- Do you think for teaching and in general, thinking about new concepts, do you think it's better to plug in the numbers or to think more abstractly? So looking at theorems and proving the theorems or actually building up a basic intuition of the theorem or the method, the approach, and then just plugging in numbers and seeing it work?

- Yeah, well, certainly many of us like to see examples. First, we understand, it might be a pretty abstract sounding example like a three-dimensional rotation. How are you gonna understand a rotation in 3D? Or in 10D? And then some of us like to keep going with it to the point where you got numbers, where you got 10 angles, 10 axes, 10 angles.

But the best, the great mathematicians probably, I don't know if they do that 'cause they, for them, an example would be a highly abstract thing to the rest of us. - Right, but nevertheless, working in the space of examples. - Yeah, examples. - It seems to-- - Examples of structure.

- Our brains seem to connect with that. - Yeah, yeah. (upbeat music) (upbeat music) (upbeat music) (upbeat music) (upbeat music) (upbeat music)