Explore the emergence of higher dimensions in geometry during the 19th century in this 33-minute lecture from the Sociology and Pure Mathematics series. Delve into the key developments that led mathematicians to understand and study higher dimensions, examining where these concepts originated. Discover various aspects of higher-dimensional geometry, including projective geometry, cyclography, spaces of lines and conics. Learn about the projective line, projective space, the space of circles in 2D (cyclography), the space of lines in 3D (Plucker), and the space of planar curves. Gain insights into this pivotal period in the history of mathematics and its impact on our understanding of geometric concepts beyond three dimensions.