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Quote by David Foster Wallace

“The real irony is that the view of infinity as some forbidden zone or road to insanity - which view was very old and powerful and haunted math for 2000+ years - is precisely what Cantor's own work overturned. Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting.”

Quote by David Foster Wallace

Author

David Foster Wallace
David Foster Wallace

American novelist known for his unique literary style and profound insights into modern life. His works include 'Infinite Jest' and 'The Broom of the System'. more

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“Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.”

“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.”

“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.”