Numerals and Arithmetic in the Middle Ages

2012

After Arabic into Latin in the Middle Ages: The Translators and Their Intellectual and Social Context and Magic and Divination in the Middle Ages: Two Texts and Techniques in the Islamic and Christian Worlds, this third Variorum volume from Charles Burnett's hand collects papers dealing with the period and process of adoption of the Hindu-Arabic numerals. The collection shows us the intricacies of this process, a process which was probably the 'most momentous development in the history of pre-modern mathematics' [IX.15]. Intricacies are certainly not unexpected in a process of this kind; but their precise portrayal can only be painted by someone as familiar as Burnett with the original documents, their languages, their style and context.

2012

After Arabic into Latin in the Middle Ages: The Translators and Their Intellectual and Social Context and Magic and Divination in the Middle Ages: Two Texts and Techniques in the Islamic and Christian Worlds, this third Variorum volume from Charles Burnett's hand collects papers dealing with the period and process of adoption of the Hindu-Arabic numerals. The collection shows us the intricacies of this process, a process which was probably the 'most momentous development in the history of pre-modern mathematics' [IX.15]. Intricacies are certainly not unexpected in a process of this kind; but their precise portrayal can only be painted by someone as familiar as Burnett with the original documents, their languages, their style and context.

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.

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 volume gathers together a selection of eleven papers originally published by Burnett between 1996 and 2009. The papers deal with the various numeral forms used in the Middle Ages in mathematical and other contexts and show the complexity of the process of adoption of Hindu Arabic numerals over a period that extends from the tenth century, when the first reports of these numerals reached Europe, to their final adoption in the thirteenth century. Ordered according to the chronology of the subjects, this highly cohesive and stimulating set of essays will be essential reading for scholars studying the area, either thoroughly or tangentially.

IN The Shape of Script: How and Why Writing Systems Change , Stephen Houston, ed., pp. 229-254. Santa Fe: School of American Research Press . , 2012

Die Sprache, 2000

Signs of Writing: The Cultural, Social, and Linguistic Contexts of the World’s First Writing Systems, 2014

Across multiple disciplines, written numerical notation is a topic of keen interest, yet several unresolved issues in its analysis are either elided or taken as settled. Numerical notation is a complex phenomenon with multiple independent histories—more than 100 distinct systems used over the past 5,500 years, interweaving with, rather than strictly paralleling, the histories of writing systems. Social, semiotic, and cognitive approaches are brought to bear on six incompletely answered questions about numeration in relation to the earliest writing. Is numerical notation a necessary precursor to writing? Does the earliest numerical notation initially serve a bookkeeping function for early states? What is the relationship between tallying and numerical notation? Does the use of numerical notation change human cognition about the domain of number? How does the emergence of numerical notation relate to linguistic representations of number? Finally, among all domains of knowledge, why is number so widely represented using graphic notations? Recognizing that these issues are not resolved, and identifying different possible resolutions, must be preliminary to fully integrating numerical notation within the broader history of writing.

Arts of Calculation: Numerical Thought in Early Modern Europe, ed. David Glimp and Michelle R. Warren (New York: Palgrave, 2004)