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.

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.

Computers are very powerful tools, but in the simulated world of the computer, everything has to be calculated.

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.

Science is not just for an elite few. Science's vision of the universe is becoming increasingly inaccessible. That doesn't mean it's wrong. On some levels, general relativity is right, because we have to take its calculations into account to produce accurate GPS systems. Instrumentally, it's correct to something like twenty decimal places. But epistemologically and psychologically, it is not available to most of our population.

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".