Mathematical Problems Quotes

• The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

  Morris Kline

  Teaching, Math, Challenges

  Morris Kline (1964). “Mathematics in Western Culture”, p.470, Oxford University Press

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• One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

  George Polya

  Teacher, Science, Opportunity

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

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• A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

  David Hilbert

  Successful, Order, Effort

  "Mathematical Problems". Lecture delivered before the International Congress of Mathematicians at Paris, translated by Maby Winton Newson, mathcs.clarku.edu. 1900.

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• Each problem that I solved became a rule, which served afterwards to solve other problems.

  Rene Descartes

  Success, Witty, Humorous

  "Discourse on the Method". Book by Rene Descartes (Part 2), 1637.

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• Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

  George Polya

  Teacher, Book, Hard Work

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• One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed.

  Leon Henkin

  Teacher, Math, Answers

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• One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

  Leon Henkin

  Teacher, Book, Math

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• It's not that I'm so smart, it's just that I stay with problems longer.

  Albert Einstein

  Inspirational, Motivational, Leadership

  Albert Einstein (2015). “Bite-Size Einstein: Quotations on Just About Everything from the Greatest Mind of the Twentieth Century”, p.19, St. Martin's Press

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• If you think it's simple, then you have misunderstood the problem.

  Bjarne Stroustrup

  Simple, Thinking, Misunderstood

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• All the mathematical sciences are founded on relations between physical laws and laws of numbers.

  James Clerk Maxwell

  Education, Math, Numbers

  "The Scientific Papers of James Clerk Maxwell".

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• By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

  Alfred North Whitehead

  Learning, Race, Brain

  Alfred North Whitehead (1958). “An Introduction to Mathematics”, p.39, New York : Oxford University Press, 1958 [c1948]

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• The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

  John Edensor Littlewood

  Math, Thinking, Numbers

  John Edensor Littlewood, Béla Bollobás (1986). “Littlewood's Miscellany”, p.74, Cambridge University Press

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• If I found any new truths in the sciences, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.

  Rene Descartes

  War, Math, Battle

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• It isn't that they can't see the solution. It is that they can't see the problem.

  Gilbert K. Chesterton

  Funny, Math, Statistics

  Scandal of Father Brown (1935) "Point of a Pin"

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• This paper gives wrong solutions to trivial problems. The basic error,however, is not new.

  Clifford Truesdell

  Math, Errors, Giving

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• Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

  Gustave Flaubert

  Ocean, Math, Boys

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• The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

  Freeman Dyson

  Math, Bridges, Design

  "Freeman Dyson: Mathematician, Physicist, and Writer". The College Mathematics Journal Interview with Donald J. Albers, January 1994.

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• There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

  Carl Friedrich Gauss

  Lying, Math, Science

  "The World of Mathematics". Book by J. R. Newman, 1956.

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• The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.

  C. West Churchman

  Math, Intellectual, Answers

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• If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

  George Polya

  Education, Knowledge, Math

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• When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

  R. Buckminster Fuller

  Beauty, Beautiful, Niece

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• Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

  Carl Pomerance

  Fun, Math, Science

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• The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.

  Israel Gelfand

  Believe, Statistics, Problem

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• More people have access to education today than ever before. But I cannot help but feel that the modern educational experience is not preparing us adequately to attend the rich banquet of life. Certainly the young people of today have mastered the use of technology and are capable of solving complex scientific and mathematical problems, but who and what do these serve if they cannot think for themselves? If they have no understanding of the meaning and purpose of their own lives? If they do not know who they are as individuals?

  Matthew Kelly

  Education, Technology, Thinking

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• Even with the most stupid video games, kids learn more about learning than they ever did before, because they want to learn codes and moves before other kids figure them out. They're motivated to seek out someone or search the Net for help. A student who makes a video game has to solve mathematical problems to make special effects happen on the screen.

  Seymour Papert

  Stupid, Moving, Kids

  "Sunday Interview - Seymour Papert/ Computers in the Lives of Our Children/ an Mit Mathematician and Philosopher Is Exploring How Technology Can Educate the Next Generation - and Their Parents". www.sfgate.com. February 2, 1997.

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