As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas fr…

- William Thurston

Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for th…

- William Thurston

I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that…

- William Thurston

Mathematics is an art of human understanding.

- William Thurston

The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of …

- William Thurston

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to d…

- William Thurston

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

- William Thurston

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

- William Thurston

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing…

- William Thurston