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. — William Thurston Copy Share Image
The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians… — William Thurston Copy Share Image
As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from… — William Thurston Copy Share Image
Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide. — William Thurston Copy Share Image
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 Copy Share Image
Mathematics is much less formally complete and precise than computer programs. — William Thurston Copy Share Image
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. — William Thurston Copy Share Image
Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of… — William Thurston Copy Share Image
The real satisfaction from mathematics is in learning from others and sharing with others. — William Thurston Copy Share Image
I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn… — William Thurston Copy Share Image
Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated… — William Thurston Copy Share Image
