It turns out that hyperbolic structures are very common in nature, and the place where lots of people encounter them is coral reefs. Sea slugs, and a lot of other organisms with frilly forms, are biological manifestations of hyperbolic geometry, which is also found in the structure of lettuce leaves and kales, and some species of cactus.

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

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.

This is what I call the "cosmological problem" of science. Science has the instrumental function that has given us computers and so on, but its cosmological function is to give us a picture of the world we inhabit as human beings, and on that level it's failing a vast number of people.

For ten years, I wrote regular columns about science for women's magazines, and to my knowledge I'm the only person in the world who can say that. This has no kudos in either the science-writing world or the academic world, but it's one of the most challenging things I've ever done. It's much harder to write about cosmology for a magazine like Vogue than for the New York Times, which I've also written for, because you have to imagine that on the page opposite there'll be an advertisement for eyeliner, or an article about the latest trends in skirt length.

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.

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.