William Thurston Quotes

• Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

  William Thurston

  Science, Numbers, Understanding

  53 Copy quote

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

  William Thurston

  Real, Math, Satisfaction

  41 Copy quote

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

  William Thurston

  Math, Thinking, People

  34 Copy quote

• The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.

  William Thurston

  Math, Ideas, Community

  30 Copy quote

• 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

  Seeing

  23 Copy quote

• Mathematics is an art of human understanding.

  William Thurston

  Art, Understanding, Mathematics

  20 Copy quote

• 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 and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.

  William Thurston

  Math, Thinking, Skills

  22 Copy quote

• 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.

  William Thurston

  Teaching, Math, Ideas

  William P. Thurston (2014). “Three-Dimensional Geometry and Topology, Volume 1”, p.9, Princeton University Press

  20 Copy quote

• 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

  Real, Understanding, Way

  8 Copy quote

• 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 do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.

  William Thurston

  Math, Thinking, Errors

  12 Copy quote

• 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.

  William Thurston

  Independent, Thinking, Civilization

  9 Copy quote

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

  William Thurston

  Science, Computer, Mathematics

  4 Copy quote

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