How does the physical world in which we live shape the abstract world in which we think? I address this question by exploring the origin and development of uniquely human geometric understanding. My lab uses cognitive, developmental, and computational approaches to gain insight from the full range of human encounters with geometry, from the basic spatial sensitivities of infants to the untutored use of spatial symbols and language by children to the high-level spatial concepts of adults. I broaden and deepen this exploration to ask how mathematical formalisms might have been ignited in the first geometers like Euclid and how they might be reignited in the minds of our children, those future mathematicians we send to school every day. In addition, I ask how our basic mechanisms of perception and cognition about spaces, objects, agents, and social partners might even shape our cultural production of pictorial art. Elucidating the geometry and communicative intent in children’s drawings may help reveal the role human cognition plays in the production of art.