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.
Margaret WertheimOne of the great sources of employment for people with Ph.D.s in geometry is the animation industry.
Margaret WertheimScience 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.
Margaret WertheimWave 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.
Margaret WertheimOne 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.
Margaret Wertheim