Quotessence
Home / Quotes / Quote by William Thurston

Quote by 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 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.”

Quote by William Thurston

Create image

Author

William Thurston
William Thurston

William Thurston was a renowned mathematician known for his groundbreaking contributions to geometric topology. His research involved the classification of three-dimensional manifolds and the Poincaré conjecture, which had a profound impact on the mathematical community. more

You May Also Like

“A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.”

RealFactsAbleEnemyTreeCreaturesMathematicsMathClimbsMathematicianMonkeysUp And DownMath And ScienceGeneralizationIncessantlyMathematics And ScienceMath EducationMathematics By MathematiciansMath Is Like
Author:George Polya
Create image

“The question you raise, 'How can such a formulation lead to computations?' doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand - and it always turned out that understanding was all that mattered.”

WholeWould BeUnderstandingPossibilityRaisesMathWhole LifeBotherMathematicianElegantBotheredSuitableThoroughExplicitComputation
Author:Alexander Grothendieck
Create image

“It is hard to communicate understanding because that is something you get by living with a problem for a long time. You study it, perhaps for years, you get the feel of it and it is in your bones. You can't convey that to anyone else. Having studied the problem for five years you may be able to present it in such a way that it would take somebody else less time to get to that point than it took you. But if they haven't struggled with the problem and seen all the pitfalls, then they haven't really understood it.”

IfsWayFeelsYearsMayLongHardProblemAbleUnderstandingStudyFiveHavensLong TimeUnderstoodCommunicateBonesMathFive YearsPitfalls
Author:Michael Atiyah
Create image

“This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.”

FeelsIdeasFactsMotivationCommonTheoryPerceptionUnderstoodObviousMathDuesMathematicalUnfortunateAdequatePresentationReluctantBinary
Author:Mikhail Leonidovich Gromov
Create image