William Thurston Quotes

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

  William Thurston

  Science, Numbers, Understanding

  54 Copiar cita

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

  William Thurston

  Real, Math, Satisfaction

  41 Copiar cita

• 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

  35 Copiar cita

• Mathematics is an art of human understanding.

  William Thurston

  Art, Understanding, Mathematics

  20 Copiar cita

• 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

  Ver

  23 Copiar cita

• El producto de las matemáticas es la claridad y la comprensión. No los teoremas, por sí mismos. ... En resumen, las matemáticas sólo existen en una comunidad viva de matemáticos que difunde la comprensión y da vida a ideas tanto antiguas como nuevas.

  William Thurston

  Math, Ideas, Community

  30 Copiar cita

• 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 Copiar cita

• 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 Copiar cita

• 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 Copiar cita

• 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 Copiar cita

• Creo que las matemáticas son un vasto territorio. Las afueras de las matemáticas son las afueras de la civilización matemática. Hay ciertos temas sobre los que la gente aprende y se reúne. Luego hay una especie de desarrollo inevitable en esos campos. Se llega a un punto en el que un determinado teorema está destinado a ser demostrado, independientemente de cualquier individuo en particular, porque está justo en el camino del desarrollo.

  William Thurston

  Independent, Thinking, Civilization

  9 Copiar cita

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

  William Thurston

  Science, Computer, Mathematics

  4 Copiar cita

También te puede gustar:

Mijail Leonidovich Gromov

Grigori Perelman

Lipman Bers

Henri Poincare

Terence Tao

David Hilbert

Albert Einstein

Leonhard Euler