When you're in a room with twenty people who've all got the True Theory of the universe, it's difficult to know what to do. And the paradox is that so much important science is now being done by huge teams. With Higgs boson, for example, it's estimated there were around ten thousand scientists and engineers involved in building the machines that made this discovery possible.

One of the great sources of employment for people with Ph.D.s in geometry is the animation industry.

All gradients of reality, all existential distinctions, have finally been annihilated.

I don't know of any science writing going on in women's magazines, unless you count medical stories about things like breast cancer. I still think there's a huge problem about how we can actively engage a wider range of women. I'm not saying women must be a separate audience - I'm just responding to the reality that the majority of people who do read science magazines are male. That's not a value judgment; it's a statistical fact.

Almost all major scientific projects today are huge collaborations, yet we still have this public obsession with the idea of the individual scientific genius. One of my goals as a science communicator is to celebrate the collaborative dimensions of science, which I think will be critical for facing the ecological and resource challenges ahead. In a sense, we are all corals now.

Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male.

One way to think about a pure hyperbolic surface is that it's the geometric opposite of a sphere. If you look at a sphere, the curvature is the same everywhere, as opposed to, say, an egg, which clearly does not curve the same everywhere. This is what makes spheres geometrically important. Mathematically speaking, a sphere has positive curvature and a hyperbolic surface has negative curvature, but both have constant curvature everywhere.