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The paradoxes and the infinite dazzled ancient mathematics and continue to do so today (2401.02806v1)

Published 5 Jan 2024 in math.HO and cs.LO

Abstract: This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were handled arithmetically and the continuous magnitude quantities which were handled geometrically. We look at how approximations and mixed numbers (whole numbers with fractions) helped develop the arithmetization of geometry and the development of mathematical analysis and real numbers.

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References (7)
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  2. Heath. The 13 Books of Euclid’s Elements. Dover, 1956.
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  7. Roshdi Rashed. Entre arithmétique et algèbre: Recherches sur l’histoire des mathématiques arabes. Ouvrage publié avec le concours de l’Unesco. Société d’édition ”Les Belles Lettres”. Paris, 1984.

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