What is the relationship between language and thought? Traditional approaches to this question have staked out extreme positions: either that language determines the shape of the thoughts you can entertain, or else that natural language is only an overlay on top of a more basic "language of thought." My work in the domain of numerical cognition supports a middle view: that language is a tool that can help with complex cognitive tasks, and that the structure of linguistic representations matters immensely to how they are used. In this talk, I'll describe cross-linguistic and cross-cultural evidence from Brazil, India, and Papua New Guinea, showing some of the incredible variation in number representations across the world and how these representations affect the numerical cognition of their users.