Mathematics Quotes - Page 39

• Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work.

  Paul Lockhart

  Teacher, Math, Ideas

  "A Mathematician's Lament". Book by Paul Lockhart, www.huffingtonpost.com. 2009.

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• The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous.

  Herbert Wilf

  Math, Tuning, Function

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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.

  Gian-Carlo Rota

  Cutting, Math, Ideas

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• 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

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• All problems in mathematics are psychological.

  Pierre Deligne

  Math, Problem, Psychological

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• To ask the right question is harder than to answer it.

  Georg Cantor

  Math, Answers, Harder

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• Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

  W. W. Sawyer

  Math, People, Would Be

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• The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.

  Carl Gustav Hempel

  Math, Information, Matter

  Carl Gustav Hempel (2001). “The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality”, p.13, Oxford University Press on Demand

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• Apart from two periods of intense study, of music between the ages of 12 and 14 and of mathematics between the ages of 14 and 16, I coasted, daydreaming, through most of my school years.

  James Black

  School, Math, Years

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• To sum up: I am the man who when the concern pressed him and his way was straitened and he could find no other device by which to teach a demonstrable truth other than by giving satisfaction to a single virtuous man while displeasing ten thousand ignoramuses - I am he who prefers to address that single man by himself, and I do not heed the blame of those many creatures.

  Maimonides

  Education, Science, Men

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• The only time a question should be asked is when all other possibilities of finding the answer for yourself have been eliminated.

  Benjamin Franklin

  Education, Answers, Possibility

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• I write rhymes with addition and algebra, mental geometry.

  Ice T

  Education, Writing, Algebra

  Song: Mind Over Matter, Album: O.G. Original Gangster

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• There is a famous formula, perhaps the most compact and famous of all formulas - developed by Euler from a discovery of de Moivre: e^(i pi) + 1 = 0... It appeals equally to the mystic, the scientist, the philosopher, the mathematician.

  Edward Kasner

  Education, Discovery, Philosopher

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• I never got a pass mark in math ... Just imagine - mathematicians now use my prints to illustrate their books.

  M. C. Escher

  Education, Book, Math

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• Getting the degree meant more to me than an NCAA title, being named All-American or winning an Olympic gold medal.

  Patrick Ewing

  Education, Winning, Ncaa

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• Education is worth little if it teaches only how to make a living rather than how to make a life.

  Mary Hatwood Futrell

  Education, Littles, Teach

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• New facts often trigger new ideas

  T.L. Osborn

  Education, Ideas, Facts

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• If you go fishing you may not catch any fish. If you don't go fishing, you'll never catch any fish.

  Alex Faickney Osborn

  Education, Fishing, May

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• We think it's about little techniques and tricks, but techniques only take you so far. We need teachers who care about kids, who care about what they teach, and who can communicate with kids.

  Parker J. Palmer

  Education, Teacher, Kids

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• Science and art sometimes can touch one another, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the boderline between the two respective domains.

  M. C. Escher

  Education, Art, Jigsaw Puzzles

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• The pursuit of learning is not a piece of content that can be taught. It is a value that teachers model. Only teachers who are avid, internally motivated learners can truly teach their students the joy of learning.

  Martin Haberman

  Education, Teacher, Avid

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• Mathematics is about making up rules and seeing what happens.

  Vi Hart

  Math, Happens, Seeing

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• Those who condemn the supreme certainty of mathematics feed on confusion, and can never silence the contradictions of the sophistical sciences which lead to eternal quackery.

  Leonardo da Vinci

  Inspirational, Life, Confusion

  Leonardo (da Vinci), Irma A. Richter, Thereza Wells (2008). “Notebooks”, p.9, Oxford University Press

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• Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.

  Leonardo da Vinci

  Art, Nature, Travel

  Leonardo da Vinci (2008). “Notebooks”, p.105, OUP Oxford

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• Detest it [a certain difficult mathematics problem] just as much as lewd intercourse; it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.

  Farkas Bolyai

  Math, Leisure, Problem

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