Geometry, Robots, and Society
Abstract:
How do we move a robot quickly from one position to another? To answer this question, we need to understand its “space of possibilities”, a “map” where we can find every possible position of the robot. Unfortunately, these spaces are very large, they live in very high-dimensions, and they are very difficult to visualize. Fortunately, mathematicians have encountered and studied these kinds of spaces before. Thanks to the tools they’ve developed, we can build “remote controls” to navigate these complicated spaces; this allows us to move (some) robots optimally.

As the imaginary border between “pure” and “applied” mathematics disappears before our eyes, we face an important ethical questions that we cannot ignore: What’s the role of mathematicians and scientists in building a more just and equitable society?