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Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham (965 in Basra – c. 1040 in Cairo) was a prominent scientist and polymath from the ‘Golden Age’ of Muslim civilization. He is commonly referred to as Ibn al-Haytham, and sometimes as al-Basri, after his birthplace in the city of Basra. He is also known by his Latinized name of Alhzen or Alhacen.

 

Ibn al-Haytham made significant contributions to the principles of optics, as well as to physics, astronomy, mathematics, ophthalmology, philosophy, visual perception, and to the scientific method. He was also nicknamed Ptolemaeus Secundus ("Ptolemy the Second") or simply "The Physicist" in medieval Europe. Ibn al-Haytham wrote insightful commentaries on works by Aristotle, Ptolemy, and the Greek mathematician Euclid.

 

Ibn al-Haytham used experimental evidence to check his theories, which was unusual for his time because physics before him was more like philosophy, without experiment. He was the first to introduce experimental evidence as a requirement for accepting a theory, and his Book of Optics was actually a critique of Ptolemy’s book Almagest. A thousand years on, this optics book is still quoted by professors training research students to be factual and not be swayed by opinions or prejudice. Some science historians believe that Snell’s Law, in optics, actually resides in the work of Ibn Sahl and Ibn al-Haytham.

Neuroscientist Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method." From this point of view, Ibn Al-Haytham developed rigorous experimental methods of controlled scientific testing to verify theoretical hypotheses and substantiate inductive conjectures. Other historians of science place his experiments in the tradition of Ptolemy and see in such interpretations a "tendency to 'modernize' Alhazen ... [which] serves to wrench him slightly out of proper historical focus."

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics ('ilm tabi'i) with mathematics (ta'alim; geometry in particular) in terms of devising the rudiments of what may be designated as a hypothetico-deductive procedure in scientific research. This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the refraction of light). His legacy was further advanced through the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).

The concept of Occam's razor is also present in the Book of Optics. For example, after demonstrating that light is generated by luminous objects and emitted or reflected into the eyes, he states that therefore "the extramission of [visual] rays is superfluous and useless."

 

 Abū ʿAbdallāh Muammad ibn Mūsā al-Khwārizmī, (c. 780 – c. 850) was a Persian mathematicianastronomer and geographer, a scholar in the House of Wisdom in Baghdad. In the twelfth century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources. He revised Ptolemy's Geography and wrote on astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations

Al-Khwārizmī's contributions to mathematicsgeographyastronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala).

He also wrote on mechanical devices like the astrolabe and sundial.

He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.

 When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

 When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

 Abd al-Rahman Ibn Khaldun was born in Tunis North Africa in 1332 CE. His ancestors were Yemeni Arabs who settled in Spain in the eighth century. After the fall of Seville his family emigrated to Tunis. Ibn Khaldun memorized the Qur`an by heart at an early age, studied grammar, jurisprudence, hadis,  philology, and poetry in Tunis.  He continued his studies until the age of nineteen, when he lost both his father and mother to the plague. 

Ibn Khaldun entered the service of the Tunisian ruler Ibn Tafrakin as a writer of fine calligraphy while he was still a teenager.  Here he got a first-hand look at the inner workings of court politics. In 1352 CE Abu Ziad, the Emir of Constantine attacked and conquered Tunis. Ibn Khaldun escaped to Fez, the capital of Morocco.

Ibn Khaldun is considered the forerunner of several social science disciplines, like historiography, demography, sociology, cultural history and modern economics. He is also considered the father of the science of sociology. Ibn Khaldun’s main work was initially conceived as a universal history.  He divided it into seven books in which  the first book, commonly known as the Muqaddema, was transformed into a unique work of its own. This book is considered a masterpiece of literature on the philosophy of history and sociology. Books two to five dealt with the history of mankind up to the time of Ibn Khaldun, including the history of the Arabs, contemporary Muslim and European rulers, the ancient history of Arabs, Jews, Greeks, Romans, Persians, Egyptians, and Islamic history. The sixth book covers the history of Berbers and the Maghreb, and the last volume covers the events of his own life, known  as Al-Tasrif. 

No doubt Ibn Khaldun was one of the most versatile universal thinkers and philosopher of the Islamic civilizations. His work has been translated into many languages both east and west, and have inspired following writers in the development of new disciplines.   The British historian Arnold Toynbee called the Muqaddema the greatest work of its kind that has never been created by any mind in any time or place–the most comprehensive and illuminating analysis of how human affairs works.

Ibn Khaldun’s remained a nonentity among Muslim thinkers till the west discovered him in the 19th century as one of the great mind of the Middle Ages