indica and Canon Mas’udicus respectively. Ibn al-Nafis' commentary on the last part of Avicenna's The Canon of Medicine concerning Remedy was translated into Latin by Andrea Alpago (d. 1522) and published in Europe in 1547. Ibn al-Nafis' Commentary on the Anatomy of Canon of Avicenna, which first described pulmonary circulation, may have also been translated into Latin and available in Europe around that time, and it may have had an influence on Michael Servetus and Realdo Colombo. Anatomy and Physiology, Islamic Medical Manuscripts, United States National Library of Medicine. Translations of Omar Khayyám's works on algebra and geometry were later influential in the development of non-Euclidean geometry in Europe in the 18th century.D. S. Kasir (1931). The Algebra of Omar Khayyam, p. 6-7. Columbia University Press, Columbia University, New York. English translations of the Brethren of Purity's Encyclopedia of the Brethren of Purity and Arabic manuscripts of Ibn Miskawayh's al-Fawz al-Asghar were available in European universities by the early 19th century, and these works possibly had an influence on Charles Darwin, who was a student of Arabic, and his inception of Darwinism.

Fields In the Middle Ages, especially during the Islamic Golden Age, Muslim scholars made significant advances in science, mathematics, medicine, astronomy, engineering, and many other fields. During this time, early Islamic philosophy developed and was often pivotal in scientific debates — key figures were usually scientists and philosophers.

Applied sciences -operated reciprocating engine suction piston pump of al-Jazari, the father of modern day engineering. humanoid robots of al-Jazari, the father of robotics.

Fielding H. Garrison wrote in the History of Medicine:

In the applied sciences, a significant number of inventions and technologies were produced by medieval Muslim scientists and engineers, including inventors such as Abbas Ibn Firnas, Taqi al-Din, and especially al-Jazari, who is considered the father of robotics and the father of modern day engineering. 1000 Years of Knowledge Rediscovered at Ibn Battuta Mall, MTE Studios. Some of the inventions produced by medieval Muslim scientists and engineers include the camera obscura, coffee, hang glider, Soap bar, shampoo, pure distillation, liquefaction, crystallisation, purification, oxidisation, evaporation, filtration, Distilled beverage alcohol, uric acid, nitric acid, alembic, crankshaft, valve, Reciprocating engine suction piston pump, mechanical clocks driven by Water clock and weights, Computer programming humanoid robot, combination lock, quilting, pointed arch, scalpel, bone saw, forceps, surgical catgut, windmill, inoculation, smallpox vaccine, fountain pen, cryptanalysis, Frequency analysis (cryptanalysis), three-course meal, stained glass and Fused quartz, Persian carpet, modern cheque, celestial globe, explosive rockets and incendiary devices, torpedo, and royal pleasure gardens.

Astrology Islamic astrology, in Arabic language ilm al-nujumis the study of the heavens by early Muslims. In early Arabic sources, ilm al-nujum was used to refer to both astronomy and astrology. In medieval sources, however, a clear distinction was made between ilm al-nujum (science of the stars) or ilm al-falak (science of the celestial orbs), referring to astrology, and ilm al-haya (science of the figure of the heavens), referring to astronomy. Both fields were rooted in Greece, Persian Empire, and Indian subcontinent traditions. Despite consistent critiques of astrology by scientists and religious scholars, astrological prognostications required a fair amount of exact scientific knowledge and thus gave partial incentive for the study and development of astronomy.

The first semantic distinction between astronomy and astrology was given by al-Biruni in the 11th century.S. Pines (September 1964). "The Semantic Distinction between the Terms Astronomy and Astrology according to al-Biruni", Isis 55 (3), p. 343-349.

was a polymath who resolved significant problems in the Geocentric model with the Tusi-couple, which played an important role in Copernican heliocentrism.

Astronomy In astronomy, the work of Egyptians astronomer Ptolemy, particularly the Almagest, and the Indian astronomy work of Brahmagupta, were significantly refined over the years by Muslim astronomers. The astronomical tables of Muhammad ibn Mūsā al-Khwārizmī and of Maslamah Ibn Ahmad al-Majriti served as important sources of information for Latinized European thinkers rediscovering the works of astronomy, where extensive interest in astrology was discouraged.

