Algebra and Arabic numerals

The aim of this study is to evaluate and examine the scientific root of binary digits from the Islamic point of view and the impact of Arabic numerals to the development of mathematics and advancement of modern science and technology. The study utilizes contend analysis and secondary source of data as its methodology. The findings of the study revealed that the world now becomes a digital one and transformation to a global village was due to the remarkable achievement made from mathematics by the use of Arabic Numerals. No profound achievement was made in mathematics and generally in science and technology until the inception of Islam in seventh century. This is because Islam is in harmony with science. From its inception, Islam made knowledge and its advancement a religious obligation. Being at a middle-course, Islam synchronizes together the secular and spiritual knowledge for the benefit of this world and the hereafter. Binary numbers or digits as the building block of all digital technology are being perceived as being pure secular which have nothing in common with religion. This paper traces the scientific and mathematical origin of 0 and 1, the binary digits to Islam as well as its contribution to the development and advancement of modern science and technology. It is therefore concluded that the world as a global village does not just happen by mistake; rather it is a making of Almighty God, Allah is beyond the horizon of human philosophy and imagination.

Atti del Convegno della Società Italiana di Storia della Scienza, 2023

Within medieval and early modern mathematics, arithmetic and algebra were closely related to each other in terms of rules, methods, and problems.As a result, they were characterized by several types of interactions-or contaminations-. In this paper, I focus on one of these contaminations, related to the study of numbers. I take into account several case studies from Mediterranean medieval mathematics, belonging to two different traditions of arithmetician-algebraists. The first is the Arabic tradition of the ḥussāb (calculators), represented here by the mathematician Abū Bakr al-Karajī (d. beg. 11th c.) and his successors al-Samaw'al (d. 12 th c.) and al-Zanjānī (d. mid 13 th c.). The second is the Italian tradition of the maestri d'abaco, within which I focus on two authors-Paolo Gherardi and an anonymous author-of the 14th century. Within my investigation of the notion of number, I concentrate on integers and fractions and-only in relation to the Arabic context-on expressible and surd numbers (i.e. rational and irrational numbers). First, I clarify the polysemic nature of the term "arithmetic" and mention some aspects related to the historical context that characterized my authors. Second, I analyze the primary sources and present some further observations that build upon earlier studies dedicated to these same sources. My main goal is to show that the development of algebra contributes to the expansion of the domain of numbers, and hence to the expansion of arithmetic.

Abstract The aim of this paper is to examine, analyze and ascertain the root of the modern mathematical numeral system between the Indian-Hindu Brahmagubta, Islamo-Arabic and the Western numeral systems. The paper utilized secondary source of data. The methodology adopted by the paper is content analysis. The findings of the paper revealed that the origin of the shapes of our ten modern numerals do not concern the Indian mathematics history, as Hindus do not have full-fledged mathematical numeral system before the development of Arabic Numerals between 8th-15th Centuries. The character of Hindu-Indian numerals in whatever form and categories it belongs- Brahmagubta or anyone else, does not have any genealogical affiliations to the present modern mathematical numeral versions, as well the same thing applies to the Western mathematical systems. The paper argued that, the root/origin of the modern Arabic numeral is traced to its original and independent Arabic character versions, which transmuted from one stage to another with some state of galvanization - from Abjadi, Mashriki to Ghubari. The paper argued that apart from the non-reliability of the thesis of disparity in characters or shapes of the Arabic numerals compare to that of the Hindu-Indian Brahmagubta, there is also that of philosophical caricature fiction of genealogical linkage as well as the phonological misplacement of language or terms. The paper also argued that during the Golden-Age of Islam between 7th and 15th centuries, European arithmeticians especially in the eleventh, twelfth and part of thirteenth centuries, knew nothing about Arabic numerals; it was incredibly absent, they knew only the use of antiquated Roman numerals and Abacus in counting. In that regard, the Arabic numeral symbols (or system) were developed by Islamo-Arabic mathematicians, learned by Indians and some Europeans who cares about knowledge. In the east, the numeral system attracted the Indian mathematicians, while in Europe, the numeral system was first employed in Italy, then later France for practical purposes after the translation of the work of Al-Khwarizmi Mohammed Ibn Musa (Latin Algorithm) in 12th century into Latin by Gerard of Cremona, also known as Leonardo Fibonacci.

The essay surveys the history of the origin and spread of the Indian Numerals (1,2,3,...,9,0) through the ages , first to China and then, through the mediation of the Arabs, to other parts of Asia and Europe. The decimal system was adopted without any active promotion by any agency. It was because of the efficacy that it ultimately replaced all other number systems; no prejudice or narrow-mindedness could stand in its way.

