Shing-Tung Yau:

We physicists always try to bridge two important discoveries in physics together. One is general relativity, and the other is quantum mechanics. There were many efforts to discover such a unification field, [but none was successful] until string theory came along. So far that’s the only consistent theory. In order to make quantum mechanics consistent with general relativity, there is no other choice but to make space-time be 10-dimensional. On the other hand, we do have to try to understand the space-time that we perceive. So we make six dimensions very, very tiny.

We still see the four-dimensional space-time that we experience in general physics, special relativity and all that. This six-dimensional space is what we call “internal space.” There are a lot of models for this, but the most effective and useful model is Calabi-Yau space, where We can do all the calculations. And in fact, if we can choose the right Calabi-Yau space, we should be able to calculate the properties of the particles in the universe. But the trouble is, right now, we have many candidates for these calculations. One day, if we have the fundamental physics that can lead us to know how to calculate such geometry, and if we pick the right geometry, we will be able to calculate the masses of all the particles in the universe.

In any case, a great number of important discoveries have been made, in terms of philosophical principles as well as mathematics. So as a mathematician I’m very excited about this.