From the 11th century, Muslim astronomers began questioning the Ptolemaic system, beginning with Ibn al-Haytham, and they were the first to conduct elaborate experiments related to astronomical phenomena, beginning with Abū al-Rayhān al-Bīrūnī's introduction of the scientific method into astronomy.Dr. A. Zahoor (1997), Abu Raihan Muhammad al-Biruni, Hasanuddin University. Many of them made changes and corrections to the Ptolemaic model within a geocentrism framework. In particular, the corrections of al-Battani, Ibn al-Haytham, Averroes, Nasir al-Din al-Tusi (Tusi-couple), Mo'ayyeduddin Urdi (Urdi lemma) and Ibn al-Shatir were later adapted into the Copernican heliocentrism model.M. Gill (2005). Was Muslim Astronomy the Harbinger of Copernicanism?Richard Covington (May-June 2007). "Rediscovering Arabic science", Saudi Aramco World, p. 2-16. Several Muslim astronomers also discussed the possibility of a heliocentrism model with ellipse orbits, such as Ja'far ibn Muhammad Abu Ma'shar al-Balkhi, Ibn al-Haytham, Abū al-Rayhān al-Bīrūnī, Abu Said Sinjari, 'Umar al-Katibi al-Qazwini, and Qutb al-Din al-Shirazi.A. Baker and L. Chapter (2002), "Part 4: The Sciences". In M. M. Sharif, "A History of Muslim Philosophy", Philosophia Islamica.

Other developments in astronomy include al-Biruni's discovery of the Milky Way galaxy being a collection of numerous Nebula stars, and the development of a planetary model without any Deferent and epicycle by Ibn Bajjah (Avempace).Bernard R. Goldstein (March 1972). "Theory and Observation in Medieval Astronomy", Isis 63 (1), p. 39-47 . The optical writings of Ibn al-Haytham are reported to have laid the foundations for the later European development of telescope astronomy.O. S. Marshall (1950). "Alhazen and the Telescope", Astronomical Society of the Pacific Leaflets 6, pp. 4-11.

Botany Further information: Islamic Golden Age#Agricultural Revolution

During the Muslim Agricultural Revolution, Muslim scientists made significant advances in the field of botany. They developed a scientific approach to botany and agriculture based on three major elements; sophisticated systems of crop rotation, highly developed irrigation techniques, and the introduction of a large variety of crops which were studied and catalogued according to the season, type of land and amount of water they require. Numerous encyclopaedias on botany were produced, with highly accurate precision and details.Al-Hassani, Woodcock and Saoud (2007), Muslim heritage in Our World, FSTC publishing, 2nd Edition, p. 102-123.

Muslim botanists and agriculturists demonstrated agrotechnical and economic knowledge in areas such as meteorology, climatology, hydrology, soil occupation, and the economy and management of agricultural enterprises. They also demosntrated agricultural knowledge in areas such as pedology, agricultural ecology, irrigation, preparation of soil, planting, spreading of manure, killing herbs, sowing, cutting trees, grafting, pruning vine, prophylaxis, phytotherapy, the care and improvement of Plant tissue culture and plants, and the harvest and storage of crops.Toufic Fahd (1996), "Botany and agriculture", in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 3, p. 813-852 . Routledge, London and New York.

Chemistry (Geber) was a polymath who is regarded as the father of chemistry and a founder of the perfume industry.

The 9th century chemist, Geber (Jabir ibn Hayyan), is considered the father of chemistry,John Warren (2005). "War and the Cultural Heritage of Iraq: a sadly mismanaged affair", Third World Quarterly, Volume 26, Issue 4 & 5, p. 815-830.Dr. A. Zahoor (1997). JABIR IBN HAIYAN (Geber). University of Indonesia.Paul Vallely, How Islamic Inventors Changed the World, The Independent, 11 March 2006. for introducing the first experimental scientific method for chemistry, as well as the alembic, still, retort, pure distillation, liquefaction, crystallisation, purification, oxidisation, evaporation, and filtration.

Al-Kindi was the first to debunk the theory of the Philosopher's stone,Felix Klein-Frank (2001), "Al-Kindi", in Oliver Leaman & Hossein Nasr, History of Islamic Philosophy, p. 174. London: Routledge. followed by Abū Rayhān al-BīrūnīMichael E. Marmura (1965). "An Introduction to Islamic Cosmological Doctrines. Conceptions of Nature and Methods Used for Its Study by the Ikhwan Al-Safa'an, Al-Biruni, and Ibn Sina by Seyyed Hossein Nasr", Speculum 40 (4), p. 744-746. and Avicenna.Robert Briffault (1938). The Making of Humanity, p. 196-197. Avicenna also invented steam distillation and produced the first essential oils, which led to the development of aromatherapy. Al-Razi first distilled petroleum, invented kerosene and kerosene lamps, soap bars and modern recipes for soap, and antiseptics. In the 13th century, Nasīr al-Dīn al-Tūsī stated an early version of the law of conservation of mass, noting that a body of matter is able to change, but is not able to disappear.Farid Alakbarov (Summer 2001). http://azer.com/aiweb/categories/magazine/92_folder/92_articles/92_tusi.html A 13th-Century Darwin? Tusi's Views on Evolution, Azerbaijan International 9 (2). von Humboldt regarded the Muslim chemists as the founders of chemistry.Dr. Kasem Ajram (1992). Miracle of Islamic Science, Appendix B. Knowledge House Publishers. ISBN 0911119434.

