Euclid

In this course

Euclid's axiomatic system of geometry provides the foundational spatial framework against which the course measures alternative geometric and computational models of space. The readings invoke Euclidean geometry as both a historical baseline—the dominant spatial paradigm before non-Euclidean mathematics—and as a specific mathematical structure useful for formalizing possibility spaces and pattern recognition in contemporary AI systems. His influence marks the threshold between mythic, non-linear space and the rationalized, metric space that underlies much of modern computation and machine learning.

Background

Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Mentioned in 4 readings