Mathematics Quotes - Page 29

• This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

  Roger Penrose

  Relationship, Book, Physics

  "Secrets of the Old One". "Groks Science" with Frank Ling, grokscience.wordpress.com. January 18, 2009.

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• It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

  Andrew Wiles

  Work, Long, Interesting

  "Andrew Wiles on Solving Fermat". NOVA Interview, www.pbs.org. November 1, 2000.

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• We sometimes think of being good at mathematics as an innate ability. You either have "it" or you don't. But to Schoenfeld, it's not so much ability as attitude. You master mathematics if you are willing to try.

  Malcolm Gladwell

  Inspirational, Motivational, Attitude

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• We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

  Augustus De Morgan

  Believe, Eye, Science

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• [I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

  G. H. Hardy

  Inspiration, Science, Firsts

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• I cannot judge my work while I am doing it. I have to do as painters do, stand back and view it from a distance, but not too great a distance. How great? Guess.

  Blaise Pascal

  Work, Distance, Math

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• I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.

  G. H. Hardy

  Apology, Science, Needs

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• If all of mathematics disappeared, physics would be set back by exactly one week.

  Richard P. Feynman

  Would Be, Physics, Week

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• Physics is much too hard for physicists.

  David Hilbert

  Math, Physics, Physicist

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• Legal training has been quite useful in developing critical thinking. Whether one attains it in mathematics, philosophy or law, an analytic grounding can add great value in defining and confronting complex problems, or laying out a path to implement a vision.

  James M Strock

  Philosophy, Thinking, Training

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• Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".

  Bertrand Russell

  Facts, Logic, Study

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• When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong. Perhaps the adjective 'elderly' requires definition. In physics, mathematics, and astronautics it means over thirty; in the other disciplines, senile decay is sometimes postponed to the forties. There are, of course, glorious exceptions; but as every researcher just out of college knows, scientists of over fifty are good for nothing but board meetings, and should at all costs be kept out of the laboratory!

  Arthur C. Clarke

  Mean, College, Elderly

  Profiles of the Future ch. 2 (1962).

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• Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

  Alfred Renyi

  Information, Principles, Needs

  Alfréd Rényi (1984). “A diary on information theory”

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• There's a tendency for adults to label the math that they can do (such as identifying patterns, choosing between competing offers in a supermarket, and challenging statistics published by the government) as "common sense" and labeling everything they can't do as "math" - so that being bad at math becomes a self-fulfilling prophecy.

  Robert Eastaway

  Education, Math, Government

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• Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

  Richard Askey

  Education, Math, Skills

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• I recognize the lion by his paw.

  Jacob Bernoulli

  Education, Math, Lions

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• The solution "cost me study that robbed me of rest for an entire night."

  Johann Bernoulli

  Education, Math, Night

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• I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours. I found it quite enthralling.

  Agatha Christie

  Education, Father, Math

  Agatha Christie (1991). “Agatha Christie: An Autobiography”, Berkley Publishing Group

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• How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

  David van Dantzig

  Education, Attitude, Math

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• I suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain.

  Charles Darwin

  Education, Math, Two

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• Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

  Keith Devlin

  Education, Real, School

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• What makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game.

  Keith Devlin

  Education, Fashion, Math

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• The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

  Leonhard Euler

  Education, Math, Opportunity

  Opera Omnia, Series 1, Volume 2, 1913.

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• A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some "dreaming" time.

  Howard Whitley Eves

  Education, Dream, Math

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• Imagine that you wanted your children to learn the names of all their cousins, aunts and uncles. But you never actually let them meet or play with them. You just showed them pictures of them, and told them to memorize their names. Each day you'd have them recite the names, over and over again. You'd say, "OK, this is a picture of your great-aunt Beatrice. Her husband was your great-uncle Earnie. They had three children, your uncles Harpo, Zeppo, and Gummo. Harpo married your aunt Leonie ... yadda, yadda, yadda."

  Brian X. Foley

  Education, Cousin, Uncles

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