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Could today’s technology exist without the invention of number systems, zero, decimals, algebra, trigonometry, algorithms, etc.? Many historians credit Arab scholars, for these ideas, but Arab records themselves reveal that they learnt these concepts from the Hindus of India.
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As far back as 772 CE, a great Indian astronomer visited the Baghdad court of Caliph al-Mansur. He shared astronomy & math formulas from the Brahma-Sphuta-Siddhanta of Brahmagupta(~628 CE). Famous astronomer Al-Fazari translated it - in a book called “Al-Sindhind al-Kabir”
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Concepts from Brâhma-Sphuta-Siddhânta of Brahmagupta & Sûrya-Siddhânta, were translated from Persian into Arabic in a book called Al-Sindhind al-Kabir” referring to Al-Kabîr (great) & "sindhind" as “centuries of centuries”. The astronomical tables were called "zij as- Shah"
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Brahmagupta's Brahma-Sphuta-Siddhanta elaborated on astronomy & the initial origins of Pati-ganita (algorithms), Bija-ganita (algebra) - operations, using zero, negative numbers, indeterminate equations, “Pythagorean” triples & interpolation formulas for computing sines.
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One of the Arab world’s most famous mathematicians from the “House of Wisdom” at Baghdad, Al-Khwārizmī (780-850 CE) edited 2 versions of the zij as-Sindhind (astronomical tables) from these translations of Hindu works - which formed the basis of his mathematical knowledge.
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Al-Khwārizmī is so famous that the Latin versions of his name & book are considered to be the origin of the terms "algorithm" & "algebra". Al-Khwarizmî’s most famous book is on the topic of arithmetic formulas, most of which he explicitly borrowed from India.
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The original Arabic version of his book was lost, but a Latin translation (8th c. )“Algoritmi de numero Indorum” ( Al-Khwārizmī on the Hindu Art of Reckoning) clearly shows that even the title of his book attributed the Hindus with numerals & arithmetical calculations.
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Al-Khwārizmī's work was critical as it first transmitted crucial mathematical concepts such as Hindu numerals, zero as a placeholder, decimal numeration & place value system developed by the Hindus to the Western world, becoming the foundation of all modern mathematics today.
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Al-Khwārizmī was an advocate of the Hindu place value system based on 1,2,3,4,5,6,7,8,9 and 0 & how it simplified mathematics. In his treatise on Hindu numerals, his phrase “Dixit Algorizmi” (meaning simply "Al-Khwarizmî has said") became the word “algorithm” used today.
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Khwarzimi's specific mention of the “sign rule”for multiplying algebraic quantities can be traced to the Kuttaka-ganita of Brahmagupta (7th c. CE) whose method of solving indeterminate quadratic equations, including Pell's equation & chakravala method -a cyclic algorithm.
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Another famous Arab mathematician who based his works on Hindu mathematics was Al-Karajî (953-1029 CE). He is famous for his work on algebra & polynomials. Among historians, his most widely studied work is his algebra book "al-fakhri fi al-jabr wa al-muqabala".
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Al Karaji is said to have introduced the theory of algebraic calculus, given the first formulation of the binomial coefficients & discovered the binomial theorem. But Al-Karaji’s works clearly reveal that he too based most of his knowledge on the ideas of Hindu mathematicians.
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In his book, Al-Karajî focuses on addition, subtraction & extraction of square roots of irrational numerical polynomials. He gives an example of the extraction of the square root of the sum of a number of irrational roots without mentioning its Hindu origin.
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This polynomial is already found in Kuttaka-Ganita by Brahmagupta (6th. c). The same polynomial is also found in Bhâskara II's (1114- 1185 CE), Bijaganita. Yet historians credited Al-Karajî with the invention when it was obvious both were only extending Brahmagupta's idea.
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Al-Karajî’s method of extraction of square root of an algebraic polynomial is attributed to Hindus by Al-Karajî himself. He informs us that he followed the method used in “Indian reckoning” (hisâb al-Hind) to extract square roots of “known quantities”, of numerical polynomials
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Al-Karajî’s student, Al-Samaw’al (1130-1180 CE) is credited with extending arithmetic operations to handle polynomials & using induction. In his book Al-Bâhir (The Dazzling), he too clearly attributes the method of division of two algebraic polynomials to the Hindus of India.
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Al-Samawal was 13, when he began serious study, starting with the Hindu methods of calculation and study of astronomical tables. In his book, he elaborates a general method for extraction of square roots which applies to both polynomial term addition & subtraction.
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He attributed this discovery to himself, but at the end of the chapter he gives the “sign rule”, in the most complete form found in the mathematics of Islam. As mentioned earlier, this complete “sign rule” already appears in the Kuttaka-ganita of Brahmagupta (7th c. CE).
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Al-Samawal also mentions rules for multiplying & dividing algebraic quantities. These rules were described more completely by Bhâskara II. Both mathematicians lived during the same era, but Bhāskara II was extending the established tradition of Hindu mathematics before him.
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Historical records by Arab mathematicians reveal they acquired & attributed much of their mathematical knowledge to Indian masters. Hindus invented the foundations of modern mathematics but the Arabs deserve credit for translating these ideas & disseminating them to Europe.
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Beginning with the Vedas which expressed infinity, nothingness & huge numbers as combinations of powers of 10, to the algorithms which allow you to read this tweet & run the world today, none of it would be possible without the Hindu genius for mathematics.
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Hindus must claim their mathematical heritage & correct such myths, but it's even more important to preserve, study, analyze & extend the knowledge of our ancient masters. Many of their brilliant insights still lie undeciphered, which may help humanity scale greater heights.
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Sources:
“India’s contribution to Arab Mathematics” by Khalil Jaouiche, Indian Journal of History of Science, 46.2 (2011)
A History of Mathematics by Carl Boyer
Muhammad
Ibn Musa al-Khwarizmi, Le calcul indien, by A. Allard
Britannica.com
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