Will Durant wrote in The Story of Civilization IV: The Age of Faith:

George Sarton, the father of the history of science, wrote in the Introduction to the History of Science:

Earth sciences was a Polymath who is regarded as the father of Indology, the father of geodesy, "the first anthropology" and one of the first geology.

Muslim scientists, notably Abū Rayhān al-Bīrūnī, made a number of contributions to the Earth sciences. In particular, Biruni is regarded as the father of geodesy for his important contributions to the field,H. Mowlana (2001). "Information in the Arab World", Cooperation South Journal 1. along with his significant contributions to geography and geology.

Among his writings on geology, Biruni wrote the following on the geology of India:

John J. O'Connor and Edmund F. Robertson write in the MacTutor History of Mathematics archive:

Fielding H. Garrison wrote in the History of Medicine:

George Sarton, the father of the history of science, wrote in the Introduction to the History of Science:

In geology, Avicenna hypothesized on two causes of mountains in The Book of Healing. In cartography, the Piri Reis map drawn by the Ottoman Empire cartographer Piri Reis in 1513, was one of the earliest world maps to include the Americas, and perhaps the first to include Antarctica. His map of the world was considered the most accurate in the 16th century.

Mathematics , the father of algebra and father of algorithms.

John J. O'Connor and Edmund F. Robertson wrote in the MacTutor History of Mathematics archive:

Muhammad ibn Mūsā al-Khwārizmī (780-850), from whose name the word algorithm derives, contributed significantly to algebra, which is named after his book, The Compendious Book on Calculation by Completion and Balancing, the first book on elementary algebra.Eglash (1999), p.61 He also introduced what is now known as Arabic numerals, which originally came from Indian mathematics, though Muslim mathematicians did make several refinements to the number system, such as the introduction of Decimal separator notation. Al-Kindi (801-873) was a pioneer in cryptanalysis and cryptology. He gave the first known recorded explanations of cryptanalysis and Frequency analysis (cryptanalysis) in A Manuscript on Deciphering Cryptographic Messages.Simon Singh, The Code Book, p. 14-20.

The first known Mathematical proof by mathematical induction appears in a book written by Al-Karaji around 1000 AD, who used it to prove the binomial theorem, Pascal's triangle, and the sum of integral Cube (algebra).Victor J. Katz (1998). History of Mathematics: An Introduction, p. 255-259. Addison-Wesley. ISBN 0321016181. The historian of mathematics, F. Woepcke,F. Woepcke (1853). Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi. Paris. praised Al-Karaji for being "the first who introduced the theory of algebraic calculus." Ibn al-Haytham was the first mathematician to derive the formula for the sum of the fourth powers, and using the method of induction, he developed a method for determining the general formula for the sum of any integral Exponentiation, which was fundamental to the development of integral calculus.Victor J. Katz (1995). "Ideas of Calculus in Islam and India", Mathematics Magazine 68 (3), p. 163-174. The 11th century Persian literature-mathematician Omar Khayyám was the first to find general geometry solutions of cubic equations and laid the foundations for the development of analytic geometry and non-Euclidean geometry. Sharaf al-Din al-Tusi (1135-1213) found algebraic and Numerical analysis solutions to cubic equations and was the first to discover the derivative of Cubic function, an important result in differential calculus.J. L. Berggren (1990). "Innovation and Tradition in Sharaf al-Din al-Tusi's Muadalat", Journal of the American Oriental Society 110 (2), p. 304-309.

Mechanics was a polymath, who is considered the father of modern medicine and the father of the concept of momentum, and regarded as one of the greatest thinkers and medical scholars in history.

