You don't see what you're seeing until you see it but when you do see it, it lets you see many other things.

Mathematics is much less formally complete and precise than computer programs.

Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide.

The real satisfaction from mathematics is in learning from others and sharing with others.

Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of the real world, often in ways no one could have envisioned before the theory was developed.

I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.