1,721,042 research outputs found
Surmounting obstacles: circulation and adoption of algebraic symbolism
Full text linkThis introductory paper provides an overview of four contributions on the epistemological functions of mathematical symbolism as it emerged in Arabic and European treatises on algebra. The evolution towards symbolic algebra was a long and difficult process in which many obstacles had to be overcome. Three of these obstacles, related to the circulation and adoption of symbolism, are highlighted in this special volume: 1) the transition of material practices of algebraic calculation to discursive practices and text production, 2) the transition from manuscript production to printed works involving material limitations of typefaces, and 3) the transition of algebraic symbolism from a system of notation and representation to a tool of mathematical analysis. This paper will conclude with the observation that the whole development towards symbolization can be considered an obstacle by itself in the sense of ‘epistemic obstacles’ as used by Broussea
Bibliographie d'Henri Bosmans
Full text linkHeeffer Albrecht, Hermans Michel, Stoffel Jean-François. Bibliographie d'Henri Bosmans. In: Bulletin de la Classe des sciences, tome 21, 2010. Le Père Henri Bosmans SJ (1852-1928) historien des mathématiques. pp. 253-298
Hesitating progress : the slow development toward algebraic symbolization in abbacus- and related manuscripts, c. 1300 to c. 1550
Full text linkFrom the early fourteenth century onward, some Italian Abbacus manuscripts begin to use particular abbreviations for algebraic operations and objects and, to be distinguished from that, examples of symbolic operation. The algebraic abbreviations and symbolic operations we find in German Rechenmeister writings can also be seen to have antecedents in Italian manuscripts. This might suggest a continuous trend or perhaps even an inherent logic in the process. Without negating the possibility of such a trend or logic, the paper will show that it becomes invisible in a close-up picture, and that it was thus not understood – nor intended – by the participants in the process
Dutch algebra and arithmetic in Japan before the Meiji restoration
No full textThis paper gives an overview of the scarce occasions in which Japan came into contact with Western arithmetic and algebra before the Meiji restoration of 1868. After the refutation of persistent claims on the influence through Japanese students at Leiden during the seventeenth century, it concentrates on the reception of Dutch works during the last decades of the Tokugawa shogunate and the motivations to study and translate these books. While some studies based on Japanese sources have already been published on this period (Sakaki [1994a, 2002]) , this paper draws from Dutch sources and in particular on witness accounts from Dutch officers at the Nagasaki naval school, responsible for the instruction of mathematics to selected samurai and rangakusha. Two Japanese textbooks on arithmetic from that period are viewed within the context of this naval training school
Incommensurability in Mathematics: Methodological Considerations for the History of Algebra
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Regiomontanus and Chinese mathematics
Full text linkThis paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem (CRT) through the Shù shū Jiǔ zhāng (SSJZ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ. CRT problems appear in earlier European arithmetic and can be solved by the method of the Sun Zi, as did Fibonacci. Secondly, we pro-vide evidence that remainder problems were treated within the European abbaco tradition independently of the CRT method. Finally, we discuss the role of recre-ational mathematics for the oral dissemination of sub-scientific knowledge
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