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

Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.

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.

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.

I have an abiding interest in how ordinary people produce knowledge, and what it means for individuals to know the world. I thought I'd be a theoretical physicist because I love physicists' views of the world - I find general relativity and quantum theory thrilling - but I have always felt uneasy with the idea of an Ultimate Truth. One of the functions of science is to help us instrumentally; it helps us to build things like microchips and GPS satellites. But another function of science in the modern world is to help us feel "at home in the universe".

When I was a physics major in the late 1970s, my very few fellow female students and I had high hopes that women would soon stand equal with men in science. But progress has proved slower than many of us imagined.