As a child it was clear to me that in some sense math was in the world around us. I became fascinated by what this means. When you look at the shape of the sun and the moon, they're circles, so every time you see a circular thing, there's pi embedded in it.

Wave particle duality is a core feature of our world. Or rather, we should say, it is a core feature of our mathematical descriptions of our world. But what is critical to note here is that, however ambiguous our images, the universe itself remains whole and is manifestly not fracturing into schizophrenic shards. It is this tantalizing wholeness and the thing itself that drives physicists onward like an eternally beckoning light that seems so teasingly near. It is always out of reach.

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.

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.

Nature rarely does anything mathematically perfect, and naturalism results from imperfections and deviations.

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

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".