We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric… — 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 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
