Unfortunately, some of the most beautiful mathematics is hidden from most people because it is so difficult to visualize. A good explanation has limited reach when the discussion at hand is about geometry, especially when it spans more than two dimensions. We may have an abundance of technology to help illustrate the subject, but someone still needs to spend an enormous of time and energy creating the kind of visualizations that are mathematically accurate, yet breathtaking. Fortunately, a group of French engineers, mathematicians, and education enthusiasts have done some of this hard work and produced Dimensions, an incredible nine part animated film that is nothing short of a visual feast featuring some of the most important and beautiful ancient and modern mathematics
The first chapters of the film introduce geography and the geometry of the sphere. Later chapters extend our intuition about two and three dimensions to four dimensions. The final chapters are more advanced but present a fairly elementary treatment of complex numbers and some topology. Every new idea is presented by an important mathematical personality, putting the whole narrative into a historical context. Although you can watch all nine chapters in one sitting, they are not all connected and it might be easier to watch them separately. The film website has a useful guide to help you choose what to watch, and we can’t recommend watching it enough.