Everyone knows that our world is three-dimensional. It seems indeed obvious that there are three independent spatial directions, no less, no more. But can we really be sure? After all, everything we know about our world comes from our senses and from what our brains interprete. Does the fact that we see in 3D really proves that the world is in 3D? Can we have a mathematical proof, based on experimental observations, that the world is three-dimensional? This question is totally relevant, and several scientists and philosophers, like Immanuel Kant, have been interested in it (see for example this blog post in French for a nice review).