One of the things we've learned is that in the universe there's obviously stars and galaxies, which are made up of atoms, which as far as we know are just like the atoms we can study in lab. But there is also some stuff out there which is very important because it exerts a strong gravitational force, which is a kind of particle, which we don't know about and haven't yet discovered here on Earth.
So the nature of the so-called dark matter is a big issue for physics and for astronomy at the moment, but there is also another other deeper mystery, which is related to the nature of space itself. There's evidence, which has come about in the last ten years or so that even empty space, when you take away all the dark matter and all the atoms, still exerts a kind of force. It exerts a sort of push or tension on everything.
And this therefore means that even empty space has a kind of structure, and we don't understand that at all. In fact, most of us would guess that empty space does have a structure but on a tiny, tiny scale, a scale a billion, billion times smaller than an atomic nucleus.
And we would have to understand space on that tiny scale to understand its structure. One of the fascinating ideas is that if you could chop up space on a very tiny scale, you would find that what we think of as just a little point in space is actually a tightly wrapped origami of extra dimensions.
We're used to the idea of three dimensions of space, backwards and forwards, left and right, up and down. But if you look at space on a tiny scale, you would find evidence for extra dimensions.
See also: "Martin Rees asks: Is this our final century?" Ted Talks, July 2005