Diophantus, al-Karaji, Stevin: some aspects of the tradition of algebraic problems

Friday the 21st, LAMOP salle Perroy, Sorbonne. 14-18h. Organisation: Stéphane Lamassé and Alain Bernard. Participants: Jean Christianidis, Jeffrey Oaks, Giovanna Cifoletti, Jean-Marie Coquard

This workshop is devoted to the examination of two chapters of the future publication that will conclude the “series of problems” project.

The first one, by J. Oaks and J. Christianidis, draws on previous sessions (2017, 2018) and will bear on the technique known in Arabic as «al-istiqrāʾ», which has also recently been dubbed the «plasso-method». The early eleventh-century mathematician al-Karajī classified polynomials for his explanations of the step of al-istiqrāʾ in his book al-Badīʿ. Christianidis and Oaks will investigate possible relationships between the seriality in al-Karajī’s classification and the seriality of its application in the surviving Greek and Arabic books of Diophantus’s Arithmetica.

The second one, proposed by Jean-Marie Coquard, amplifies his contribution to the 2015 online publication (2015). The objective was then to show how Stevin’s Dialectike and its method, following a linguistical and philosophical tradition, is used in his L’Arithmetique (1585). With a series of problems, Stevin strengthened and renewed arithmetical texts which go progressively from integers to algebraical numbers. We can go further demonstrating this series of problems supports mathematical developments, on the definition of numbers and on the importance of operations, allowing a movement towards symbolic algebra. We can particularly articulate the series of problems and Diophantus’ Arithmetica with the role played by geometrical series in the writing of a new “arithmetica integra”.

The workshop will give us an opportunity to discuss the format of the contributions and the way by which access could be given to original translations of the texts discussed.


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