MatNat · The Mathematization of Nature: The Origin of Mathematical Physics in Plato and Early Pythagoreanism

‘The Book of Nature is written in geometrical characters’, wrote Galileo in 1623. The view that mathematics provides the language of nature has been an axiom of physics since Copernicus, Galileo and Kepler. Behind the founders of modern science stood, by their own admission, ‘our genuine masters, Plato and Pythagoras’ (Kepler 1597). But how did the early Pythagoreans and Plato conceive of and justify their mathematical world view? MatNat investigates the question of the historical origin of the mathematization of nature from the point of view of a deep conceptual puzzle: How can necessary mathematical truths concerning unchanging abstract entities explain the contingent, variable and inexact happenings evident to the senses? MatNat shows that the mathematical world view was born through answering this puzzle. As MatNat will argue, the early Pythagoreans and following them Plato showed why exactly mathematics, and mathematics alone, is the appropriate way to explain nature by demonstrating how nature itself is mathematically structured. They developed the mathematics of their day specifically to the tasks of explaining change, body and perceptibility, the basic features of nature, as the ancients understood it. This mathematical model of nature appeared already in the early Pythagoreans, particularly Philolaus and Archytas, but was fully developed by Plato in his Timaeus. To establish the claim MatNat innovates methodologically by triangulating newly established evidence for early Pythagoreanism with the reports of Plato's first students in the Early Academy and detailed readings of Plato's Timaeus. The methodology enables MatNat to offer groundbreaking interpretations of Plato's natural philosophy showing for the first time how the Timaeus, the foundational text for Western mathematical science, answered the basic conceptual question of the applicability of mathematics to nature.