What is the Poincaré Conjecture?
It is no more, actually. Now that Perelman has proved it, it’s a theorem—a classic theorem of topology, one of the most wonderfully weird mathematical disciplines. Much of topology is concerned with things that are essentially the same as other things, even if at particular moments in time they happen to look different. For example, if you have a blob that can be reshaped into a sphere, then the sphere and the blob are essentially similar, or homeomorphic, as topologists say. Poincaré asked, in essence, whether all three-dimensional blobs that are not twisted and have no holes in them are homeomorphic to a three-dimensional sphere. It took more than a hundred years to prove that yes, they are. What is the significance of this discovery? A discovery like this generally has far-reaching repercussions that are rarely evident at the moment of the breakthrough. It will almost certainly have profound consequences for our understanding of space—the universe we inhabit. How were you able to wr
