Semantic Reading in the Context of the History of Mathematics

Abstract

This article is adjacent to our two previous works on semantic reading (see the references), but may be read independently of them. It has three plots: from geometrical algebra to the solving the cubic equations; from ancient theory of ratios to modern theory of real numbers; from one problem in "Arithmetic" by Diophantus to modern problems of mathematics and mathematics teaching. Since all three plots originate in ancient Greece, before the main content of our article we give historical background on the part of the mathematics of ancient Greece that we need.