The Poincaré Conjecture

What is the shape of our universe?

Let’s start off easy. We know the shape of the earth. It is more or less spherical. Next, our galaxy, the Milky Way. Somewhat surprisingly to Edwin Hubble who discovered it, it is barred spiral shaped, i.e. the shape of a disk with spiral arms. What about the observable universe? Is it spherical? It certainly seems to be, as it is expanding outwards and light is more redshifted the further we look. What about the global universe, beyond the horizon of what is observable to us?

The answer is, we do not know. We can conjecture. It may be finite or infinite, with or without boundary, with or without curvature, simply connected like a sphere, or multiply connected like a donut. What we do know, is that it seems to be expanding. Into what? We do not know. But we can conjecture. Continue reading