Explore the mathematics of connection in this 22-minute conference talk by John Baez from the University of California, Riverside. Delve into the world of category theory and its applications to open systems, presented at IPAM's Mathematics of Collective Intelligence Workshop. Discover how this mathematical language can describe the interface between open systems and their environments, the composition of open systems, and the relationship between composite system behavior and its parts. Learn about the paradigm shift from modeling single self-contained systems to open systems interacting with unmodeled environments. Examine real-world examples, including chemical reaction networks, algebraic Julia, and compositional epidemiological modeling. Gain insights into the challenges and progress in applying category theory to open systems, and understand why intelligence is fundamentally collective.