Erdem, 1986

A close investigation o f O ld B abylonian second-degree algebra shows that its m ethod and conceptualization are not arithm etical and rhetorical, as is grosso modo the al-jabr presented b y A l-K h w â rizm î. Instead, it appears to be based on a " naive" geom etry o f areas very sim ilar to that used b y lbn T u rk and A l-K h w â rizm î in their justifications o f the algorithm s used in al-jabr to solve the basic m ixed second-degree equations. T h is raises in a new ligh t the question w hether the early Islam ic use o f geom etric justifications was a graft o f G reek methods upon a " sub-scientific" m athem atical tradition, as often m aintained, or the relation o f early Islam ic algebra to its sources must be seen differently. N ow , the Liber Mensurationum o f one A b û Bakr, knovvn from a tvvelfth-century L atin translation, refers repeatedly to tw o different methods for the solution o f second-degree algebraic problems: A basic m ethod, m ay be identified as " augm entation and dim inution" (al-jamc wa' l-tafrîq?), and another one labelled al--jabr, w hich coincides w ith al-K h w â rizm r's use o f num erical Standard algorithm s and rhetorical reduction. Since the Liber Mensurationum coincides in its phrasing and in its choice o f gram m atical forms w ith O ld B abylonian texts, and because o f p eculiar details in the term inology and the m athem atical contents o f the text, it appears * T h e follovving is a slightly revised version o f m y contribution to the In ter national Sym posium on lb n T u rk , K hvvârizm î, F ârâb î. B eyrûn î, and lb n Sîn â, A n kara, Septem ber 9-12, 1985. A n abridged version o f the article w ill be found in the Proceedings o f the Sym posium . M y sincere thanks are due to Professor A yd ın Sayılı, w ho invited me to the Sym posium , and w ho insisted to have the full article published in the present journ al. * * Jens H oyrup, Roskide U n iversity Ç enter, Copenhagen, Denm ark. * T h is and sim ilar exam ple o f its kind in the follovving pages should be read as a fraction (or, a num ber follovved b y a com m on fraction).

The Unity of Science in the Arabic Tradition, 2008

Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of 'mathematics as calculation' had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the 'equation' as known in Arabic algebra.

Historia mathematica, 2006

Algebra, defined as a method to determine the unknown by means of what is known, given the link between the two, took its initial steps toward disciplinary status during the third/ninth century when al-Khwārizmī produced the first systematic study on the subject. Later Muslim mathematicians followed his lead due to this novel discipline’s propensity for improvement and beneficial application. Thus they applied arithmetic to algebra to make it more practical and open and, as a result, derived great benefits from employing it in matters of inheritance, commerce, land surveys, architecture, and other areas. Roughly 550 years after its formation as a discipline, algebra reached its peak in the aforementioned areas. One of its most famous practitioners, Ibn al-Hā’im, had a lasting and widespread influence first with his commentary on Yāsamīnī and then with his versified work al-Muqni‘ and its commentary al-Mumti‘. However, the latter work eluded the researchers’ attention – perhaps it was overshadowed by the former or lost among the other commentaries – despite its remarkable presentation of the entire conceptual and methodical reper-toire of algebra as it was known at that time, not to mention its analysis of the problems and discussion of the philosophical implications in a long-lasting debate on Islamic mathematical history: Should algebra be arithmetical, geometrical, or both? Which track would be more conducive to improving the discipline so it could break new ground in the historical studies of mathematics? Thus, this article seeks to present the status of Ibn al-Hāim’s al-Mumti‘ fī sharh al-Muqni‘ in the history of mathematics, along with its outstanding features and mathematical analysis. Keywords: mathematics, algebra, Ibn Haim, al-Muqni, al-mumti.

2019

A Significant Step Toward the Development of Algebra: Al-Samawʾal Ibn Yaḥya Al-Maghribi, a Twelfth Century Mathematician Mustapha Nadmi Mathematics of the Islamic medieval world is still not sufficiently studied. As a result, a goldmine of Islamic medieval books and materials lie unexplored. One manuscript that certainly deserves attention is al-Bāhir fi’l-Jabr (The Shining Treatise on Algebra) of al-Samaw’al ibn Yahya al-Maghribi, a twelfth century mathematician. Al-Bāhir fi’l-Jabr is a manuscript written in Arabic and has never been translated except for a few excerpts in French. The purpose of this study was to explore the mathematical and pedagogical contribution of al-Samaw’al through an analysis of al-Samaw’al’s mathematical techniques and methods in al-Bāhir fi’l-Jabr. Moreover, the treatise provides a precise description of the “arithmetization of algebra”, and gives an accounting of the original ideas of another mathematician, al-Karaji, whose original documents have been l...