Explore the complex history and development of non-Euclidean geometry in this 51-minute lecture. Delve into the contributions of Gauss, Lobachevsky, and Bolyai, and examine the long-standing study of Euclid's parallel postulate. Discover how spherical geometry, known to astronomers for millennia, played a crucial role in this field. Learn about a novel interpretation of non-Euclidean geometry involving three-dimensional linear algebra and projective techniques, which anticipated Einstein's work on relativity. Gain insights into the connections between ancient mathematical knowledge and modern geometric concepts, challenging conventional narratives and offering a fresh perspective on this fundamental area of mathematics.