In the mechanics field of physics, Ja'far Muhammad ibn Mūsā ibn Shākir (800-873) of the Banū Mūsā was a pioneer of astrophysics and celestial mechanics, as he was the first to discover that the Astronomical object and celestial spheres were subject to the same Physical law as Earth, unlike the ancients who believed that the celestial spheres followed their own set of physical laws different from that of Earth.George Saliba (1994). "Early Arabic Critique of Ptolemaic Cosmology: A Ninth-Century Text on the Motion of the Celestial Spheres", Journal for the History of Astronomy 25, p. 115-141 . In his Astral Motion and The Force of Attraction, he was also the first to discover that there was a force of Gravitation between Astronomical object,K. A. Waheed (1978). Islam and The Origins of Modern Science, p. 27. Islamic Publication Ltd., Lahore. foreshadowing Newton's law of universal gravitation.Robert Briffault (1938). The Making of Humanity, p. 191. Thābit ibn Qurra (836-901) rejected the Peripatetic school and Aristotelian physics notions of a "natural place" for each Classical element. He instead proposed a theory of Motion (physics) in which both the upward and downward motions are caused by weight, and that the order of the universe is a result of two competing Gravitation (jadhb): one of these being "between the Wiktionary:sublunar and celestial elements", and the other being "between all parts of each element separately".Mohammed Abattouy (2001). "Greek Mechanics in Arabic Context: Thabit ibn Qurra, al-Isfizarı and the Arabic Traditions of Aristotelian and Euclidean Mechanics", Science in Context 14, p. 205-206. Cambridge University Press. Al-Kindi (801-873) described an early concept of relativity, which some see as a precursor to the later theory of relativity developed by Albert Einstein in the 20th century. Like Einstein, al-Kindi held that the physical world and physical phenomena are relative, that time, space, motion and Physical body are all relative to each other and not independent or Absolute (philosophy), and that they are relative to other objects and to the observer. The Theory of Relativity, Foundation for Science Technology and Civilisation, 2003.

Ibn al-Haytham (965-1039) discussed the theory of Gravitation between masses, and it seems that he was aware of the Magnitude (mathematics) of acceleration due to gravity and he discovered that the heavenly bodies "were accountable to the Physical law".Duhem, Pierre (1908, 1969). To Save the Phenomena: An Essay on the Idea of Physical theory from Plato to Galileo, p. 28. University of Chicago Press, Chicago. Ibn al-Haytham also discovered the law of inertia, known as Newton's first law of motion, when he stated that a body moves perpetual motion unless an external force stops it or changes its direction of motion.Dr. Nader El-Bizri, "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), Medieval Islamic Civilization: An Encyclopaedia, Vol. II, p. 343-345, Routledge, New York, London. He also discovered the concept of momentum, part of Newton's second law of motion.Seyyed Hossein Nasr, "The achievements of Ibn Sina in the field of science and his contributions to its philosophy", Islam & Science, December 2003.

Nobel Prize winning physicist Abdus Salam wrote the following on Ibn al-Haytham:

Avicenna (980-1037) discovered the concept of momentum, when he referred to impetus as being proportional to weight times velocity, a precursor to the concept of momentum in Newton's second law of motion.A. Sayili (1987), "Ibn Sīnā and Buridan on the Motion of the Projectile", Annals of the New York Academy of Sciences 500 (1), p. 477–482: He is thus considered the father of the fundamental concept of momentum in physics.Seyyed Hossein Nasr, "Islamic Conception Of Intellectual Life", in Philip P. Wiener (ed.), Dictionary of the History of Ideas, Vol. 2, p. 65, Charles Scribner's Sons, New York, 1973-1974. His theory of motion was also consistent with the concept of inertia in Newton's first law of motion. Abū Rayhān al-Bīrūnī (973-1048) was the first to realize that acceleration is connected with non-uniform motion, part of Newton's second law of motion.

In 1121, al-Khazini, in The Book of the Balance of Wisdom, was the first to propose that the gravity and gravitational potential energy of a body varies depending on its distance from the centre of the Earth. This phenomenon was not proven until Newton's law of universal gravitation centuries later. In statics, al-Khazini first clearly differentiated between force, mass, and weight, and he showed awareness of the weight of the air and of its decrease in density with altitude, and discovered that there was greater density of water when nearer to the Earth's centre.Salah Zaimeche PhD (2005). Merv, p. 5-7. Foundation for Science Technology and Civilization. Ibn Bajjah (Avempace) (d. 1138) was the first to state that there is always a Reaction (physics) force for every force exerted, a precursor to Gottfried Leibniz's idea of force which underlies Newton's third law of motion.Shlomo Pines (1964), "La dynamique d’Ibn Bajja", in Mélanges Alexandre Koyré, I, 442-468 468, Paris.
(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History of Ideas 64 (4), p. 521-546 .) His theory of motion had an important influence on later physicists like Galileo Galilei.Ernest A. Moody (1951). "Galileo and Avempace: The Dynamics of the Leaning Tower Experiment (I)", Journal of the History of Ideas 12 (2), p. 163-193. Hibat Allah Abu'l-Barakat al-Baghdaadi (1080-1165) was the first to negate Aristotle's idea that a constant force produces uniform motion, as he realized that a force applied continuously produces acceleration, a fundamental law of classical mechanics and an early foreshadowing of Newton's second law of motion.{{cite encyclopedia | title = Abu'l-Barakāt al-Baghdādī , Hibat Allah | encyclopedia = [Dictionary of Scientific Biography | volume = 1 | pages = 26-28 | publisher = Charles Scribner's Sons | location = New York | date = 1970 | isbn = 0684101149 -->
(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory

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