The Mathematics of Harmony. Proclus’ Hypothesis and New View on Euclid’s Elements and History of Mathematics Starting since Euclid

摘要

We are discussing one of the most unlikely hypotheses in the history of mathematics—Proclus’ hypothesis, which overturns a traditional view on Euclid’s Elements and the history of mathematics, starting since Euclid. According to Proclus, the main goal of Euclid, when writing the Elements, was to build a complete geometric theory of Platonic solids (Book XIII), associated in the ancient philosophy (Pythagoras, Plato) with the Universe harmony. To construct this theory, Euclid introduced in Book II the problem of dividing a segment into extreme and mean ratio (the “golden section”). It follows from Proclus’ hypothesis that Euclid’s Elements are the first attempt to create the “Mathematical Theory of the Universe Harmony”, based on Platonic solids and the “golden section”.